COMMUTATIVE ALGEBRA IN STRUCTURAL ANALYSIS OF DEPLOYABLE TENSION-STRUT STRUCTURES

摘要

Non-linear finite element procedure requires many load steps so that a non-linear structural system reaches the equilibrium state at a pre-defined load level. This is due to the fact that conventional finite element procedure is formulated basing on linear algebra. In this paper, a new finite element procedure is proposed in which one load step is required for the nonlinear structural system to reach the desired equilibrium state. The key idea is to use polynomials for approximation of any description of structural system and thus the final equilibrium equations, which are formed by polynomials only, can be solved by modern commutative algebra. In this manner, computational efficiency can be achieved in practical engineering design where only the final state of structural equilibrium is required. An illustration on the proposed structural analysis methodology for deployable tension-strut structures is provided using the improved finite element technique. Verification study is performed by comparing the results of structural analysis using the conventional finite element procedure and the proposed finite element procedure. The results are similar between the two methods while the control of the load step size is not needed in the proposed finite element procedure, based on the commutative algebra concept.