Nonlinear bending analysis of arbitrary-shaped porous nanocomposite plates using a novel numerical approach

Abstract

In this paper, an efficient numerical strategy is used to study the geometrically nonlinear static bending of functionally graded graphene platelet-reinforced composite (FG-GPLRC) porous plates with arbitrary shape. Porous nanocomposite plates including cutout with various shapes can be modeled by the present approach. Four types of porous distribution scheme and four GPL dispersion patterns are selected, and the material properties are calculated based on the closed-cell Gaussian random field scheme, the Halpin–Tsai micromechanical model together with the rule of mixture. First, the variational statement of governing equations based on the virtual work principle and higher-order shear deformation theory (HSDT) is derived and presented in vector–matrix form for computational aims. Then, using the ideas of variational differential quadrature and finite element methods (VDQ and FEM), a numerical approach called as VDQ-FEM is used to address the considered problem. In VDQ-FEM, the domain of problem is first transformed into a number of finite elements. In the next step, the VDQ discretization technique is implemented within each element. Then, the assemblage procedure is performed to obtain the set of Studying effects of porosity and GPL distributions and porosity coefficient matricized governing equations which is finally solved by means of the pseudo arc-length continuation algorithm. One of the main novelties of the present work in implementing VDQ-FEM is proposing an efficient way based on mixed-formulation to guarantee the continuity condition of first-order derivatives in entire domain for the used HSDT model. A detailed parametric study is conducted to investigate the nonlinear bending of FG-GPLRC porous plates with different shapes. In the numerical results, the effects of porosity coefficient, porosity distribution pattern, GPL distribution pattern and boundary conditions on the nonlinear bending response of plates are analyzed.