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Elastic-Plastic Analysis of Pipe Structure by Transfer Matrix Method


 Pipe systems have been widely used in industrial plants such as power stations. In these systems, it is often required to predict the displacement and stress distribution. Analytical and numerical methods such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM) are typically adopted to predict the displacement and stress distribution. The analytical methods are solved based on the Timoshenko beam theory, but the problem that can be solved is limited to simple geometry under simple boundary conditions. Both FEM and BEM can be applied to more complicated problems, although this usually involves a large number of degrees of freedom in a stiffness matrix. The structure is modeled by a beam element in FSM. However, the stiffness matrix still becomes large, as does the matrix size constructed in FEM and BEM. In this study, the transfer matrix method (TMM) is studied to effectively solve complicated problems such as a pipe structure under a small size of the stiffness matrix. The fundamental formula is extended to apply to an elastic-plastic problem. The efficiency and simplicity of this method is demonstrated to solve a space-curved pipe system that involves elbows. The results are compared with those obtained by FEM to verify this method.