Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

Abstract

This research proposes a computationally efficient methodology using a Constrained Variational Asymptotic Method (C-VAM) for non-linear buckling analysis on a hat-stringer panel with delamination defects. Starting with the geometrically non-linear kinematics, the VAM procedure reduces the three-dimensional (3-D) strain energy functional to an analogous 2-D plate model and evaluates the closed form warping solutions. Utilising the resulting warping solutions and recovery relations for the skin and the stringer, displacement continuity at the three-dimensional level is enforced between the stringer and the skin based on the pristine and delaminated interface regions. Consequently, the constrained matrices obtained from C-VAM is incorporated into an in-house developed non-linear finite element framework. Using the developed formulation, a stiffened panel with delamination of 40 mm between the stringer and the skin is analysed under compression. The results have been validated locally and globally, employing experimental data and 3-D finite element analysis (FEA). Experiments are carried out on the co-cured panel by applying quasi-static loading with displacement-controlled conditions, and 3-D FEA is carried out in Abaqus. Load-response plots have been obtained to validate the results at the global level, and they are in excellent agreement with experiments and 3-D FEA. Subsequently, out-of-plane displacement contour plots are obtained; the number of half waves and wave intensity in 3-D FEA and C-VAM are comparable, although there are minor differences compared to the experimental findings. The proposed framework is shown to be computationally efficient by over 55% as compared to 3-D FEA for performing non-linear buckling analysis on the stiffened composite structure considered in the current work.