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A simple and efficient method of analyzing mechanical behaviors of multi-layered orthotropic plates in rectangular shape

We apply the Rayleigh-Ritz method to analyze multi-layered plates with residual stresses for membrane and bending deformation. The method is very simple, straightforward, and easily programmable, but it should be applied to structures only with simple shapes. We derive coupled variational equations using the principle of virtual displacement, and investigate what kind of basis functions are desirable for the analysis of rectangular plates with various boundary conditions. We demonstrate the effectiveness and usefulness of the present method through several examples. The analysis results obtained with the present method are in good agreement with those available in the literature. A multi-layered microelectromechanical plate example shows that the coupling effect between membrane and bending deformation should not be ignored and that residual stresses do significantly influence the stiffness of the structure.