Trigonometric shear deformation theories for geometric nonlinear analysis of curved composite laminated shells: Post-buckling prediction using a parallelized approach

This paper introduces a set of trigonometric shear deformation theories for the nonlinear geometric analysis of generally curved laminated composite shells with focus on post-buckling prediction. The suggested framework uses a degenerated shell element associated to trigonometric expansion and a generalized displacement control method to get a stable, accurate, and computationally efficient solution. One important benefit of adopting a higher-order shear theory is getting better stress fields without using correction factors, in addition to the solution stability in geometric nonlinear analysis, although at the cost of a moderate increase in the number of degrees of freedom (DOF) per node. The theory is implemented in MATLAB using an improved object-oriented programming and parallel processing approach to assemble the stiffness matrices, enhancing the efficiency of the analysis. Comparisons with published data for moderately thick and curved shells and composite laminated plates corroborate the suggested theory’s accuracy and efficacy. The findings reveal that trigonometric shear deformation theories overcome the limits of first-order shear deformation theories and other expansions, producing accurate results with just a minor increase in computational complexity.