Buckling of thin skew isotropic plate resting on Pasternak elastic foundation using extended Kantorovich method

Abstract

The extended Kantorovich method (EKM) is implemented to numerically solve the elastic buckling problem of thin skew (parallelogram) isotropic plate under in-plane loading resting on the Pasternak elastic foundation. EKM has never been applied to this problem before. Investigation of the EKM accuracy and convergence is conducted. Formulations are based on classical plate theory (CPT). Stability equations and boundary conditions terms are derived from the principle of the minimum total potential energy using the variational calculus expressed in an oblique coordinate system. The resulting two sets of ordinary differential equations are solved numerically using the Chebfun package in MATLAB software. In-plane compression and shear loads are considered along with various boundary conditions and aspect ratios. Results are compared to the analytical and numerical solutions found in the literature, and to the finite element solutions obtained using ANSYS software. The effects of the skew angle, stiffness of elastic foundation, and aspect ratio on the buckling load are also investigated. For plates with zero skew angle, i.e. rectangular plates, with various boundary conditions and aspect ratios under uniaxial and biaxial loading resting on elastic foundation, the single-term EKM is found accurate. However, more terms are needed as the skew angle gets bigger. The multi-term EKM is found accurate in the analysis of rectangular and skew plates with various boundary conditions and aspect ratios under uniaxial, biaxial, and shear loading resting on elastic foundation. Using EKM in buckling analysis of thin skew plates is found simple, accurate, and rapid to converge.

Abstract

Civil engineering; Mechanical engineering; Structural engineering; Foundation Engineering; Structural Analysis; Structural Mechanics; Extended Kantorovich method (EKM); Thin plate; Skew plate; Buckling; Pasternak elastic foundation; Galerkin's weighted residual method