An efficient semi-analytical approach for postbuckling analysis of laminated composite plates with straight edges

Postbuckling in thin-walled aircraft structures can lead to a redistribution of loads while the structure continues to carry load. This behavior is particularly important in stiffened panels, where local buckling does not necessarily imply failure. Accurately modeling this behavior is essential, but the analysis is often computationally expensive. A computationally efficient methodology is developed to predict postbuckling behavior, supporting preliminary design and multidisciplinary optimization of aerospace structures. The formulation is based on the Rayleigh–Ritz method using hierarchical polynomials as shape functions. These polynomials enable closed-form integration of the energy functional and allow the application of various boundary conditions. Two solution schemes are implemented: a perturbation-based expansion and an iterative correction method based on the Normal Flow Algorithm. The solutions are verified against results from the literature and finite element simulations. Results show that the methodology accurately predicts postbuckling behavior while substantially reducing computational cost. The efficiency and flexibility in modeling different boundary conditions make the approach well-suited for integration into structural design and optimization frameworks that require repeated postbuckling evaluations.