Deformation Analysis of Binary Tree Structures by Transfer Matrix Method

Abstract

A complex structure composed of piping is modeled as a simple frame system with an arbitrary curved beam with branches. The transfer matrix method (TMM) is one of the methods used to analyze the displacement and stress fields in such modeled structure. The transfer matrix method (TMM) is highly popular because it reduces the stiffness matrix and facilitates high-speed calculation. However, the application of the TMM has been limited to structural vibration and static problems for a simple straight beam without branches. In this study, we generalized the theory of the TMM for application to binary tree structure, which is a branching structure without a closed paths and with at most three elements connected to branch points. Additionally, a problem based on a statically indeterminate beam with branch was analyzed to verify the generalized theory in this study.