Discrete Optimum Design Of Truss Structure Undergoing Large Geometric Deformation

In this paper, employing the ANSYS Software Platform, a new method is presented to solve the minimum weight design problems of truss structures with discrete variables according to the direction-difference-quotient method. The ANSYS secondary development program is made. Several numerical examples are given, and the results obtained show that the method has higher accuracy, and converges fast and identically for various initial designs, which proves that it is feasible and efficient to do discrete optimization based on ANSYS Software Platform for truss structure.In addition, an efficient algorithm based on ANSYS Software Platform's secondary development function is presented for nonlinear structure analysis of the large span truss structure undergoing large deflection. In the projects, some large-span structure, due to its structure forms and the special characteristics of the work load, have a relatively larger geometric deformation, but the absolute quantity is still little. To ensure a normal performance of structure, linear relationship between stress and strain is requested. For analysis of such structures, geometric nonlinear theory of large deformation must be applied. The minimum potential energy principle is employed for the calculation of such problems in the traditional way. The approximate expression of nonlinear geometric equations of the large deformation and linear expression of stress and strain are put in the total potential energy functional, and then the expression with each nodal displacement is got after the discrete treatment, finally according to the condition that the potential energy should be minimal, we can have the Euler equations of nodal displacements which is the nonlinear balance equations of node displacement. The equation is of the nodal displacements after deformation, so it is unified and coordinated with the deformation state. Because the balance equation is nonlinear function of displacement, it is very difficult to solve, especially for complex structures of multi-degree. In this paper, an efficient numerical method based on ANSYS Software Platform's Secondary Development ability is presented to do the structure analysis on the geometric large deformation of the large span truss structure. The main idea of this paper is establishing the equilibrium equations after the deformation and getting their solutions, by using Two-step alternative Iteration and successive approximation to make sure that the equilibrium state is coordinated with the deformation state. In other words, firstly the node displacement continuous equations are established and solved by the known internal force; and then the equilibrium equations to get the internal force are established and solved by using the known node displacements; through many Iterations the accurate solutions of the structure analysis on nonlinear large deformation are obtained in the condition that the equilibrium state and deformation state are coordinated with each other.The new idea of optimization design of the truss structure with the geometric large deformation is present, because it has obvious advantage, analyzing only the structure once in the total solving process. This method is especially useful for flat truss structure and large span truss structure. The ANSYS secondary development program is made. Several examples are calculated, and the results obtained show that this method has validity,more accurate solution, and converges fast. One more thing, it also useful for the optimization design of the truss structure with the geometric small deformation.