Effect of Elastic Foundations on Stochastic Thermally Induced Post Buckling Response of Functionally Graded Materials Plates with Uncertain Material Properties

The abrupt change in material properties across the interface between different materials can result in large inter-laminar stresses leading to delimitation, cracking, and other damage mechanisms which result from the abrupt change of the mechanical properties at the interface between the layers. Initially the uncertainty in material properties at micro level is finally reflected as macro level. Existing uncertain variations in material parameters may have significantly affects on fundamental structural characteristic and consequently these must affect the final design. Therefore, for accurate prediction of system behavior required for sensitive application favours a probabilistic/stochastic approach. The stochastic approach is a mathematical tool capable of handing uncertainties in the material properties to compute the statistic of structural response for example, post buckling response. FGMs are composite and microscopically heterogeneous in which the mechanical properties vary smoothly and continuously from one surface to the other [1]. This is achieved by gradually varying the volume fraction of the constituent materials. Typically, these materials are made from a mixture of ceramics and metal or a combination of different materials. The ceramic constituent of the material provides the high-temperature resistance due to its low thermal conductivity and protects the metal from oxidation. The structures subjected to thermal loading with spatial gradients in composition and microstructure is of considerable interest in numerous technological areas such as tribiology, optoelectronics, biomechanics, nanotechnology and high temperature technology. The graded transition in composition across an interface of two materials (metal and ceramics) can essentially reduce the thermal stresses and stress concentration at intersection with free surfaces. Due to the boundary constraints, compressive stresses acting on edges of the component arise due to thermal loading are induced, which may cause buckling, especially in thin walled structures. Buckling and post-buckling characteristics are one of the major design criteria for plates/panels for their optimal usage. Hence, it is important, to study the buckling and post-buckling characteristics of FGM plates under thermal loading for accurate, efficient and reliable design.