Recent advances in the mathematical formulations for structural design optimization using thermoelasticity concepts play pivotal role in the development of science and technology especially aerospace engineering. As thermoelasticity is a branch of science that deals with the analysis of stresses caused by thermally induced strains which are in the elastic (recoverable) range, but the material interfaces also plays a pivotal role in the actual performance of a structure, often dictating lifetime and failure characteristics, tolerances and processing choices.The motivation of the present study is to highlight the influence of materials (i.e. homogeneous and non-homogeneous) during thermoelastic engineering problems involving structural compliances. To understand this book one must have knowledge of Residue Theory, Differential Equation, Analysis, Integral Transform and Thermoelasticity. The investigations in the present volume are based on the research work of Roychoudhury, Chenet, Tanigawa, Noda, Deshmukh, Erslan, Wankhede and Nowacki where they have studied the direct and inverse problems of thermoelasticity on homogeneous and functionally gradient materials.