Transfer Matrix Analysis for Curved Beam Structure

Abstract

The curved beam structure such as pipe system has been widely used in industrial plants or power stations. In this study, the reduction technique of stiffness matrix, which is refered to “transfer matrix method (TM)“, is developed to solve effectively the problem. For achieving the purpose, the transfer matrix Fk to transfer deformation, rotation, force and moment from node i to node i+1, which are named for both edges in k-th beam element, is formulated. The global transfer matrix is then constructed by multiplying as R(θk+1,k)·Fk···R(θ2,1)·F1···R(θk+1,k) is the coordinate rotation matrix. The efficiency and simplicity of this method is demonstrated by solving the problem of a curved pipe line with elbow which is subjected to external forces and displacements. The results are compared with those obtained by FEM.