© 2022, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.This two-paper series proposes a unified theory that gives rise to a family of quasi-3D composite elements. The first paper presents the element formulation and its basic capabilities: the ability to capture transverse normal (σz) and shear (τyz, τxz) stresses, suitability for thermoelastic analyses and compliance to both displacements and transverse stress continuity requirements. These capabilities are inherent to the element since a global–local superposition approach is devised that, from inception, guarantees that equilibrium equations, continuity consistency and boundary conditions are fully met. A simple validation analysis was conducted in part I that initially pointed to a very promising direction with high numerical efficiency of the element. This second paper investigates the element numerical performance under different scenarios: use of three- and four-node parent elements, degree of global interpolation functions, adequacy of different local interpolation functions (F0, F1, G0, G1, H0, H1) and consideration of a more practical configuration of a reinforced panel consisting of multiple laminates. Through-the-thickness displacements, strains and stresses are obtained and shown to be of reasonable accuracy. Results are compared against a highly refined mesh of 3D brick elements implemented in a commercial software that provide a benchmark for the elements capabilities.

© 2022, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.In a series of two papers, a unified formulation for new plate composite elements is proposed that captures through-the-thickness effects, specifically normal and transverse shear stresses and strains. Thermal effects are also considered, including thermal effects through-the-thickness. This first paper is devoted to the fundamentals of the proposed unified formulation. The elements proposed are displacement based and the number of degrees of freedom is kept as small as possible, all of them possessing clear physical meaning. The elements are built using local functions defined at each layer and global functions defined along the thickness. The consistency of the kinematic assumptions is guaranteed through the imposition of displacement continuity along the thickness direction, transverse stress continuity and boundary conditions at the bottom and top surfaces of the elements. The formulations are developed for either isotropic or orthotropic materials. The formulations shall prove substantially more efficient than those based on solid elements traditionally used to capture normal transverse stresses. In the sequel, a second paper presents a variety of numerical results obtained using the proposed formulation and discusses its capabilities and potential.

© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.Composite materials present challenging gaps to be studied due to their unique characteristics. The finite element method has been used to analyze composite materials subjected to the most distinctive situations. In the present work, the advantages of three element solutions studied previously are combined to develop a fourth element solution. First, decreasing the degree of the polynomials representing the axial displacement at the bottom and at the top surfaces circumvents shear locking in beams. Second, including the homogeneous solution ensures the continuity of the displacements between elements, but in this case the determination of the stiffness matrix requires a huge amount of computational time. However, it is shown that only modifications close to the original block diagonal matrix need to be considered, since far from the diagonal the contribution of the homogeneous solution is negligible. Additionally, a procedure is described to calculate a more accurate value for the stress σz.

© 2022 Elsevier Masson SASThe use of composite materials in several sectors has been gaining distinction in recent years. However, due to their high costs, as well as unique characteristics, they present challenging gaps to be studied. The finite element method has been used as a way to analyze composite materials subjected to the most distinctive situations. Three element solutions are compared, which can be applied to composite beams. The accuracy of the outcomes does not improve with higher degree polynomials, but the inclusion of the homogeneous solution to solve a system of differential equations results in a better outcome when considering the normal strains. Special attention is paid to the continuity of the displacements between adjacent elements. Finally, it is explained why the calculated axial normal stress looks much better than the transverse normal stress.

© 2021The determination of the fatigue behavior at a component level usually requires dedicated test rigs and an expressive amount of time. The hours spent on such machinery are expensive; therefore, solutions to reduce experimentation time are most welcomed. In this context, this investigation aims at developing a procedure for rapid determination of the fatigue strength of crankshafts by means of a thermographic methodology. The use of infrared cameras for fatigue strength analysis was first assessed in standard dog-bone specimens. Crankshafts were then tested in an in-house fatigue test rig using the conventional staircase method and the thermographic method. Sample batches with different manufacturing parameters were produced and tested to assess the robustness of the proposed alternative technique. Results of the dog-bone test campaign revealed a good correlation between fatigue strength estimates obtained with the conventional Wöhler curve and the thermographic methodology. Finally, the thermographic technique also delivered results in close agreement with the staircase method for all crankshaft batches. The proposed procedure was found to be a viable, rapid alternative to conventional fatigue test programs, with potential application for complex structural components such as crankshafts, among others.

© (2022) by International Council of Aeronautical Sciences (ICAS) All rights reserved.This work employs a micromechanical theory and kinematic relationships to describe the displacement field in individual unidirectional composite plies. The technique relies on an incremental approach where the misalignment angle of fibers is the main variable in the analysis. Upon convergence at a certain loading level, stresses and strains are evaluated in the fibers and matrix using micromechanics, and a specific failure criterion is applied. The Ramberg-Osgood relations are used to correct degraded mechanical properties of the resin in the nonlinear regime. The Hashin-Rotem failure criterion and experimental data obtained in the literature are used to validate the technique. It is observed that the numerical and experimental results obtained correlate well.

© The Author(s) 2021.This paper describes a classical laminate theory-based constitutive model for portraying thermoplastic composites’ mechanical properties and the development of residual stresses during consolidation. The extended Hillier model is applied to describe the material’s crystallisation and as such is able to provide final part quality as a function of the process cooling history while taking into account the first and second crystallisation mechanisms occurring concurrently. With the developed model, a parametric study was performed taking into account layups that are commonly used in the aerospace industry, where general design guidelines are suggested. Some of the advantages of using cross-ply and quasi-isotropic laminates became clear as no shear residual stresses were predicted for those laminates. However, highly anysotropic laminates may also offer structural advantages. Numerical simulations indicate that the crystallisation residual strains can be, although smaller than thermal residual strains, relevant to final part quality. The combination of both effects may result in high residual stresses at ply level which in turn can compromise the ultimate strength of the laminates and make it difficult to attain the desired part’s geometrical tolerances.

© 2021, Springer-Verlag London Ltd., part of Springer Nature.Different residual stress magnitude and profile are generated after every crankshaft manufacturing stage. The processes are often investigated separately, regardless of their possible influence. The acknowledgement of the stress evolution can be useful when investigating crankshaft fatigue behavior. This study contributes to the matter by evaluating the resultant residual stress generated at the fillet region after crankshaft’s machining and deep rolling processes. Prior to it, a procedure was developed to guarantee the position of the samples in the X-ray diffractometer after surface electropolishing and depth measurement. Repeatability and reproducibility analyses attest the measurements’ accuracy. An in-depth profile assessment was made at the crankpin radii top and bottom regions in two stress directions. The influence of the machining process over the residual stress left after deep rolling can be inferred. The results were also compared with the outcomes from a finite element model for the deep rolling process. They pointed out that new features should be included in its development in order to account for the influence of previous processes. Moreover, unexpected residual stress results, and consequently fatigue behavior, can be better understood with more data regarding the whole manufacturing chain.

© 2021 Universidade Federal de Sao Carlos. All rights reserved.The objective of the present paper is to propose a framework, utilizing the OpenCV library, for post-processing infrared images obtained using Long-Pulse Thermography (LPT), with the goal of segmenting the images into defective and sound areas. A series of thermograms of a carbon fiber/epoxy specimen, containing precision milled flat-bottom holes, was acquired using an LPT system comprised of an uncooled microbolometer imager and halogen optical sources. Flaw detectability and planar size estimation were used to evaluate the results obtained with the proposed post-processing framework, in comparison to raw images, and images subjected only to pre-processing algorithms.

© 2020 Elsevier LtdA unified theory to formulate a family of quasi-2D composite finite elements that capture through-the-thickness effects is proposed. The formulation is based on the superposition of global and local displacement fields and includes thermal effects, as a response to the claim of the scientific community. First are presented the fundamentals of the unified formulation: the kinematic assumptions; the imposition of continuity of displacements and transverse stresses, and of non-homogeneous boundary conditions; and the mathematical manipulations that render its numerical efficiency. Then, the new family of elements is assessed in problems involving different boundary conditions. Results are compared to analytical and highly refined 2D finite elements solutions, providing a benchmark of the elements capabilities. Mesh convergence is assessed, together with the influence of the global and local displacement fields. The numerical efficiency of the formulation is attested and an expansion for a 3D formulation is outlined.

© 2020 World Scientific Publishing Company.In this paper, a canonical transformation is proposed to solve the eigenvalue problem related to the dynamics of rotor-bearing systems. In this problem, all matrices are real, but they may not be symmetric, which leads to the appearance of complex eigenvalues and eigenvectors. The bi-iteration method is selected to solve the original eigenproblem whereas the QR algorithm is adopted to solve the reduced or projected problem. A new canonical transformation of the global eigenproblem which reduces the quadratic eigenproblem to a linear eigenproblem, maintaining numerical stability since all that is required is that the stiffness matrix is well-conditioned, which is always true when it comes to applications in dynamic problems. The proposed technique is good for obtaining dominant eigenvalues and corresponding eigenvectors of real nonsymmetric matrices and it possesses the following properties: (i) the matrix is not transformed, therefore sparsity is maintained, (ii) partial eigensolutions can be obtained and (iii) use may be made of good eigenvectors predictions.

© 2020, The Brazilian Society of Mechanical Sciences and Engineering.The bearing investigation on mechanical joints of composite materials is extensive. The main reason for bearing investigation, in a certain aspect, is related to the variability of parameters associated with bearing behavior. In this sense, theoretical and/or experimental studies have been exhaustively conducted. Depending on the solution obtained, there is a cost/benefit relationship for the problem in question. However, in the case of aeronautical applications, an important factor to be considered is the safety, which reflects into safety margin. In this sense, an excess of tests is needed for design that reflects in high cost and time-consuming. Therefore, simpler approaches are necessary in the pre-design phase, where quick answers are required for the initial product definition. In this way, the present work presents composite bearing tests with two distinct environmental conditions, i.e., low-temperature dry (LTD) and room-temperature dry (RTD) in order to show that there is one procedure to simplify the process and gain cost and time. For this, five different configurations specimens with 12 coupons each one were tested in two different environmental conditions. The fastened joint manufactured used protruding fastener, two different diameters (3/16″ and 5/32″) and three laminates (10, 12 and 14 plies). Based on the ASTM D5961 standard, the experimental results showed a linear response not showed in the literature for composite materials. The proposal presented here showed an excellent way to avoid others tests with different conditions, i.e., with different layups and fastener diameters.

© 2020 SAE International. All Rights Reserved.Residual stress prediction arising from manufacturing processes provides paramount information for the fatigue performance assessment of components subjected to cyclic loading. The determination of the material model to be applied in the numerical model should be taken carefully. This study focuses on the estimation of residual stresses generated after deep rolling of cast iron crankshafts. The researched literature on the field employs the available commercial material codes without closer consideration on their reverse loading capacities. To mitigate this gap, a single element model was used to compare potential material models with tensile-compression experiments. The best fit model was then applied to a previously developed crankshaft deep rolling numerical model. In order to confront the simulation outcomes, residual stresses were measured in two directions on real crankshaft specimens that passed through the same modeled deep rolling process. Electrolytic polishing was used to etch the region of interest and enable in-depth residual stress analysis through X-ray diffraction method. The comparison revealed the model's ability to follow the residual stress state tendency, predicting compressive stresses at the surface, a subsurface peak and eventual transition to the tractive state. Magnitude discrepancies were discussed and hypotheses related to the specimen preparation procedure were raised. Overall, the activities described in this study yielded in a model confidence increase, which further enables its usage into the crankshaft design stage.

© 2020, © 2020 Taylor & Francis.The present study investigates the evolution of the residual stresses in TWIP steels induced by manufacturing chain for the production of automotive body-in-white. Two different manufacturing routes were considered. The first route encompassed a plastic deformation prior to the welding stage, whereas the second involved the spot welding followed by a baking treatment. A convergent approach was adopted to isolate the effects of the first and final manufacturing steps. The findings showed that the plastic deformation prior to the welding stage is not annihilated by the welding thermomechanical cycle. Abrupt hardness gradients along small material fractions are observed. The residual stresses state changes, although its profile is still defined by the welding stage. The post-weld bake treatment showed to promote slight residual stresses relaxation, but it is not effective in inducing the same post-weld residual stresses state for different RSW parameters set.

© 2019 Wiley Publishing Ltd.The requirements for mechanical reliability of automotive crankshafts are continuously increasing, thus pushing the demand for an optimized processing. Nonetheless, the manufacturing-induced residual stresses at critical sites for fatigue enhancement are not clarified in the state-of-the-art on the topic. In particular, there is a lack of information on the effect of final manufacturing stages to improve the component life endurance, such as deep rolling, in the overall stress state while the component is under operational loads. This study deepens the validation of a finite element deep rolling model under development with the aid of an in-house developed crankshaft resonance fatigue test rig. The stress state obtained from the deep rolling simulation was input as a predefined stress field for the simulation of operational conditions experimented at the test rig. Test results produced cracks at the fillet radii of the cast iron crankshafts as anticipated. Overlapping the fractography with the simulation's final stress field yielded interesting correlation with the crack morphology. This contributed with a strong indication of the model correctness. Moreover, it can be further implemented to indicate whether the process parameters such as roller force and angle are fully optimized for each particular crankshaft application.

© 2019 Elsevier Masson SASThe accuracy of the results obtained with Finite Element Methods depends on the basis functions employed to approximate the displacement fields. If the beam is very thin, there can be shear locking and the numerical approximation leads to erroneous solutions. In this work, shear locking is analyzed by calculating expressly the curves of the transverse deflection, the cross-section rotation, and the shear strain in different approaches. The influence of the ratio between the shear stiffness and the bending stiffness is explicitly shown when force and moment loads are applied. It is concluded that the locking behavior at nodes is not the decisive factor to assess the quality of the solution. The important point is to analyze the entire curves when the ratio between the stiffnesses is varied. It is verified that the mixed interpolation and the discrete shear gap approaches are superior to the pure displacement and to the field consistency approaches.

© 2019 Elsevier B.V.Manufactured components are submitted to thermo-mechanical loads that can blemish their surface integrity and change the inherent residual stress distribution. The discontinuous machining process is relevant to the integrity conception because of their potential application at the end of the manufacturing chain. In order to consolidate a method to predict the residual stress state with a reduced CPU effort, this paper addresses the prediction of residual stress fields resulting from the milling process. The approach is using the hybrid FEM approach combined with the analysis of the plastic flow. The results obtained point out to the validity of the combination of the hybrid method and the visualization of the equivalent stress and equivalent strain rates. Moreover, a direct correspondence between the references and experimental dataset was observed, even when the input data for the model is associated with macro-loads obtained by piezoelectric platform measurements. The determination of the stress state as residual stress in mainly associated to the mesh convergence and the time to equilibrate the plastic flow. A conclusion is drawn regarding the viability of applying the same combination for other manufacturing processes.

© 2019, The Brazilian Society of Mechanical Sciences and Engineering.The residual stresses generated during the deep rolling process made on crankshafts are still not fully understood to this day. Comprehending and correctly simulating the process dynamics are key to investigate the process influence over the material microstructure. A numerical model using an explicit formulation was developed in order to accurately simulate deep rolling dynamics. Real boundary conditions, contact and a converged mesh were set. Diverse mass scaling and load rate were tested for comparison. The results were evaluated in terms of the simulation energy balance, as the internal, kinetic and artificial energies outputs were confronted. Conclusions could be inferred on the accuracy of the model representation of the real process based on this analysis.

© 2018 Elsevier B.V.TWIP steel weld spots were produced by varying the following welding parameters: welding current, welding time and electrode clamping force. Hardness distributions along the weld spots cross section were obtained by Vickers microindentations. The mechanical strength and failure modes of the weld spots were assessed by tensile-shear tests. Weibull statistics was applied to statistically analyse the data from tensile-shear loading. The results highlighted the influence of welding parameters variations on the Vickers hardness and residual stress state. These properties have a positive correlation to the failure modes and so the mechanical reliability of the weld spots. Welds that failed in pullout mode and partial-interfacial failure mode have statistically higher load bearing capacity than those in interfacial failure mode. The combination of a welding current of 8 kA with a welding time of 16 cycles and an electrode clamping force of 2 kN showed to be the optimum parameters for the investigated TWIP steel weld spots. By using this optimum setup, it was possible to supress interfacial failure mode and to obtain pullout as the predominant failure mode, considerably increasing the mechanical reliability of the weld spots.

© 2018, Brazilian Association of Computational Mechanics. All rights reserved.Shape distortions and warpage are a major source of problems for composite manufacturers. These distortions are usually accompanied by built up residual stresses. They can deform a component so that it becomes useless. It also has the capability to reduce the strength of the structure. In this paper, the three-dimensional version of the constitutive model originally proposed by Svanberg and Holmberg is employed to predict the warpage of a wing planform. The model takes into account important mechanisms such as thermal expansion, resin shrinkage and frozen-in strains developed during curing cycles. The model was implemented into ABAQUS Finite Element code as a user subroutine UMAT. The macromechanical properties of each composite layer were predicted using a micromechanics based approach, implemented into MATLAB. Results show that wings with cross ply laminates with reducing thickness along the span experienced more warpage than quasi-isotropic laminates. Furthermore, for wings with equal thickness along the span, the results show that the quasi-isotropic laminates experienced more warpage than cross ply laminates. Lastly, the results show that wings with progressively reducing thickness experience twist that is varying from the wing root to the wing tip while wings with a constant thickness experience twist mainly at the centre of the wing.

© 2018, Universidade Federal de Uberlandia. All rights reserved.This study discusses the microstructure, quasi-static mechanical strength and failure modes of TWIP steel weld spots. Weld spots were produced by varying the main resistance spot welding parameters: welding current, welding time and electrode compression force. All the samples showed a remarkable material hardness mismatch between the fusion zone, the heat affected zone and the base material, as evidenced by microindentation maps. Hardness at the fusion zone is lower than that of heat-affected zone and base metal, which facilitates interfacial failure mode during tensile-shear tests. However, high heat inputs promoted the failure mode changes to partial interfacial mode and then to pullout mode during tensile-shear tests as confirmed by Scanning Electron Micrographs. These changes in failure mode were accompanied by a notable increase in tensile-shear strength and energy absorption capability.

© 2018, The Brazilian Society of Mechanical Sciences and Engineering.As shown in the literature, there is plentiful information about sandwich panels. Two of the most common points under discussion are the failure modes and the efficiency of numerical simulations considering the stiffness and interlaminar stress. The failure modes in the literature are not always likely to happen in practice, and representing them becomes a challenging task. Regarding the numerical simulations, new assumptions and formulations appear in order to consider the shear stress in the honeycomb CORE and to minimize processing time in 3D models. Although new mathematical solutions emerge, in some cases they are unpractical for engineering applications and must be evaluated and compared with test results in order to verify their consistency. Therefore, experimental results are necessary to validate theories to comply with the failure modes observed in sandwich panels and to validate the finite element model. Also, the main focus of the literature is on the theoretical formulation and not in engineering applications. In this sense, the main contribution of this paper is to bring forward experimental results of aeronautical sandwich panels whose data are scarce and therefore contributes to the validation of new developments. In addition, the purpose of this work contributes to the use of the finite element models with composite sandwich panels where the appropriate input for 2D (plate) and 3D (solid) elements is unclear. It should be pointed out that for failure investigation the first step is validating the finite element model. In this sense, a typical aircraft panel with experimental results is presented. The finite element model and the input parameters that are not mentioned in the classical literature are also presented. The experimental strain from specimen tested agreed well with the numerical simulations results.

© 2018, © IMechE 2018.Deep rolling is performed on crankshafts since the 1960s, yet there is still a knowledge gap regarding residual stress generation. Until this moment, there is no consolidated and widespread procedure to predict such stresses during the crankshaft design cycle. This study establishes an analysis procedure and correlates it with experimental results. An explicit finite element model with real boundary conditions is developed together with a converged mesh for the fillet radius. Simulation nodal displacement and strain output are compared to geometrical measurements using a coordinate-measuring machine. Outputs in terms of residual stresses are related to X-ray diffraction measurements taken along fillet depth. The experimental results attest to the accuracy of the model and correctness in predicting the process outcomes.

© 2017 Elsevier LtdA beam element is proposed that captures through the thickness effects in composite laminated beams, namely, transverse shear and normal stresses and strains. Stress continuity along the thickness is inherently enforced leading to a system of algebraic equations that is solved in the element level, permitting independence between the number of layers and the number of degrees of freedom, with all of them possessing a clear physical significance. Global-local superposition is performed in the thickness direction, where a cubic global displacement field, that guarantees imposition of the boundary conditions at the top and bottom surfaces of the beam, is combined with a layerwise linear local displacement distribution that assures zig-zag behavior of the stresses and displacements. The element behavior for different length-to-thickness ratios is assessed and compared to the analytical elasticity solution, as well as a commercial finite element alternative.

© 2018, Brazilian Association of Computational Mechanics. All rights reserved.An adaptation of the conventional Lanczos algorithm is proposed to solve the general symmetric eigenvalue problem Kϕ = λKGϕ in the case when the geometric stiffness matrix KG is not necessarily positive-definite. The only requirement for the new algorithm to work is that matrix K must be positive-definite. Firstly, the algorithm is presented for the standard situation where no shifting is assumed. Secondly, the algorithm is extended to include shifting since this procedure may be important for enhanced precision or acceleration of convergence rates. Neither version of the algorithm requires matrix inversion, but more resources in terms of memory allocation are needed by the version with shifting.

© 2017, Brazilian Association of Computational Mechanics. All rights reserved.A new C1 element is proposed to model Euler-Bernoulli beams in one and two-dimensional problems. The proposed formulation assures C1 continuity requirement without the use of rotational degrees of freedom, used in traditional elements, through the use of an Overhauser interpolation scheme for bending displacements. The principle of virtual displacements is used to determine the equilibrium equations and boundary conditions for one and two-dimensional Euler-Bernoulli beams. The Overhauser interpolation is introduced and the new bending interpolation functions are defined. Finally, beam and frame problems are solved with the new formulation and the results are compared to the traditional Euler-Bernoulli element and exact solutions.

© The Author(s) 2015.The metallic airplane structure fuselage design is characterized by skin, frames, stiffeners, and attachments. In most airplanes, the attachments between these components are made by rivets. The influence of the attachments in the panel behavior under diagonal tension can be verified in the metallic Wagner beam. For stiffened composite panels, like metallic Wagner beams, there is insufficient data about attachment design. In order to design and build lightweight composite structures, the analyst must consider different ways in which the skin is connected to the stiffeners and frames. Therefore, the objective of this paper is to investigate different conceptions of a real-reinforced composite panel used in the aeronautical industry. Experimental and numerical results for strains showed good agreement. The finite element model and the criteria used in the failure analysis are also presented. Comparisons between different panel configurations are made, and conclusions are drawn about attachment efficiency.

© 2016 Elsevier Masson SAS. All rights reserved.This work investigates the aeroelastic stability boundary of flutter in Shape Memory Alloy Hybrid Composite laminates (SMAHC). The SMAHC consists of SMAs wires and continuous carbon fibers embedded into a polymeric matrix resulting in a three constituent composite material. The derivation of the effective mechanical properties of the SMAHC is based on micromechanical model which accounts for temperature and fraction of martensite/austenite transformation phases of the shape memory alloy. Hamilton's principle is used for the formulation of the energy functional and to obtain the equilibrium equations and boundary conditions of the aeroelastic problem. The finite element method is employed to numerically solve the equations. Different geometric configuration, laminate stacking sequence, boundary conditions and curvatures are investigated. The study shows that the stiffening effect induced by the changes in the fraction of martensite/austenite transformation phases of the shape memory alloy increases the rate of occurrence of flutter, stabilizing the plate. Thus, one can control the occurrence of flutter speed by controlling the temperature of the SMA wires and the proper design of the geometric properties of the panel and tailoring of the composite laminate.

© 2016, European Conference on Composite Materials, ECCM. All rights reserved.Shape Memory Alloy Hybrid Composite (SMAHC) laminates are built with continuous carbon fibers and Shape Memory Alloy (SMA) wires, both embedded in a polymeric matrix thereby forming a three constituent composite material. The SMA actuation is triggered by temperature changes, resulting in modifications in the structural responses of SMAHC laminates. A particularly important structural characteristic of SMAHC laminates which is investigated in this paper is the aeroelastic stability boundary of flutter. The derivation of the effective mechanical properties of the SMAHC is based on micromechanical model which accounts for temperature and fraction of martensite/austenite transformation phases of the shape memory alloy. The mathematical problem is formulated using Hamilton's principle, allowing for derivation of the equilibrium equations and boundary conditions of the aeroelastic response. The governing equations are then discretized and solved by the finite element method. A parametric study is conducted where different geometric configurations, laminate stacking sequence, boundary conditions and curvatures are investigated. It is observed that the SMAHC structure is stabilized against flutter by proper tailoring of stiffening effects induced by the changes in the fraction of martensite/austenite transformation phases of the SMA. Therefore, it is possible to increase critical flutter speed by controlling the temperature of the SMA wires.

& Sons, Ltd.This paper presents a new optimization technique applicable to optimization of composite structures subjected to multiple objectives. The composite structures may be composed of an arbitrary number of laminates. The technique is especially suited for the case where the layers of the laminates may assume a discrete number of orientations. However, given the efficiency of the technique, it is readily extendable to situations where the ply orientations vary quasi-continuously, for instance, by one degree in one degree. The high efficiency is obtained through application of lamination parameters, which, in the case of symmetric laminates, consist of only 10 parameters per laminate. Three traditional structures, a rectangular composite plate, a cantilever composite beam, and a stiffened composite panel, are optimized against buckling when subjected to multiple load cases. © 2015 John Wiley

© 2014 Elsevier B.V. All rights reserved.The arc welding process involves thermal cycles that cause the appearance of undesirable residual stresses. The determination of this thermal cycle is the first step to a thermomechanical analysis that allows the numerical calculation of residual stresses. This study describes the formulation of a 2D finite element with through the thickness parabolic temperature distribution, including an element estabilization procedure. The 2D element described in this paper can be used to perform thermal analysis more economically than 3D elements, especially in plates, because the number of degrees of freedom through the thickness will always be three. A numerical model of a tungsten arc welding (GTAW) setup was made based on published experimental results. Size and distribution of the heat source input, thermal properties dependent on temperature, surface heat losses by convection and latent heat during phase change were considered. In parallel the same setup was modeled using ANSYS software with 3D elements (SOLID70) to compare against 2D numerical results. The results obtained by 2D model, 3D model and experimental data showed good agreement.

This work investigates the aeroelastic stability boundary of flutter in aircraft composite panels, curved or flat, subject to the effect of stress stiffening caused by the piezoelectric actuator (PZT). Hamilton's principle is used for the formulation of the energy functional and to obtain the equilibrium equations and boundary conditions of the problem. The finite element method is employed to numerically solve the equations. The aeroelastic behavior of panels manufactured in composite material (boron-epoxy) or conventional material (aluminum 2024-T3) are assessed. Two layers of piezoelectric material (ACX QP10N) are attached to the panels: one on the top surface one on the bottom surface of the panels. Prescribed voltages are statically applied to the piezoelectric actuators, inducing a prestress field which is responsible for the stress stiffening effects when coupled with the nonlinear strain components. Different geometric configuration, laminate stacking sequence, boundary conditions and curvatures are investigated. The study shows that mechanically strain-induced piezoelectric effect increases the rate of occurrence of flutter, stabilizing the plate. This stiffening of the structure is related to the voltage applied on the actuators and the geometrical parameters of the plate. Thus, one can control the occurrence of flutter speed by controlling the voltage applied and the proper design of the geometric properties of the panel and tailoring of the composite laminate. © 2012 Elsevier Ltd.

This paper presents a ballistic impact simulation of an armour-piercing projectile in hybrid ceramic/fiber reinforced composite armour. The armour is composed by an alumina plate and an ultra high molecular weight polyethylene composite. In order to model the armour behavior three different constitutive models were formulated and implemented into ABAQUS/Explicit finite element code. Comparisons between numerical predictions and experimental results in terms of damage shape/extent and V 50 are also presented and discussed in the paper. © 2011 Elsevier Ltd. All rights reserved.

This paper proposes a strategy to achieve robust optimization of structures against high-cycle fatigue when a potentially large number of unceratin load cases are considered. The strategy is heavily based on a convexity property of some of the most commonly used high-cycle design criteria. The convexity property is rigorously proven for the Crossland fatigue criterion. The proof uses a perturbation technique and involves the principal stress components and analytical expressions for the applicable fatigue criteria. The multiplicity of load cases is treated using load ratios which are bounded but are otherwise free to vary within certain limits. The strategy is applied to a notched plate subject to traditional normal and shear loadings that possess uncertain or unspecified components.

The nonlinear response of initially imperfect composite plates with piezoelectric actuators is investigated. The nonlinearity is limited to the prebuckling regime, where higher order terms present in the strain energy expression can be neglected. The advantage of the electromechanical coupling is exploited in two ways. First, the in-plane piezoelectric stress stiffening effect is used to tailor a stress distribution that inherently increases the critical buckling loads of perfect composite plates by posing an optimization problem that efficiently handles eventual uncertainties involved in the application of mechanical loadings. Second, piezoelectric bending moments are applied in order to avoid or ameliorate the undesirable effects of initial imperfections. An actuation strategy, where the piezoelectric membrane forces and bending moments are decomposed via an appropriate selection of voltages applied to piezoelectric patches that are symmetrically bonded to the top and bottom surfaces of the plate, is proposed and shown to be effective. © 2011 American Society of Mechanical Engineers.

This work presents the optimization of a frame under uncertain loadings when two design criteria are taken simultaneously into account. The uncertainty relates to the applied loading and is inherent to the operation of structures since real structures are designed to sustain a large variety of load cases of practical relevance. The design criteria considered are two of the most important from a practical point of view: buckling load and natural frequency. The technique developed is based in convex modeling where a load space is defined and all the elements of that load space have equal probability of occurrence. The outcome of the technique is an optimal design for which one loading or several loadings of the load space are the most dangerous or harmful to the structure. On the other hand, it is guaranteed that all the other loadings contained in the load space are conservative in the sense that they are less harmful to the optimal design. Copyright © 2010 by ABCM.

A technique for enhancement of buckling loads of composite plates is proposed. The technique relies on using stress stiffening to create a non-zero tensile force acting along the plate plane which ultimately permits the application of higher external compressive forces that lead to traditional buckling instabilities. The idea is to completely restrain the plate movements in its plane direction, at all edges, and to apply voltages to pairs of symmetrically bonded piezoelectric patches. This voltage is applied such that the piezoelectric patches contract resulting in a uniform tensile force over the plate plane.

This work presents the optimization of a composite plate under uncertain loadings when buckling and fundamental frequency are taken simultaneously into account. A combination of convex modeling and minimax strategy is proposed in order to solve the optimization problem. This association reduces the strategy complexity and computational cost.

The aim of this paper is to explore the structural optimization using CATIA's built in capabilities of finite element analysis and optimization. Initially, the environment available for the integrated design, structural analysis and general optimization is discussed. Then, the characteristics of the general optimization algorithms that conduct the structural optimization are briefly reviewed. Thereafter, three problems are stated and solved, with a critical and detailed appreciation of the results obtained. Also, some simple ideas are proposed and tested to improve doing structural optimization with CATIA1. Copyright © 2008 SAE International.

This work presents the optimization of a frame under uncertain loadings when two design criteria are taken simultaneously into account. The uncertainty relates to the applied loading and is inherent to the operation of structures since real structures are designed to sustain a large variety of load cases of practical relevance. The design criteria considered are two of the most important from a practical point of view: buckling load and natural frequency. The technique developed is based in convex modeling were a load space is defined and all the elements of that load space have equal probability of occurrence. The outcome of the technique is an optimal design for which one loading or several loadings of the load space are the most dangerous or harmful to the structure. On the other hand, it is guaranteed that all the other loadings contained in the load space are conservative in the sense that they are less harmful to the optimal design. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

Crooked beams and plates with arbitrary initial geometric imperfections are optimized in order to improve their prebuckling response in the presence of uncertain loadings. A novel optimization approach is presented to simultaneously handle the two types of uncertainties: arbitrary initial imperfection patterns and arbitrary loadings. A remarkable improvement in the prebuckling response of optimal designs is achieved by reducing the level of prebuckling displacements measured in some appropriate norm, irrespective of the uncertain imperfection pattern or loading. Two different norms are proposed, each one applicable to the beam or to the plate problem. The definitions of appropriate norms allow for the use of a minimax optimization approach that can consider the arbitrariness of both geometric imperfections and loadings. It is shown that the minimax procedure leads to optimum structural designs, in terms of optimal stiffness distribution, that are at the same time insensitive to perturbations in the loading space and to the pattern of initial imperfections in structure. Copyright © 2007 by ABCM.

A general technique is proposed to maximize the lowest natural frequency of structures subjected to an arbitrary state of initial stresses. The arbitrary states of initial stresses are represented by nondimensional loading parameters that describe an admissible loading space, i.e. every possible initial stress state lies within the admissible loading space. The key to the proposed optimization strategy is shown to be the concavity of the first natural frequency with respect to variations of the loading parameters within the admissible loading space. A rigorous demonstration is presented to show that, provided buckling has not occurred, all the possible initial stress states must not be considered. Instead, assessment of only a small number of initial stress states must be done in order to guarantee that the first natural frequency does not decrease for all the other initial stress states within the admissible loading space. A minimax optimization technique is used to maximize the lowest natural frequency of a simply supported rectangular plate where the thickness distribution is the design variable and normal and shear initial stress states are considered. Copyright © 2005 John Wiley & Sons, Ltd.

The vibration of a spherical cap with a moving force or mass is investigated using finite element method (FEM). It is observed that the use of Mindlin-type elements introduces substantial numerical errors in the response of the shell under concentrated loads that are applied at off-nodal positions. Given that a moving load will necessarily lie at off-nodal positions at several instants of time, an adaptive mesh strategy is proposed to improve the numerical accuracy. The dynamic numerical simulation is based on the Newmark time-integration scheme and a perturbation technique. The latter is motivated by practical scenarios where the inertia effects of the moving mass are significantly smaller than those of the main structure. The implemented finite element model is validated by comparing results of both static and free vibration analyses with those from a commercial finite element software. Thereafter, the dynamic response of a spherical cap in the presence of a traversing load is investigated. © 2005 Elsevier B.V. All rights reserved.

Typically, aircraft wing structural panels are designed against buckling for a very large number of possible loadings that may occur during the operation of the aircraft. If the optimisation procedure accounts only for a limited number of design loads, the structure may be vulnerable to a specific type of loading that may cause the structure to fail. A novel approach for the optimisation of ribs or plates of arbitrary shapes under uncertain loads is proposed. The geometry of the rib is defined by a single closed spline or several connected splines. The loading distribution is not considered to be uniform but it is allowed to vary within an admissible set, conferring uncertainty to the applied loads. The admissible load space comprises distributed normal and shear loadings that can be represented through a collection of piecewise linear functions defined along the plate boundary. A special procedure is applied to handle the constraint that the loading must be self equilibrating. A minimax strategy is used to deal with the loading variability such that the resulting optimal design is able to withstand an entire class of linear piecewise loadings along the rib boundary. The refinement of the loading representation may be completely independent of the refinement of finite element mesh. The validity of the proposed approach is assessed by applying it to an aeronautical wing rib.

The Brazilian Multi Mission Platform (MMP) is a modem satellite architectural concept that shall provide support for several of low Earth orbit missions whose attitude control subsystem includes a three-axis stabilized platform carrying different payload modules. This paper presents the dynamic analysis of the Brazilian MMP solar array generator (SAG) deployment. The objective of the study is to analyze the shock spectrum due to the SAG latch up. The transient response or time history was verified at typical hinges, yoke, solar array drive assembly, solar cells and at the sandwich panel. The finite element technique has been used to obtain the numerical results with the software package MSC.Nastran. The problem is an initial value problem whose initial conditions were derived from the SAG deployment mechanism simulation. The results of the study have shown that the satellite solar array response fulfills the requirements associated with the latch up shock spectrum.

Optimization plays a very important role in space applications since mass and structural flexibility are critical requirements for space missions, i.e., the structure should be as lightweight and stiff as possible. As a contribution to this area this paper investigates compliance optimization of structures under multiple load cases. The problem can be solved through a multi-criterion optimization where the load cases associated with each and every loading configuration are treated as components of multi-objective function vector. However, numerical evaluation is not an easy task because it sometimes involves a very intensive computational effort. Alternatively, the multi-objective optimization problem can be re-formulated using a min-max strategy that does not require simultaneous consideration of all the load cases as components of multi-objective function vector. Instead, this formulation shows that, for compliance optimization purposes, it is sufficient to consider only those loads, which define the convex hull of the applicable load set, i.e., the selected set of loads which will effectively lead to the optimum design. Through the min-max formulation the number of load cases involved in the design procedure is drastically reduced. The efficiency of the proposed technique is illustrated by one example consisting of a variable thickness beam subjected to uncertain loadings.

Composite rectangular plates are traditionally optimized for buckling assuming that perfectly uniform loadings are applied. However, this assumption is clearly not realistic for composite structures in real applications, particularly when the multiplicity of potential load cases is considered. Composite plate optimization is addressed differently in this paper: the loading distribution is not assumed to be uniform but it is allowed to vary within an admissible set, conferring uncertainty to the applied loads. The admissible load space comprises loadings that can be represented through a collection of piecewise linear functions defined along the plate edges. The uncertainty of the loading is treated with the aid of a minimax formulation where the loading configuration and piecewise constant plate thicknesses are taken simultaneously as design variables. The choice of design variables imply in variable thickness non-homogeneous composite plates characterized by nonzero thermal residual stresses, inherited from the thermal processing. These residual stresses must also be accounted for in the buckling calculation as they significantly affect elastic behavior of the plate. The optimal composite plates obtained by the present optimization strategy satisfactorily withstand not only perfectly uniform loadings but an entire class of piecewise linear loadings. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The vibration of Mindlin plates with moving concentrated load is investigated using the finite element method (FEM). The use of Mindlin elements may, depending on the refinement of the mesh, yield poor results if the loads are located at off-nodal positions. A new strategy that is based on an adaptive mesh scheme and on the use of perturbation technique in the structural vibration simulation is proposed in this paper to overcome this problem. The strategy supports the use of the traditional finite elements and arbitrary geometry and boundary conditions for both plates and shells. © 2004 Elsevier Ltd. All rights reserved.

A new technique for enhancement of buckling loads of composite beams is proposed whose extension to the case of composite plates is immediate. The technique relies on using stress stiffening to create a non-zero tensile force acting along the beam axis which ultimately permits the application of higher external compressive forces that lead to traditional buckling instabilities. The computation of the non-zero tensile force in the case of composite beams is very simple and can be done without resorting to numerical procedures such as finite elements. The stress stiffening equation and the governing buckling equation are derived from a variational principle that applies to the conservative system at hand. Through this variational principle it is demonstrated that the pin-force model must be used with caution when it comes to buckling of composite beams although it can be used to correctly predict the stress stiffening effects. © 2003 Elsevier Ltd. All rights reserved.

The vibration of a cylindrical panel with a moving force or mass is investigated using the finite element method. The panels considered are assumed to be thin such that out-of-plane shear effects can be disregarded and the classical theory of shells can be applied. A perturbation technique is used to simplify the numerical problem such that the resulting nonlinear governing equations are split into a series of linear sub-problems. The effects of the panel curvature, moving load velocity and moving mass to main structure ratio on the dynamic response are investigated. It is observed that the dynamic response is relatively insensitive to variations in the panel curvature but is significantly affected by rapid traversing velocities or heavy moving masses. Moreover, a critical traversing speed is characterized for the moving force problem whereas a safe traversing speed is observed for the moving mass problem. © 2004 Elsevier SAS. All rights reserved.

This paper investigates compliance optimization of structures under multiple load cases. The problem can be solved through a multi-criterion optimization where the load cases associated with each and every loading configuration are treated as components of a multi-objective function vector. Alternatively, the multi-objective optimization problem can be re-formulated using a minimax strategy that does not require simultaneous consideration of all the load cases as components of a multi-objective function vector. Instead, it is shown that, for compliance optimization purposes, it is sufficient to consider only those loads which define the convex hull of the applicable load set, thereby drastically reducing the number of load cases involved in the design procedure. The efficiency of the technique proposed is illustrated through two examples consisting of variable thickness beams and plates subjected to uncertain loadings.

Optimization of heterogeneous composite aerospace structures that operate in a range of temperatures is considered. It is observed that heterogeneous composite plates optimized to operate at a fixed service temperature may perform poorly when that temperature is varied, that is, those plates may be highly sensitive to thermal loadings. A strategy is presented to obtain optimal designs of heterogeneous composite plates that operate within a given temperature range and under arbitrary mechanical loading, such that the significant and undesired sensitivity of these optimal designs to both thermal and mechanical loadings are effectively suppressed. It is assumed that the mechanical loading distribution is arbitrarily piecewise linear and that the operating temperature is within a specified range. Hence, the applied loadings are uncertain or not fixed in nature. Results for heterogeneous composite plates demonstrate the effectiveness of the strategy proposed and the danger of utilizing composite designs sensitive to variations in the thermal and mechanical loadings.

This note assesses the impact of the quality of the bonding layer on the sensing capability of plane piezoelectric patches. The bonding layer between the piezoelectric material and the main structure is assumed to be elastic, having a finite stiffness and considerable thickness as compared to the thickness of the piezoelectric sensor. The equations governing the mechanical equilibrium are simplified by assuming a pure shear stress state in the bonding film. The equilibrium equations are derived, the associated functional is obtained and, subsequently, the finite-element method is employed to solve the problem in two dimensions. The displacements found are those occurring on the contact surface between the bonding film and the piezoelectric sensor. The numerical solution obtained in terms of displacements allows the calculation of the effective voltage 'observed' by the piezoelectric sensor. This investigation addresses shear lag effects and shows that end-bonding must be carefully assessed in order to enhance the quality of the sensing output.

The problem of optimizing buckling loads of plates with variable thickness is addressed within the scope of a novel approach where the variability or uncertainty of the loading distribution is taken into account. The loading distribution is not uniform as traditionally assumed but is of a linear piecewise nature otherwise arbitrary. The importance of this investigation lies in the fact that the actual loading distributions acting upon structural components are rarely perfectly uniform although they are usually treated as so in traditional design approaches. A min-max strategy is used to handle the loading variability such that the resulting optimal design is able to withstand an entire class of linear piecewise loadings. © 2003 Elsevier Science Ltd. All rights reserved.

The performance assessment of commercial optimization codes was carried out for a satellite interface. The satellite interface consisting of a rectangular plate with reinforcements was used to connect the launcher to the satellite body, which enables to withstand loads transmitted by the launcher. Constraints were imposed in such way that longitudinal and transverse vibration modes do not couple with the launcher frequencies. The diversity of the optimization was found related to the different aspects of the interface design due to the objective-function, constrains and the choice of the design variables involved. The results indicate the potentiality of the optimization tools for the design of an aerospace structure.

Piezoelectric actuators are usually mounted to the top and bottom surfaces of plates and may induce in-plane extension, bending and localized shear deformations at the structural element. The in-plane stresses may have a significant influence on the mechanical behavior of thin plates as initial and/or residual stresses affect the flexural stiffness and in turn the dynamic and stability characteristics of plates. In this work, the effect of the in-plane piezoelectric induced stresses on the natural frequencies of composite plates is numerically and experimentally investigated. A finite element formulation is presented for the analysis of laminated plates with an arbitrary number of piezoelectric actuators and/or sensors. Von Kàrmàn non-linear strain-displacement relations are used and ideal linear behavior is assumed for the piezoelectric actuation. The problem is decomposed into an in-plane problem where the strain field induced by the piezoelectric actuators is computed. The natural frequencies and vibration modes are then computed taking the stress stiffening effects of these piezoelectric stresses into account. A number of different configurations are numerically and experimentally analyzed to verify the proposed theory. The configurations use eight PZT actuators bonded to three layer glass fiber/epoxy plates. The plates are square and clamped along two opposing edges and free along the other two. Good agreement is obtained between the predicted and measured natural frequencies. © 2002 Elsevier Science Ltd. All rights reserved.

The problem of optimal design for elastic buckling loads of composite plates under uncertain loading conditions is considered. It is observed that this is a multicriterion optimization problem whose solution is time consuming. Thus, an alternative minimax formulation is proposed and demonstrated. The buckling load is maximized with respect to the structural parameters and minimized with respect to variations in the load parameters. The mechanical loads applied to the rectangular plates are a combination of normal compression and shear. Moreover, the admissible loading configurations belong to a convex hull which significantly enhances the optimization procedure. The consideration of an uncertainty degree in the mechanical loads leads to optimal designs which are inherently insensitive to perturbations and/or randomness in the applied loads. Copyright © 2001 John Wiley & Sons, Ltd.

In the aeronautic industry it is known that optimal layout design of wing boxes is achieved through weight minimization with obvious improvements in the design process. Thus, a wing box pre-design optimization tool is developed using a knowledge-based engineering approach. The objective is to find an initial minimum weight design that satisfies structural constraints as well as design requirements (e.g. wing loft), based on load envelopes and stress analyses. All the calculations involved are performed using analytical expressions and graphs available in the literature. The numerical procedure implemented obtains the optimal number of ribs per wing box (main and trailing), the optimal number of stringers per rib bay and optimal sizing of all structural components (skin, spars, ribs and stringers). This procedure guarantees that acceptable margins of safety and functionality requirements are met. The automation of the process is important in this particular application given the enormous amount of data to be considered in a short period of time. Copyright © 2002 Society of Automotive Engineers, Inc.

This paper proposes a technique to optimize structural components for buckling when the applied loads are partially unknown or unpredictable. As opposed to the traditional buckling optimization situation where the loading configuration is specified, the load ratios are assumed uncertain and are incorporated as variables in the optimization problem formulation. As a result, the optimal designs obtained are insensitive to load variations within an admissible convex set. Additionally, in order to generalize the results and therefore provide a systematic solution procedure, a theorem concerning the shape of the stability boundary of structures whose buckling loads are the solution of linear eigenproblems is stated and proven.

Optimal elastic buckling loads of composite axisymmetric circular cylinders under uncertain loading conditions are investigated. The mechanical loads applied to the cylinder are a combination of axial compression, lateral pressure, and torsion. Additionally, these loads are allowed to vary within a certain class of admissible loads during the optimization search, as opposed to the restriction of fixed loads in the traditional optimization. The consideration of a degree of uncertainty in the mechanical loads leads to optimal designs which are inherently insensitive to perturbations and/or randomness in the applied loads. © 2001 ASME.

Optimal elastic buckling loads of composite ax-isymmetric circular cylinders under uncertain loading conditions are investigated. The mechanical loads applied to the cylinder are a combination of axial compression, lateral pressure and torsion. Additionally, these loads are allowed to vary within a certain class of admissible loads during the optimization search, as opposed to the restriction of fixed loads in the traditional optimization. The consideration of a degree of uncertainty in the mechanical loads leads to optimal designs which are inherently insensitive to perturbations and/or randomness in the applied loads. © 2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Optimal elastic buckling loads of composite axisymmetric circular cylinders under uncertain loading conditions are investigated. The mechanical loads applied to the cylinder are a combination of axial compression, lateral pressure and torsion. Additionally, these loads are allowed to vary within a certain class of admissible loads during the optimization search, as opposed to the restriction of fixed loads in the traditional optimization. The consideration of a degree of uncertainty in the mechanical loads leads to optimal designs which are inherently insensitive to perturbations and/or randomness in the applied loads.

Optimal elastic buckling loads of spatially heterogeneous plates formed from a series of composite patches is considered. Reissner-Mindlin laminated composite plate theory including thermal effects is adopted for the analysis and the problem is solved using the finite element method based on a bi-cubic Lagrange C O element formulation. The thermal residual stresses considered are those that result during elevated temperature processing because of the different laminates forming the patches of the plate. In the optimization, the fiber angles in each patch ate the design variables and three symmetric laminated plate configurations are investigated. The results illustrate that thermal residual effects can lead to optimal buckling loads which are as much as two times greater than the corresponding optimal buckling loads in which these manufacturing effects are ignored. The work demonstrates the importance of spatial heterogeneity as well as the significance of manufacturing-induced residual stresses in optimal design studies of composite structures. © 1999 ASME.

Optimal elastic buckling loads of spatially heterogeneous composite plates formed from a series of subregions is considered. Because of the plate heterogeneity thermal residual stresses develop during the cool down from the processing temperature to the operation temperature. An optimization strategy is implemented in order to take advantage of the non-zero thermal stress moments and to avoid convergence to local maxima. A min-max formulation is used to find the optimal design under the most dangerous set of admissible thermal and mechanical loads. The resulting designs are optimal within a certain class of parametrized loads as opposed to the traditional optimality under fixed loads.

The non-linear behavior of slightly crooked slender composite beams with piezoelectric actuators is addressed. Von Kármán non-linear strain-displacement relations and linear constitutive relations for both the piezoelectric and composite materials are used. The piezoelectric control of crooked beams subjected to axial compression renders its equilibrium path as close as possible to that of the ideal perfect beam. A modal analysis demonstrates that, through the application of suitable voltages to the actuators, the elimination of certain buckling mode contributions to the beam response is feasible and highly desirable. The equilibrium path of imperfect structures is shown to be dramatically changed via piezoelectric control; this has potential applications in the post-buckling of structures with negative slope of the secondary equilibrium path. © 1999 Elsevier Science Ltd. All rights reserved.

Axisymmetric static and frequency analyses of anisotropic cylindrical thin shells with one and two perfectly bonded ring piezoactuators are performed. The shell is assumed to be linear elastic and made of laminated composite materials. The electroelastic constitutive relations for the piezoelectric materials are also assumed to be linear. It is shown that, if there exists a special relationship involving the membrane and the membrane-bending coupling stiffness matrices. the analysis is greatly simplified. In such a situation, simple closed form solutions of the equilibrium equations are obtained for the case of an infinite shell with one or two actuators. Kirchhoff's assumptions are used for the analysis and the dynamic formulation is derived from a variational principle which includes the total structural potential energy and the electrical potential energy of the piezoelectric material, involving both mechanical and electrical variables. The finite element method is then applied to obtain the stiffness and mass matrices. The computer code developed to implement the formulation allows the static and dynamic analyses of arbitrary cylindrical shells with piezoelectric actuators. Good agreement is reached between the analytical solution found and the numerical procedure implemented. Results indicate that the maximum normalized displacement and it's location vary according to the actuator length. Furthermore, a frequency analysis is carried out in a broad range of frequencies to investigate the effect of mass properties on the response of a simply supported cylindrical shell.

The piezoelectric strain actuation of beams has been extensively studied. It is well known that a number of non-idealities may affect the performance of piezoelectric sensors or actuators. In particular, the existence of a finite stiffness bond between the actuator and the structure causes a reduction in the effectiveness (or sensitivity) of induced strain actuators (or sensors) mounted on the surface of a structure. This effect may be significant for short actuators and/or less stiff bonding layers. The objective of this work is to assess the influence of a finite stiffness bond between piezoelectric sensors/actuators and the structure on the active damping of beams subjected to rigid body rotations and elastic deformations. The depoling of the piezoelectric material is also taken into account in the model. A finite element formulation that incorporates this effect is proposed. The formulation uses an Euler-Bernoulli model for the beam and assumes the bond layer to be in a state of pure shear. The effect of the finite bond stiffness appears explicitly in the electro-mechanical coupling matrix. The present formulation includes the effect of the finite bond stiffness with good approximation without introducing extra degrees of freedom in the system. Active damping is introduced in the beam by a simple control law using rate feedback. A numerical example indicates that, within certain limits, the finite stiffness bond may be compensated for by using a higher gain in the control system. However, the finite bonding stiffness has to be taken into account when designing the control system.