Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections

Abstract

This paper presents a numerical assessment of different finite element models (FEM) for the static analysis of laminated composite beams of various cross-sections, considering equivalent single layer theories (Classical Lamination Theory – CLT, First-order Shear Deformation Theory – FSDT and Higher-order Shear Deformation Theories – HSDT). New mixed least-squares FEM are developed for all theories and confronted with displacement-based weak form, mixed weak form and mixed weighted residual form FEM, which are derived for comparison purposes. The governing equations consistent with the mixed formulations, derived from the Hellinger–Reissner variation principle, are also presented. A method of transforming the actual geometrical beam cross-section into an equivalent single layer, through transformation matrices and the parallel axis theorem, existing in the literature for the CLT is implemented and extended to the FSDT and HSDT. Validation and assessment of the different FEM involved the implementation of analytical solutions and comparison with numerical and analytical results available in the literature, from which conclusions in terms of accuracy and computational effort are drawn.