Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

This work for the first time presents a simple, accurate and straightforward finite element formulation that requires a C-0 continuity of transverse displacement for the transient stress analysis of curved beams under thermal shock using a new layerwise theory. The FGM sandwich curved beam is considered to be made of three layers in which the top, middle and the bottom layer is considered to be made of pure ceramic, functionally graded material (FGM) core and pure metal constituents, respectively. The proposed new layerwise theory assumes a higher-order displacement field for FGM core and first-order displacement field for both top and bottom layers. The material properties are assumed to be temperature-dependent. The governing differential equation for the present investigation is formulated using Hamilton's principle. A wide range of comparison studies are presented to establish the accuracy of the present layerwise finite element formulation. A parametric study is conducted to show the simplicity and wider applicability of the proposed formulation. It is shown here that by selecting an appropriate value of volume fraction index, core to facesheet thickness ratio, magnitude of thermal shock, curvature and thickness ratio, the transient thermal stresses induced in FGM sandwich curved beams can be reduced substantially.