To Reverse The Problem Solving And Torsion Bar Cross-section Topology Optimization

Aiming at the topology optimization of cross-section of torsion bar, this paper presents a FE method for solving the torsional problem of a bar with arbitrary cross-section, which is taken as an analysis tool during the optimization, carries out the optimization of cross-section and in view of the badly distortional deformation in thin-walled bar, discusses the multi-objective optimization which considers the torsional rigidity as well as distortional rigidity.To do the optimization, an essential precondition is that the torsional problem can be solved accurately and efficiently. So at first, according to the stress function theory, a general finite element method has been developed for the analysis of torsion bars with arbitrary shape subject to torsional loading by proposing the new idea of "turn multiply to simply". And based on the comparability between the controlling equations of the steady thermal conduct problem and of the torsional problem, a band new approach is developed which solves the torsional problem by analyzing the corresponding thermal conduct problem with the existed finite element analysis software. Numerical results show that the proposed method has the advantage of simplicity and generality in stress analyzing and torsional rigidity computing. It is an efficient method suitable to deal with torsion bars with arbitrary cross-sections. Secondly, this paper does the optimizations of the cross-sections of the torsion bars. Using the so-called Solid Isotropic Material with Penalization (SIMP) method to evaluate the macroscopic property of the material, the bar-section topology optimization model to maximize the torsional rigidity is formulated. Choosing the Optimality Criterion (OC) algorithm and updating method of variables based on the sensitivities, the optimization, which uses the above-mentioned FE method to solve the torsional problem, is given and good results are obtained. At last, as the distortional deformation of the thin-walled bars which are widely used in Aeronautic & Astronautics is so serious, this paper processes the multi-objective optimization which considers the torsional rigidity as well as distortional rigidity, in which the distortional rigidity is measured by means of the eigenvalue of a plane-strain problem.Torsion bar-sections with distortional deformation suppressing stiffeners are obtained and some examples are given to validate the feasibility, reliability and high efficiency of this method.