Improved element solution to composite beams

Abstract

© 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.