科研之友
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摘要
Stress concentration is a familiar problem in structural analyses. By using ordinary method to solve the stress concentration problem of rectangular hole, only the approximate solutions can be found. The U-transformation method is an analytical method which can be used to analyze the structures with cyclic periodicity. This paper applies the U-transformation method to study the stress concentration problem in the plates with a square hole under shearing loads. At first, the governing equation with cyclic periodicity must be established. In order to bring periodicity to the potential energy equation, the interior disfigurement made by the rectangular hole may be replaced by an additional loading. By using the U-transformation technique and the finite element method, the potential energy equation can be uncoupled, and the analytical displacement solutions of the finite element equations are derived in series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as examples to demonstrate the application of the proposed method, and the stress concentration factor is obtained.
