Elasto-plastic finite element based structural shape design optimization.

摘要

Design optimization of nonlinear structural systems is a relatively new area undergoing rapid development. The necessity for structures to survive under extreme conditions coupled with the savings in material and prototyping make nonlinear analysis not only attractive but a necessary requirement in order to compute the correct structural response. When compared to the design optimization of linear elastic systems, the computational effort for design optimization of nonlinear system is far more expensive and time consuming. Hence, to develop a robust, efficient and general integrated design program, each component of the design process must be carefully studied.; The objective of this dissertation is to develop a robust, general and efficient integrated computer program for shape optimization of nonlinear structural systems. To achieve these objectives in a reasonable manner, several strategies are adopted. First, the elasto-plastic nonlinear finite element analysis is based on the full or modified Newton-Raphson method. If the process begins to diverge, the initial stiffness method that is unconditionally convergent is used. Second, either incremental stress integration scheme or iterative stress integration scheme is employed. If the iterative stress integration scheme is chosen but the solution diverges, the incremental stress integration that is stable but slower is used instead. Third, the shape optimal design procedure is based on the hybrid natural approach. This approach is general, flexible in the sense that it, is problem independent, and provides for the use of analytical derivatives to be used with a nonlinear programming technique. The implicit differentiation method that has been successfully used in truss optimal design is modified for handling shape sensitivity analysis. Particularly, a method to compute the partial derivative of equivalent nodal force with respect to the design variables is proposed. These quantities are necessary in calculating the sensitivity of nonlinear response function. Numerical examples are solved to validate the developed methodology.