Nonlocal nonlinear finite element analysis of composite plates using TSDT

Abstract

In this work, nonlocal nonlinear finite element analysis of laminated composite plates using Reddy’s third-order shear deformation theory (TSDT) (Reddy, 1984) and Eringen’s nonlocality Eringen and (Edelen, 1972) is presented. The governing equations of third order shear deformation theory with the von Kármán strains are derived employing the Eringen’s (Eringen and Edelen, 1972) stress-gradient constitutive model. The principle of virtual displacement is used to derive the weak forms, and the displacement finite element models are developed using the weak forms. Four-noded rectangular conforming element with 8 degrees of freedom per node has been used. The coefficients of stiffness matrix and tangent stiffness matrix are presented along with nonlocal force vector. The developed finite element model can be employed to capture the small scale deviations from local continuum models caused by material inhomogeneity and the inter atomic and inter molecular forces. Numerical examples are presented to illustrate the effects of nonlocality, anisotropy, and the von Kármán type nonlinearity on the bending behaviour of laminated composite plates.