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In this article, a methodological approach for the three-dimensional (3D) static behavior of functionally graded (FG) thermo-electro-elastic doubly curved shells subjected to a thermal and electrical load is presented. A coupling procedure based on the state space, a multilayered Runge-Kutta and transfer matrix methods is elaborated for numerical solution of the 3D thermo-electro-elastic governing equations. In the thickness direction, recursive relationships using a propagator matrix are elaborated allowing to handle arbitrary functionally graded effects. A global transfer matrix is formulated permitting to investigate the effects of various types of bottom and top surface temperature loads and heat flux. Some benchmark tests are presented to validate the presented approach and to analyze the influence of the material-property gradient index, the curvature radius ratio, the span-to-thickness ratio, the temperature, normal heat flux, and the electric voltage on the mechanic, electric, and thermal variables of doubly curved shells.

Three-dimensional semi-analytical solutions of arbitrary functionally graded piezoelectric doubly curved shell panel under thermo-electric load