© 2021 by Antônio B. Guimarães Neto, Guilherme C. Barbosa, Juliano A. Paulino, Rafael M. Bertolin, Jéssica S. M. Nunes, Pedro J. González, Flávio L. Cardoso-Ribeiro, Maurício A. V. Morales, Roberto G. A. da Silva, Flávio L. S. Bussamra, Flávio J. Silvestre, Fernando J. O. Moreira, and Carlos E. S. Cesnik. Published by the American Institute of Aeronautics and Astronautics,.The challenges of modeling flexible aircraft include appropriate fidelity capturing and validation with experimental data. In fact, the validation of formulations and models for the flexible flight dynamics is indispensable to ensure that all the important phenomena are correctly captured. With this objective, two high-aspect-ratio flexible aircraft have been flight-tested, and coupled aeroelastic–flight dynamics data have been collected to support model validation. Additional ground vibration and static tests were carried out to fully characterize the structural dynamic properties. Numerical models were built based on a linear structural representation but with geometrically nonlinear aerodynamics. Low Reynolds number effects were included in a simplified way with lookup tables of two-dimensional airfoil data. Wing-tip effects were considered via the vortex-and doublet-lattice methods. Propulsive data were obtained with wind-tunnel tests. This paper describes the numerical models, the two aircraft, and their instrumentation and presents the data collected from the aircraft sensors during flight tests. Numerical and experimental results are compared for angular velocities, accelerations, and strains measured at different points of the aircraft. Despite its limitations and simplifications, the numerical model captures the real aircraft main aeroelastic and flight dynamic behaviors.

© Proceedings of the International Forum of Aeroelasticity and Structural Dynamics 2022, IFASD 2022.As economic and environmental requirements surge, aircraft manufacturers incorporate a myriad of features in aircraft design aiming to reduce fuel consumption. One endeavor to increase fuel efficiency is related to increasing wing aspect-ratios, improving the aerodynamic efficiency of wings. Even though high aspect-ratio wings contribute to improving aircraft fuel efficiency, these slender wings present high structural flexibility, undergoing large deflections under operational loads. In this case, conventional linear structural analysis fails to predict accurate structural results. Then, nonlinear structural analysis needs to be employed for properly capturing the static aeroelastic response of such wings. In this context, this work proposes a fluid-structure interaction methodology coupling a full-potential aerodynamics solver with a nonlinear structural solver to evaluate the static aeroelastic behavior of very flexible wings. The methodology is applied to the Pazy Wing, a very flexible rectangular wing, as part of an international cooperation in NASA’s Aeroelastic Prediction Workshop 3. Comparisons between simulation and wind tunnel test results found in the literature are used for validating the developed methodology. Further, the work seeks to capture deviations in the wing deformed shape and aerodynamic loading when linear and nonlinear structural models are employed in the aerostructural scheme.

© Proceedings of the International Forum of Aeroelasticity and Structural Dynamics 2022, IFASD 2022.This paper presents a static aeroelastic investigation of the rolling capability of a modern flexible wing with the objective of flight test campaign clearance. A conventional configuration transport aircraft was evaluated in transonic conditions between Mach 0.82 and 0.89. A fluid-structure interaction tool with aileron deflection was considered to simulate the wing flight deformed shape effect on rolling capability, also with the undeformed fluid dynamics simulation reference for comparison. The applied code E2-FSI, which couples Reynolds Average Navier Stokes (RANS) fluid dynamics and static structural analysis, was improved to consider the different positions of control surface. The numerical results were compared to wind tunnel test data, with and without linearized aeroelastic corrections. The comparison in terms of rolling coefficient and flow topology are presented. The improve in the method fidelity resulted in advanced understanding of extreme rolling condition.

© 2021, The Brazilian Society of Mechanical Sciences and Engineering.This paper presents a hybrid methodology for loads measurement on aircraft structures. It is based on both experimental data from the actual structure and numerical prediction from finite element models. The model is firstly adjusted based on a reduced amount of experimental data, so it can predict the structure load response in terms of simulated strain-gage bridge responses. Once adjusted, the model is loaded at several points while gathering the corresponding simulated strains responses. Based on regression analysis, the calibration coefficients are established to be used for in-flight load measurements. Comparing with the conventional calibration method, purely based on experimental tests, the new calibration methodology requires less calibration load cases, which makes the test setup also simpler. The new calibration method is applied to a horizontal empennage from a commercial aircraft, for which the conventional calibration was previously conducted, providing therefore the reference for both flight and ground test comparisons. A good correlation was found between the loads estimated by the conventional calibration and present method. Nowadays, virtual tests are getting importance for validation and demonstration purposes, and this work is adherent with this tendency.

© AIAA International. All rights reserved.An experimental remotely piloted aircraft named X-HALE was designed and built at the University of Michigan to collect experimental data for the flight dynamics of vehicles with very flexible wings. Similar aircraft with a wing span of 4 and 6 m were later developed and built at the Aeronautics Institute of Technology, Brazil, to study the flight dynamics and control of highly flexible aircraft. In the present Paper, the steady structural response of the wing of the X-HALE is investigated by the finite element method assuming 1) linear behavior (small displacement, small strain analysis) and 2) nonlinear behavior (large displacement, small strain analysis). This Paper aims to investigate the influence of geometric nonlinearities in the numerical prediction of load distribution and displacements along the wing span when compared with linear analyses results. For this purpose, four versions of the X-HALE with different structural layouts are presented. Two aircraft have a 4 m wing span constructed with fiberglass and aluminum, respectively. The other two have a wing span of 6 m and were also constructed with fiberglass and aluminum. Internal force redistributions were observed in the nonlinear structural analyses. The redistribution of these forces caused the twist angle to increase and the bending angle to decrease compared to the linear analyses when under the same loading conditions.

© 2020 Society of Plastics EngineersAdditively manufactured composites have been demonstrating promising results with the development of new materials of high mechanical performance, which draws attention from several fields, for example, biomedical, electronics and aeronautics. However, as such materials are based on novel technologies, it is necessary to better understand their resulting characteristics and properties. For instance, evaluating the effect of environmental conditions on their mechanical performance is important, especially when moisture-sensitive polymers such as polyamide (PA) are employed as matrix. This work aims to understand and to characterize the moisture effect on the mechanical properties of additively manufactured Nylon and continuous carbon fiber (CF)-reinforced Nylon-based thermoplastic. Tensile and compressive tests were carried out in accordance with ASTM standards for the printed samples at their maximum moisture content and for samples submitted to drying after the saturated condition. Moreover, moisture absorption and swelling behaviors were assessed and discussed. The experimental results showed that moisture significantly affects the fiber/matrix interface, as well as the adhesion between printed filaments. These changes led to a decrease in the general mechanical properties in saturated state, including those in the fiber direction. Furthermore, a permanent degradation was observed in some properties after drying. Thus, the importance of considering water content and aging effect on the characterization and engineering application of 3D printed CF/PA composite was evidenced.

© 2020, Brazilian Association of Computational Mechanics. All rights reserved.Hybrid-Trefftz finite elements have been applied to the analysis of several types of structures successfully. It is based on two different sets of approximations applied simultaneously: stresses in the domain and displacements on its boundary. This method presents very large linear systems of equations to be solved. To overcome this issue, most authors have been careful in the choice of the approximation fields in order to have highly sparse linear systems. The natural choice for the stress basis has been linearly independent, hierarchical and orthogonal polynomials which typically result in more than 90% of sparsity in 3-D finite elements. Functions derived from associated Legendre and Chebyshev orthogonal polynomials have been used with success for this purpose. In this work the non-orthogonal polynomials available in the Pascal pyramid are proposed to derive a harmonic and complete set of polynomial basis as an alternative to the above-cited functions. Numerical tests show this basis produces accurate results. No significant differences were found when comparing the sparsity of the linear system of equations for both functions.

© 2020, The Brazilian Society of Mechanical Sciences and Engineering.This paper presents a fluid–structure iteration method applied as a study case to a conventional transport aircraft with wing aspect ratio of 12. It evaluates the nonlinear structure effect on the calculation of static limit loads. The numerical tool presented herein is named E2-FSI, which stands for nonlinear high-fidelity static fluid–structure iteration, developed for high flexibility static aeroelastic evaluations. A discussion about the use and the applicability of high-fidelity static fluid–structure iteration for the calculation of static loads is presented as part of the conclusion, for both current and future conventional transport aircraft.

© Universal Technology Corporation, 2018.The development of modern, more efficient transport aircraft and High-Altitude-Long-Endurance (HALE) aircraft requires solutions that involve lightweight structures and high aspect ratio wings for maximum aerodynamic efficiency. However, this may result in flexible wings, such that the coupling between rigid-body and structural modes deteriorates stability and handling qualities of the aircraft. These can be improved by the continuous operation of control systems with the use of structural information, such as wing deformed shape. Strain gages can be used for such an application. However these sensors may have input interference, such as temperature variation, that can cause false strain responses other than the expected measurements due to flight loads. This work presents the analyzes of strain gage measurements due to thermal loads in the X-HALE aircraft wing. Three thermal correction methods were proposed: functions of temperature, dummy gage, and high-pass filtering. Each was tested on indoor and outdoor experiment setup, which uses a lamp and natural temperature variation throughout a full day as heat sources. All methods were effective in removing thermal drift of indoor experiment data. However, only high-pass filtering method was successful in the outdoor experiment. Indoor thermal test results done on the full 4m X-HALE aircraft, with the addition of impact excitations on the aircraft’s wing tip, showed that the high-pass filtering was able to remove thermal drift while maintaining all responses in the frequency range of interest. Therefore, this method is suitable to the present application.

© Universal Technology Corporation, 2018.This paper presents a static iterative aero-structural method applied as a study case to a transport aircraft with wing aspect ratio of 12. It evaluates the structure geometric nonlinearity effect on aerodynamic coefficients. A Nonlinear High-fidelity Static Fluid-structure Iteration tool (E2-FSI) was used in this study case. It combines Reynolds Average Navier Stokes Computational Fluid Dynamics with detailed Finite Elements Method in linear and nonlinear structural analyses. The wing body nonlinear high fidelity static aeroelastic effect on flexible pitching moment coefficient was correlated to rigid tail trimming demand showing static tail loads being modified by wing nonlinear flexibility.

Copyright © 2017 John Wiley & Sons, Ltd.Three-dimensional hybrid-Trefftz stress finite elements for plates and shells are proposed. Two independent fields are approximated: stresses within the element and displacement on their boundary. The required stress field derived from the Papkovitch-Neuber solution of the Navier equation, which a priori satisfies the Trefftz constraint, is generated using homogeneous harmonic polynomials. Restriction on the polynomial degree in the coordinate measured along the thickness direction is imposed to reduce the number of independent terms. Explicit expressions of the corresponding independent polynomials are listed up to the fifth order. Illustrative applications to evaluate displacements and stresses are conducted by hexahedral hybrid-Trefftz stress element models. The hierarchical p- and h-refinement strategy are exploited in the numerical tests.

© 2017 Elsevier B.V.Hexahedral hybrid-mixed finite elements are proposed for free vibration analysis of three-dimensional solids. The element formulation relies on the simultaneous and independent approximations of stress and displacement in the element domain as well as the displacement on their boundary. Sets of complete and linearly independent non-nodal Legendre polynomials used for the field variables lead to symmetric, highly sparse and well conditioned solving systems. Numerical tests show that the elements yield accurate results, even in the presence of high stress gradients, and they seem to be free of shear and volumetric locking and have low sensitivity to mesh distortion. The hierarchical p-refinement strategy is exploited.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.This article presents a Fluid Structure Iteration method applied as a study case to a recent conventional transport aircraft with aspect ratio of 12. It evaluates the nonlinear structure effect on the static limit loads calculation. It uses the tool called E2-FSI, which stands for Nonlinear High-fidelity Static Fluid-structure Iteration, developed for high flexibility static aeroelastic evaluations. It uses Reynolds Average Navier Stokes Computational Fluid Dynamics combined with detailed Finite Elements Method in linear and nonlinear structural analyses. A discussion about the use and applicability of high fidelity static Fluid Structure Iteration for static loads calculation is presented as part of the conclusion, for both current and future conventional transport aircrafts.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.Conventional transport aircrafts are becoming more flexible in order to achieve lower fuel consumption. Most part of the additional flexibility comes from the increased wing aspect ratio. This line of studies is composed by sequential phases which come from Aerodynamics to Structures passing through Loads and Aeroelasticity technologies. This work proposes the integration of Aerodynamics and Structures through a multidisciplinary analysis, focusing on the high flexibility aspects of the wing in-flight shape for a recent, high aspect ratio aircraft. This work aims to understand the changes in the loads and structural sizing processes due to the increased flexibility of the wing. It uses a recent and high aspect ratio aircraft as a study case. Potential Computational Fluid Dynamics and nonlinear Finite Elements Method analyses are integrated employed in this study. Large displacements was included in the process, showing impacts for future development methodologies.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.This article presents the development of a real-time flight load measurement system convertible to real-time flight geometry measurement. It uses already known full bridge strains gages in a different manufacturing possibility: inside composite layers before resin cure. The manufacturing process is validated using a composite bar prototype. The prototype is submitted to a four points structural test in order to validate the measurements and influences of the manufacturing process. The whole process is applied to X-HALE aircraft disclosing a composite built-in measurement system for real-time flight load and flight geometry.

© 2017 International Forum on Aeroelasticity and Structural Dynamics (IFASD). All rights reserved.A simple and self-contained methodology to assess the validity of the assumption of small deformations in linear structural-dynamic models was recently proposed. The advantages of the methodology lie in the fact that it does not depend on the availability of higher-fidelity, nonlinear models: it is rather based on the selection of two different structural nodes where the structural motion is to be one at a time completely constrained, typically, a node near the center of mass and another in the region of maximum structural displacements with respect to mean axes. If the two displacement vectors calculated in each case can be transformed between themselves with linear rigid-body modes of the structure, then it is still in the regime of small deformations. In the present paper, in order to demonstrate the value of this methodology, it is applied to the X-HALE aircraft in its four-, six- and eight-meter-span configurations, and the results obtained with the assumption of small deformations are compared with a higher-fidelity model that comprises large structural deformations.

© 2017 International Forum on Aeroelasticity and Structural Dynamics (IFASD). All Rights Reserved.Formulations for the flight dynamics of flexible aircraft have been commonly applied to aircraft free to fly in the three-dimensional space, having all six rigid-body degrees of freedom. For risk reduction in the future flight operations of the X-HALE testbed at ITA, however, wind-tunnel tests of the remotely-piloted, four-meter-span configuration of the aircraft were performed. In the wind tunnel, the rigid-body translations were completely constrained, but the same was not valid for the rigid-body rotations, which could be conveniently left free or not with a proper selection of the connection between the aircraft and the wind-tunnel mount. In the present paper, in order to computationally assess the response and stability characteristics of the aircraft in the wind tunnel, we derive equations of motion for a constrained flexible aircraft with up to three rigid-body rotational degrees of freedom, mounted on an also flexible wind-tunnel strut. The numerical model has its value confirmed by the wind-tunnel tests in the predicted and observed roll-control reversal for anti-symmetrical deflections of the all-moving tails, and absence of reversal for aileron deflections.

© 2017, Brazilian Association of Computational Mechanics. All rights reserved.Aerospace vehicles are mostly exposed to random vibration loads during its operational lifetime. These harsh conditions excites vibration responses in the vehicles printed circuit boards, what can cause failure on mission functionality due to fatigue damage of electronic components. A novel analytical model to evaluate the useful life of embedded electronic components (capacitors, chips, oscillators etc.) mounted on Printed Circuit Boards (PCB) is presented. The fatigue damage predictions are calculated by the relative displacement between the PCB and the component, the lead stiffness, as well the natural vibration modes of the PCB and the component itself. Statistical methods are used for fatigue cycle counting. The model is applied to experimental fatigue tests of PCBs available on literature. The analytical results are of the same magnitude order of the experimental findings.

© 2015 by Danilo C. Branco and Flávio Luiz S. Bussamra.The damage tolerance analysis, which uses the force structural management plan, is usually employed in airplane fatigue life prediction. This plan, based on a mission "mix" defined at the airplane structure design phase, induces the squadrons to follow this mix and interferes in the fleet's usage efficiency. Deviations in the mission mix have impacts on inspection intervals and maintenance costs. In this paper, a fatigue life monitoring system is proposed. It is able to incorporate each mission, individually, in a specific aircraft's fatigue life analysis, adjusting the maintenance plan into a more realistic usage profile, based on the individual aircraft tracking methodology. This monitoring system is implemented in a computer software and it is applied to F-5E fighter aircraft of the Brazilian Air Force. In addition, experimental fatigue tests that simulate critical locations of this aircraft are compared with the proposedmonitoring system, which shows ability to predict, in conservative and approximate ways, the crack length after each flight, disregarding the predefined mission mix. This makes the flexibilization of the operations possible without jeopardizing the inspection and maintenance planning.

© 2016, Brazilian Association of Computational Mechanics. All rights reserved.Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch- Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term “quasi”. In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical prefinement is exploited.

© 2015 Elsevier Masson SAS. All rights reserved.This paper presents a detailed investigation on the post-buckling behaviour of adhesively bonded stiffened panels subjected to in-plane shear loading. An experimental programme was carried to determine the buckling load, buckling shape, collapse load and failure modes of two bonded stiffened panels. A nonlinear finite element based modelling approach, accounting for geometrical and material nonlinearities as well as progressive failure in the adhesively bonded interface between the skin and the stiffener is proposed to predict the structural behaviour of the panels up to failure. This approach consists in modelling the bonded interfaces using a newly developed cohesive zone based constitutive damage model. In order to account for damage in the stiffener and the skin a Von Mises based constitutive damage model is also formulated and presented in the paper. Both constitutive models were implemented into ABAQUS/Explicit finite element code as user-defined material models. A very good agreement between experimental results and numerical predictions is obtained using the proposed modelling approach, with deviations smaller than 8% in buckling load and bonded interface failure load onset.

Copyright © 2014 Tech Science Press.Hybrid-Trefftz stress finite elements have been applied with success to the analysis of linear and non-linear problems in structural mechanics. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The stress field satisfies the Trefftz constraint a priori, i.e., it is extracted from the Navier equation solution. This type of element has provided remarkable improvement in stress predictions compared to the standard displacement-based finite elements. In this work, solution of stress concentration problems is carried out by hexahedral hybrid-Trefftz stress element models. Stress concentration factors and stress intensity factors are then identified and compared with available results. The hierarchical p-refinement strategy is exploited in the numerical tests.

This work presents a new metamodel for reinforced panels under compressive loads, typically used in light-weight aircraft structures. The metamodel represents a replicable cell structure of integrally machined panels. The presented formulation for conception is based on the synthesis of four stability criteria: section crippling, web buckling, flange buckling and column collapse. The aluminum alloy, a typical choice in modern aircraft industry, is selected and the structure is expected to work in the linear elastic domain. In order to evaluate the accuracy and to validate the analytical tool, the procedure is applied in the pre-sizing of the fuselage basic structural components of a 9-passenger executive aircraft. The pull-up maneuver, one of the critical load conditions in most of aircrafts, causes the maximum compressive stresses in lower fuselage panels. Finite element models are presented to the resulting fuselage configuration. The optimal configuration achieved through the application of the analytical tool yields to an innovative structure from those usually adopted in the aeronautical industry. This structural configuration is presented and discussed. The developed metamodel proved to be effective, presenting satisfactory results with adequate accuracy for the initial stages of light-weight aircraft structure.

Three-dimensional hybrid finite elements are proposed to the analysis of laminated composite plates. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The required stress field in point-wise equilibrium is generated by harmonic and orthogonal hierarchical polynomials, adapted from Papkovitch-Neuber solution of Navier equations for isotropic material. The solving system is symmetric, highly sparse and well conditioned. The elements are suited to p-refinement and present low sensitivity to mesh distortion. Illustrative applications are given to evaluate displacements and stresses. © 2011 Elsevier Ltd. All rights reserved.

Finite element models are proposed to the micromechanical analysis of a representative volume of composite materials. A detailed description of the meshes, boundary conditions, and loadings are presented. An illustrative application is given to evaluate stress amplification factors within a representative volume of the unidirectional carbon fiber composite plate. The results are discussed and compared to the numerical findings.

The stress model of the hybrid-Trefftz finite element formulation is applied to the elastoplastic analysis of solids. The stresses and the plastic multipliers in the domain of the element and the displacements on its boundary are approximated. Harmonic and orthogonal hierarchical polynomials are used to approximate the stresses, constrained to solve locally the Beltrami governing differential equation. They are derived from the associated Papkovitch-Neuber elastic displacement solution. The plastic multipliers are approximated by Dirac functions defined at Gauss points. The finite element equations are derived directly from the structural conditions of equilibrium, compatibility and elastoplasticity. The non-linear governing system is solved by the Newton method. The resulting Hessian matrices are symmetric and highly sparse. All the intervening arrays are defined by boundary integral expressions or by direct collocation. Numerical applications are presented to illustrate the performance of the model.

The stress model of the hybrid-Trefftz finite element formulation is applied to the linear elastostatic analysis of solids. The stresses are approximated in the domain of the element and displacements on its boundary. Complete, linearly independent, hierarchical polynomial approximation functions are used in both domain and boundary approximations. The displacement basis is defined independently on each inter-element surface. Continuity at the edges and on the corners of the elements is not enforced a priori. The stress basis is constrained to solve locally the Beltrami governing differential equation. It is derived from the associated Papkovitch-Neuber elastic displacement solution. Generalized variables are used to ensure that the approximations are independent of the geometric description of the elements. The solving system is derived directly from the fundamental relations of elastostatics. The solving system is symmetric, when the same property applies to the local elasticity condition, sparse, described by boundary integral arrays and well suited to p-refinement and parallel processing. The numerical implementation of these equations is discussed and numerical tests are presented to illustrate the performance of the finite element formulation. Copyright © 2000 John Wiley & Sons, Ltd.