Displacement-based formulation of Koiter's method: Application to multi-modal post-buckling finite element analysis of plates

Koiter's asymptotic method enables the calculation and deep understanding of initial post-buckling behaviour thin-walled structures. For single-mode analysis, Budiansky (1974) presented a clear general formulation for method, based on expansion total potential energy function. The from is herein revisited expanded multi-modal primordial importance in structures with clustered bifurcation modes. Given admittedly difficult implementation especially analysis during evaluation third– fourth–order tensors involved analysis; study proposes notation close correspondence implemented algorithms. state-of-the-art collaborative tools: Python, NumPy Cython. kinematic relations are specialized using von Kármán shell kinematics, displacement field variables approximated an enhanced Bogner-Fox-Schmit (BFS) finite element, modified to reach third-order interpolation also in-plane displacements, only 4 nodes per element 10 degrees-of-freedom node, aiming accurate representation second-order fields. verified by comparing results isotropic composite plates against established literature. Finally, fields up 5 modes corresponding factors reported future reference.