Post-buckling analysis of variable-angle tow composite plates using Koiter's approach and the finite element method

The design of lightweight structures is often driven by buckling phenomena. Increasing demands for fuel-efficient aircraft structures makes post-buckled designs attractive from a structural weight perspective. However, the need for reliable and efficient design tools that accurately model the emerging nonlinear post-buckled landscape, potentially one containing multiple branches, remains. With this aim, a previously derived flat shell element, MISS-4, is extended to the geometrically nonlinear analysis of variable-angle tow (VAT) composite plates using Koiter's asymptotic approach. The curvilinear fiber paths in VAT lamina open the design space for tailoring the buckling and post-buckling capability of plates and shells. A finite element implementation of Koiter's asymptotic approach allows the pre-critical and post-critical behavior of slender elastic structures to be evaluated in a computationally efficient manner. Its implementation uses a fourth-order expansion of the strain energy, and requires both the structural modeling and finite element discretization procedures to be, at least, of fourth order. The corotational approach adopted in the MISS-4 element readily fulfills this requirement by starting from a linear finite element discretization. VAT plates with prismatic fiber variations and different loading conditions are analyzed using the MISS-4 element and numerical results of the post-buckling paths are presented. The computed equilibrium paths are compared to benchmark results using the commercial finite element package ABAQUS, and strong asymptotic solutions of the differential equations. The results document the good accuracy and reliability of the proposed modeling approach, and also highlight the importance of multi-modal analysis when multiple buckling modes coincide as is the case in long plates, shells and other optimized thin-walled structures.