A state space approach for the analysis of doubly curved functionally graded elastic and piezoelectric shells

Based on the three-dimensional (3D) piezoelectricity, we present the exact solutions of simply-supported, doubly curved functionally graded (FG) elastic and piezoelectric shells using a state space approach. A set of the dimensionless coordinates and field variables is introduced in the present formulation to prevent from the ill-conditioned problem in the relevant computation. By means of direct elimination, we reduce the twenty-two basic differential equations to a set of eight state variable equations (or state equations) with variable coefficients of the thickness coordinate. By means of the successive approximation method, we artificially divide the shell into a NL-layered shell and the thickness of each layer is small. That leads to a reasonable manipulation to reduce the state equations of a thickness-varying system for each individual layer to those of a thickness-invariant system. Imposition of the boundary conditions on the lateral surfaces of the shell, the state variables through the thickness coordinate can then be determined using the method of propagator matrix. The direct and converse effects on the static behavior of doubly curved, multilayered and FG piezoelectric shells are studied. The accuracy and the rate of convergence of the present state space approach are evaluated.