Modeling, Solution And Interpretation Of Several Structural Topological Optimum Designs

With the extensive application of structural optimization technique, there has been an increasing demand for solving problems of a larger scale using this technique in more areas, which is now continuously challenging the theories and methods of optimum structure design. In this dissertation, intense research is carried out on the theory and engineering applications of the structural topology optimization, with focus on modeling and solution methods for several typical problems, and the interpretation of optimum results and the detailed design based on the interpretation for the characteristics of structural topology is discussed. The following problems of design optimization are studied:the structural topology optimization for maximizing structural stiffness with different boundary conditions, and the optimum topological design of elastically supported truss. The parallel structural topology optimization method based on super elements is developed and is tried out in the hierarchical structural optimum design. Using various optimization techniques, we propsed the optimum design of concentrated force diffusion structures. At last, the development of a structural optimization software SiPESC.TOPO and its application are discussed.The content and the main findings in this dissertation are introduced as follows.1. A general formulation of structural topology optimization for maximizing structure stiffness. The mathematical expression of this formula is simple and has the obvious physical significance, the sensitivity of the objective function is the same as that of classical structural compliance, and the formulation is suitable for all the three types of boundary value problems in elastic mechanics. By optimality criterion, we analyzed the black/white optimum topological design and found the uniform strain energy density is not equal to the uniform Mises stress because of the volume-change strain energy. The numerical example shows that the distribution of strain energy density in a stiffest structure is uniform except the position subjected to forces or displacements, but the Mises stress is not uniform.2. Optimum topological design of elastically supported truss. Based on the theory of Michell truss, we introduced the compatibility conditions, which are expressed via real displacements at the elastic supports, into the three-force problem. Then some analytic solutions of elastically supported Michell truss are obtained, which are verified by Sokol’s numerical program. Some typical examples are studied to reveal the impacts on the optimum truss topology from the support stiffness, the support position and the value of external forces. Besides, optimality criteria and numerical examples for the minimum compliance design of elastically supported truss are discussed, through which it is found that the optimum solution is an equal stress design and the stress depends on the specified material volume. For a proper material volume, which can be acquired by the bisection method, we will obtain a fully stress design. Based on these findings, a numerical method for solving the Michell truss under elastic supports is presented, and it may be used to forecast the solution to Michell’problem in other more complex situations.3. Parallel structural topology optimization method based on super elements and the hierarchical structural topological optimum design. For the optimum topological design of multiple components in a complex structure, a parallel structural topology optimization method based on super elements is developed. First of all, the components to be optimized must be seperated from the global structure and considered as substructures and super elements. After that, we analyzed the global structure to obtain the boundary conditions of these components, and then parallely solved the topology optimization problems of substructures. Further more, this method is trid out in the hierarchical structural optimum design. We discussed the optimization model for maximizing stiffness of a two-level structure, carried out optimization from the global structure (the first level) to components (the second level), and implemented a parallel solution. The numerical example verifeid the effectiveness of the two-level optimization method.4. Optimum structure design of concentrated force diffusion. Considering various engineering requirements of concentrated force diffusion structures, we developed an approach for concentrated force diffusion structures from a conceptual design to a detailed design, which was obtained by integrating structural topology, shape and size optimization techniques. In each stage of the optimization design process, a proper optimization model needs to be established based on the specific objectives and constraints. Result interpretation from topology optimization defines an initial design model for the following shape and size optimization, and also determines the type of the optimum design. Using this approach, the optimum designs of concentrated force diffusion for a plane structure and "radial ribs" in the short shell of a storage trunk are obtained. This task has an obvious engineering significance, the optimum designs have been used as a reference design by some design institutes, Moreover, the novel design process, in which the optimum design could be acquired from conceptual design, result interpretation and then to detailed design, can be applied in the design of some other engineering structures.5. Development of SiPESC.TOPO and its application. As a structural topology optimization system, SiPESC.TOPO inherits the superiority of SiPESC, it has good openness and extensibility and supports multiple operating systems. Based on design and dynamic management of plugins, it integrates modeling, solution, optimization, visualization of structures, etc. SiPESC.TOPO implements the key steps in structural topology optimization with creating extensions in plugin. Taking the design of the stiffest structure as an example, the detailed development of SiPESC.TOPO is introduced. Compared with other general commercial software, SiPESC.TOPO is verified by numerical examples to be superior for structural topology optimization and is particularly suitable for research on theory and algorithm.