A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors

Abstract

A three-node triangular finite element based on cubic zig-zag plate theory is developed to refine the predictions of the mechanical, thermal, and electric behaviors fully coupled. Both the displacement and temperature fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. Linear zig-zag form is adopted in the electric field. The layer-dependent degrees of freedom of displacement and temperature fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses and transverse heat flux. This non-conforming element passes the bending patch tests in arbitrary mesh configurations. Non-conforming C1 shape functions for the variables of out-of-plane displacement field are introduced. Nodal variables are displacements, temperature, and elastic potentials. Through the numerical examples of coupled and uncoupled analysis, the accuracy and efficiency of the present finite element are demonstrated. For the improvement of accuracy of interlaminar stresses, post-processing approach of integration of equilibrium equation is used. For the computation of higher order derivatives in the 3-D stress equilibrium equations, differential quadrature method is employed. The present finite element is suitable in the predictions of fully coupled behaviors of thick smart composite plate under mechanical, thermal, and electric loadings.