Abstract
The application of approximate equations of a two-dimensional theory for the analysis of stress and displacement distributions of a thick elastic plate with fixed boundaries is presented. By using the method of power series expansion of displacement components, a set of fundamental equations of a two-dimensional higher-order plate theory is derived through the principle of virtual work. In order to assure the accuracy of the present theory, the governing equations of several sets of truncated approximate theories are solved numerically by the finite difference method. Higher-order finite difference operators with error terms of o( h 4) are applied in order to validate the numerical accuracy of results. The convergence properties of the present numerical solutions have been shown to be accurate for the expanded displacement components with respect not only to the number of finite difference mesh intervals but also to the order of approximate theories. Stress components are determined by satisfying the equilibrium equations of a three-dimensional elastic continuum and the stress boundary conditions on the upper and lower surfaces of a plate. A direct comparison is also made with the numerical results of the integral method obtained by using the solutions of a three-dimensional elastic continuum.
Published Version
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