Uniaxial and biaxial post-buckling behaviors of longitudinally graded rectangular plates on elastic foundations according to the 3D theory of elasticity

Longitudinally varying the material properties may be an adequate optimization solution when there are restrictions in varying cross sections of the load carrying elements but leads to distorted and variable length buckling and post-buckling deformation waves. In the present paper, uniaxial and biaxial post-buckling behaviors of the longitudinally graded plates are investigated. Neither post-buckling nor even buckling of the longitudinally graded plates have been studied so far. Moreover, effects of the elastic foundation that significantly alter the post-buckling deformations and strength of the plate, are studied. Due to occurrence of large deformations in the post-buckling region, the exact 3D elasticity theory is employed here instead of the approximate plate theories. Furthermore, the full form of Green's strain tensor is adopted. To establish a stress field that is continuous at the mutual nodes of the adjacent elements, a C1-continuous 3D Hermitian element is employed to discretize the plate. The nonlinear post-buckling equilibrium equations are solved by Crisfield-Ramm arc-length method in conjunction with the modified Newton-Raphson technique. Results show that heterogeneity of the material properties may lead to abrupt deflection decreases or even reversals and the elastic foundation leads to increases in both the buckling strength and number of the deformation waves.