Transfer matrix method for elastic-plastic problem of space-curved beam structure

Abstract

Problems of space-curved beam structures have been extensively studied by many researchers. Stress analyses for the structural problems are conducted based on a finite element method, boundary element method, or frame structure method. In these methods, a stiffness equation, which is the connection between nodal displacement and force, is solved. The size of a stiffness matrix involved in the stiffness equation increases according to the number of nodes in the analysis model. In this study, the transfer matrix method (TMM) is considered as another analysis method to overcome such a difficulty. In principle, the TMM is based on calculating how the external force or displacement is transmitted to the structure using a state vector that involves both nodal displacement and force. With the use of the state vector, fewer fundamental equations are needed to obtain stress and displacement. However, application of the TMM has been limited to vibration problems. In this study, an incremental form for the TMM is formulated to apply the TMM to the elastic-plastic problem of space-curved beam structures, and the simple problem of a curved beam fixed at a ridged wall is solved to verify the TMM formulation.

Keywords

• beam structure
• transfer matrix method
• elastic-plastic problem