Abstract
Lower-order shear deformation theories are adequate to predict the global behavior of a smartplate. They cannot, however, predict accurate deformation and stress distributions through thethickness of laminated smart plates. Thus higher-order zigzag theories have been proposedto accurately calculate them. In most cases, a simplified higher-order zigzag theory requiresC1 shape functions in finite-element implementation that are not so common for plate andshell analysis in commercial FE software. This presents the practical limitation ofsimplified zigzag theories to the commercial FE package. In fact, an iso-parametricC0 plate model is standard for the analysis and design of composite laminated plates andshells. In this paper, an enhanced lower-order shear deformation theory (ELSDT) isdeveloped to provide a simple yet accurate tool for the analysis of smart structures undercombined loads (including thermal and electrical loads as well as mechanical loads). It issystematically derived by minimizing the least-square errors between the first-ordertheory and the higher-order theory. This makes it possible to transform the strainenergy of a higher-order zigzag theory to that of a lower-order zigzag theory. Theresulting lower-order theory, which is referred to as the ELSDT, requires theC0 shape function only, and it is applicable to fully coupled mechanical, electric, and thermalproblems. First a higher-order zigzag theory is established, which includes both a linearzigzag function and a cubic polynomial for in-plane displacements, a quadratic polynomialin the out-of-plane displacement, and a layerwise function for the electric potential. TheELSDT is then constructed via the aforementioned procedure. The accuracy androbustness of the present theory are demonstrated through numerical examples.
Published Version
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