Static Analysis of Temperature-Dependent FGM Spherical Shells Under Thermo-Mechanical Loads

Static analysis is conducted for functionally graded material (FGM) spherical shells under thermo-mechanical loads, based on the three-dimensional thermo-elasticity theory. The material properties, which vary with both the radial coordinate and temperature, introduce nonlinearity to the problem. To address this, a layer model is proposed, wherein the shell is discretized into numerous concentric spherical layers, each possessing uniform material properties. Within this framework, the nonlinear heat conduction equations are first solved iteratively. The resulting temperature field is then applied to the thermo-elastic equations, which are subsequently solved using a combined state space and transfer matrix method to obtain displacement and stress solutions. Comparison with existing literature results demonstrates good agreement. Finally, a parametric study is presented to investigate the effects of material temperature dependence and gradient index on the thermo-mechanical behaviors of the FGM spherical shells.