Stress Analysis of an undulated plate by the Combined First Order Perturbation and Alternating Method

Abstract

A new solution method is proposed for the analysis of an undulated plate of finite thickness subjected to in-plane loading conditions. The method treats the boundary conditions on the undulated surfaces by using a first order perturbation method, where the deviation of the undulating surface front a reference plane surface is treated as the small perturbation parameter of the problem. In order to satisfy the boundary conditions on the top and bottom surfaces, solutions of a semi infinite body are alternately applied, where the solution procedure utilizes relatively simple analytical expressions without tedious numerical calculations such as arising in the finite element analyses. It should be noted that an arbitrarily undulated surface of a plate may be approximated by the superpostion of two dimensional sinusoidal waves having arbitrary wave lengths, directions and phases. This means that only certain two-dimensional solutions are necessary to construct a fully three-dimensional solution. The solution accuracy of the proposed method is examined by comparing the present results with finite element solutions, and illustrative examples are also given for the stress analysis of a plate with slightly wavy surfaces in three dimension.