Study Of Heuristic Methods For Structural Topology Optimization

With the development of science and technology, structures required in engineering area are supposed to have high performance. Design of optimum structures satisfying constraints is always being sought by engineers. Structural topology optimization is an excellent design method which obtains innovative structures with optimum layouts. Therefore this method is used extensively in engineering area.Heuristic optimization and its applications are profound research topics in structural optimization area, and they derived their principle theories from very simple ideas by observing the nature itself. For example, Genetic Algorithm (GA) works on the principle of"survival of the fittest"in natural evolution. And the source of Simulated Annealing (SA) Algorithm can be tracked down to annealing procedure in manufacture. These methods lack their mathematical basis since it is difficult to study heuristic approaches analytically. However, they are less dependent on mathematical properties (e.g. continuity, differentiability, linearity & nonlinearity) of the objective function in optimization. So they are suitable for complicated problems which introduce great difficulties to other methods. With the great effort made by many scholars, great development has been achieved in this area, and heuristic optimization methods were widely utilized in industry.This paper studies heuristic methods for structural topology optimization problems. The scope of this research concerns truss structures and continuous structures, certainty optimization and probability optimization, structural static problems and structural dynamic problems, and an engineering-related approach. The study was supported by a grant from Science Foundation of China (10772112), the Key Scientific Project of Shanghai Municipal Education Commission (09ZZ17), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032), and the Research Project of State Key Laboratory of Ocean Engineering of China (GKZD010807). Some achievements are as follows:(1) Ongoing researches on structural topology optimization are comprehensively reviewed. And several key issues such as modeling, solving and numerical singularities are given in details.(2) The principle of GA is studied. Penalty functions are used to convert constrained optimization into unconstrained optimization. With the implementation of GA, optimum topologies of truss structures subject to static or dynamic constraints are obtained.(3) Heuristic self-growth evolutionary algorithm is designed for both truss structures and continuous structures subject to stress constraints. The optimization starts with a simple design domain with a few element meshes. Structures grow and evolve using element adding and eliminating techniques in which elements are added around overstressed regions of structures and are eliminated if understressed.(4) Based on the ground structure method, a speed evolutionary algorithm and its improved algorithm is designed to obtain optimum topologies of continuous structures subject to static loads. By comparing element performance indexes between two adjacent iterations and implementing a perturbation technique, values of optimization variables for the next iteration are calculated.(5) An interface for ANSYS is developed for the purpose of modeling and analyzing complicated structures for optimum design. Auto-generated arrays are used to transfer data between ANSYS and MATLAB. Large scale 3-D structures are optimized to indicate the efficiency and feasibility of the method. Besides, smoothing technique is studied to obtain topologies with smooth boundaries. Structural topology optimization is the most challenging topic in the field of structural optimization, and many aspects need further study and more efforts. At conclusion, a summary of work done in this dissertation is given and some problems of interest are also brought forward for future research.