Geometric and material nonlinear bending analysis of three dimensional functionally graded porous panels

The current study aims the comprehensive comparative analysis of linear, geometric and coupled geometric–material nonlinear bending responses of three-dimensional (3D) functionally graded (FG) panels, including uniform and non-uniform porosity distribution. In contrast to conventional FG models, the current work employs continuous material gradations in all three spatial directions simultaneously. The modified rule-of -mixture is utilised to evaluate the elastic properties of the FG-panel. At the same time, the plastic behaviour of the FG-panel is defined using the von Mises yield criterion, bilinear isotropic strain hardening, and the Prandtl-Reuss constitutive equations in combination with the Tamura-Tomota-Ozawa (TTO) model. The von Karman nonlinear strain-based kinematics and the incremental theory of plasticity are employed to capture geometric and material nonlinearity. The fundamental equation is obtained by using the principle of minimum potential energy and is further solved by the Newton-Raphson iterative technique. The accuracy and robustness of the existing model are validated against established benchmark solutions. Lastly, a detailed parametric study is performed to examine the effect of material gradient index, porosity index, aspect ratio and support condition on the nonlinear bending responses of the three-dimensional FG-panel. In addition, the development of von Mises stresses and plastic zones on the 3D FG-panels is also studied and discussed.