Geometrically nonlinear analysis of functionally graded cellular panels with material stochasticity (PhD)

Abstract

Functionally graded material is one of the modern engineered microscopically inhomogeneous and high-performance materials wherein the constituent material properties vary smoothly and continuously from one surface to the other. These materials have the ability to maintain their structural integrity in hightemperature environments. Particularly, functionally graded cellular structures possess exciting combinations of physical and mechanical properties, which improves structural stiffness, low specific weight, and energy absorption capability, etc. Owing to the fascinating properties, these materials can be utilized in various fields ranging from biocompatible bone implants to spacecraft and other engineering applications. The sophisticated fabrication process of these materials often leads to randomness in the material properties, the inclusion of microstructural defects (porosity), and the influence of initial geometric imperfections become inevitable due to the difference in the solidification temperatures between the constituent materials. The inclusion of these parameters in the analysis can ensure the realistic responses of these structures. In the present work, an effort has been made to study the large amplitude flexural vibration analysis of the geometrically nonlinear functionally graded shell panels, graded cellular panels, and sandwich panels with the graded cellular core in a deterministic and stochastic environment. The nonlinear formulations have been developed by employing von K´arma´n nonlinearity assumptions based on higher-order shear deformation theory, including Lame’s parameter. An efficient C0 finite element methodology is employed in conjunction with a direct iterative method to solve the nonlinear governing equations. The influences of material uncertainties, microstructural defects, initial geometric imperfections, thermal environment, and geometric parameters with various boundary conditions have been incorporated in the formulations. The first-order perturbation technique has been employed to assess the dispersion in the material properties. A detailed convergence and comparison studies have been performed to describe the efficiency and efficacy of the present formulation, and highlight the