Enhanced lower-order shear deformation theory for fully coupled electro-thermo-mechanical smart laminated plates

Lower-order shear deformation theories are adequate to predict the global behavior of a smart plate. They cannot, however, predict accurate deformation and stress distributions through the thickness of laminated smart plates. Thus higher-order zigzag theories have been proposed to accurately calculate them. In most cases, a simplified higher-order zigzag theory requires C-1 shape functions in finite-element implementation that are not so common for plate and shell analysis in commercial FE software. This presents the practical limitation of simplified zigzag theories to the commercial FE package. In fact, an iso-parametric C-0 plate model is standard for the analysis and design of composite laminated plates and shells. In this paper, an enhanced lower-order shear deformation theory (ELSDT) is developed to provide a simple yet accurate tool for the analysis of smart structures under combined loads (including thermal and electrical loads as well as mechanical loads). It is systematically derived by minimizing the least-square errors between the first-order theory and the higher-order theory. This makes it possible to transform the strain energy of a higher-order zigzag theory to that of a lower-order zigzag theory. The resulting lower-order theory, which is referred to as the ELSDT, requires the C-0 shape function only, and it is applicable to fully coupled mechanical, electric, and thermal problems. First a higher-order zigzag theory is established, which includes both a linear zigzag function and a cubic polynomial for in-plane displacements, a quadratic polynomial in the out-of-plane displacement, and a layerwise function for the electric potential. The ELSDT is then constructed via the aforementioned procedure. The accuracy and robustness of the present theory are demonstrated through numerical examples.