Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions

The concept of Variable angle tow placement is explored for enhancing the buckling resistance of composite plates subjected to axial compression under different plate boundary conditions. The buckling problem of VAT plate is complicated because of variation in stiffness properties across planform of the plate due to curvilinear fiber path distribution. The problem requires prebuckling analysis to be performed first to determine the non-uniform stress distribution and then the buckling analysis of VAT plates. In the present work, a solution methodology based on the Differential quadrature method (DQM) is developed for solving the partial differential equations of VAT plates with linear fiber angle orientations. Within the framework of DQM, a stress function formulation for inplane analysis and displacement formulation for buckling analysis was employed to derive the governing differential equations based on classical laminated plate theory. The novel aspect of the present work is the use of Airy’s stress function to model the prebuckling analysis of VAT plates which considerably reduces the problem size and computational effort. This approach provides more generality to handle pure
stress and mixed boundary conditions more effectively when compared to the exisiting analytical models. Furthermore, the governing differential equation derived for buckling analysis of VAT panels considers the effect of bending-twist coupling terms on the buckling load. DQM was applied first to solve the inplane elasticity problem of VAT plates subjected to cosine distributed compressive loads. DQM was then extended to solve the inplane problem of VAT plates under uniform end shortening for which the unknown stress distributions are non-uniform. Stress distributions along the edges of the plate were expanded using Legendre polynomials and the unknown coefficients were determined using a least square approach such that the displacment boundary conditions are satisfied. Later, the DQM was applied to solve the buckling problem of rectangular VAT plates subjected to axial compression under different boundary conditions, viz., simply supported, clamped and free edge boundary conditions. Comparisons were made with finite element results obtained using ABAQUS and the accuracy and efficiency of the proposed DQM approach were studied.