Buckling and post buckling analysis of spatial thin film structures under shearing based on perturbation method

Abstract

Spatial thin film structures exhibit high sensitivity to shear deformation, often exhibiting wrinkling phenomena under minimal shear loads. In this study, we used a combined experimental and theoretical approach to investigate the wrinkling and post-buckling behaviors of thin films subjected to shear forces. Initially, we designed and fabricated a high-precision experimental apparatus, which, in conjunction with the MTS Exceed 40 series universal testing machine, was a versatile experimental platform for evaluating the responses of thin films to shear. Subsequently, we extended the classical Föppl–von Kármán nonlinear plate model to capture the large deformation behaviors of thin films under shear. This development led to the formulation of governing equations that describe the shear-induced deformation of the films. We introduced two boundary conditions to characterize these deformations: one in which the non-loaded edge was free (unconstrained), and another in which the non-loaded edge was constrained (analogous to a frame constraining a painting). To solve the governing equations, we treated the incremental shear displacement angle of the thin film as a small parameter and devised a numerical method grounded in perturbation theory. We further formulated an implicit difference method of arbitrary order accuracy to enhance the precision and stability of the numerical solution. Our experimental and theoretical analyses revealed a comprehensive buckling pathway for thin films under shear, characterized by an initial wrinkling configuration (Config. 1), followed by a transition to a secondary wrinkling state (Config. 2), and culminating in a wrinkling splitting pattern (Config. 3). We also determined that by increasing the pre-stretching of thin films, their resistance to wrinkling along the entire buckling pathway could be significantly enhanced.