Analysis And Application Of Topology Optimization Model Of Continuum Structure

Topology optimization can provide much more benefits than traditional size and shape optimization, since it can achieve the structural configuration, size and shape design at the same time. This makes it become the most important structural design method in aerospace and other high-tech fields. How to establish reasonable optimization formulations and mathematical models for different design requirements has already become an important subject in the structural optimization research field.Based on the critical review on theory, method and application of structural topology optimization, this dissertation focused on topology optimization models. The optimization formulation and corresponding solution methods in which the geometric average displacement\temperature are considered as objective functions respectively are put forward to solve the problems in the maximum stiffness design and optimum heat dissipation design. Structural topology design with different tensile and compressive properties is proposed in this dissertation, and concurrent optimum design method of layouts of component and connection between components in the structure is also well presented for grid structure design. The main achievement and works of the dissertation are as following:(1) The discussion on topology optimization models. Designs of structures with maximum stiffness based on the compliance have attracted much attention and many achievements have been made. However, in practical engineering the maximum displacement is the most commonly used index in measuring structural stiffness. The difference between minimal compliance design and minimal maximum displacement is pointed out through a cantilever beam section design example in this dissertation. As a good approximation of the maximum displacement, the geometric average displacement in the design region is considered as the objective function in the new static topology optimization model in order to achieve minimal maximum displacement design. The proposed model is compared with the conventional compliance design model. The differences between these two models and their scope of application are well discussed through theory and numerical analysis. Similarly, the geometric average temperature, which is used as a good approximation of the maximum temperature, is considered as the objective function in the new heat conduction topology optimization model in order to achieve minimal maximum temperature design. The comparison on the proposed model, the conventional dissipation of heat transport potential capacity design model and the nodal temperature variance based optimization model is also carried out. By comparing the maximum temperature, the maximum temperature gradient, and the nodal temperature in the design results, the differences among these three models as well as their scope of application are discussed through theory and numerical analysis.(2) Topology optimization of continuum structures with different tensile and compressive properties. The materials of dual extension/compression modulus such as concrete and fiber reinforced composite are often encountered in the engineering problems. These materials are widely used in the construction industry, machinofacture, aircraft manufacturing, and other industries. However, conventional topology optimization with linear material can not fulfill these design requirements any longer. Consequently, the theory and method of topology optimization of continuum structures with different tensile and compressive properties have been studied thoroughly in this dissertation. In order to solve elasticity problems with dual extension/compression modulus, a technique that employ modified Heaviside function is presented to describe the nonlinear relationship of stress and material modulus smoothing the constitutive discontinuity. By utilizing Newton-Raphson algorithm, the iterative finite element numerical analysis method is proposed. Meanwhile a topology optimization model of continuum structures with different tensile and compressive properties is constructed to achieve structural layout design. Furthermore, based on this method a multimaterial model is proposed to formulate the topology optimization problem for structural topology design with multiphase materials. Two types of materials are distributed within the design domain to accommodate design need. Then, this dissertation discusses the influence of some relative design parameters in optimum design in depth.(3) Concurrent optimum design of layouts of component and connection between components in the structure. The last part of this dissertation focuses on concurrent design of layouts of components and connection between components of structure. The conventional structural topology optimization is the layouts design of structure with fixed external loads. It is obvious for the complex construction that components joined together by connection transfer the external force, thus linkage model of components of structure affect load distribution greatly. In other words, connection distribution has great effect on optimal topology of components. The connection conditions are included in the topology optimization by introducing a new set of material model that represents connective domain through material distribution. Considering the relative material density of loading-carrying domain and connective domain as design variable, a topology optimization based approach and the corresponding solving technique has been developed to simultaneously designing structure and connection distribution. This work is supported by National Basic Research Program (973 Program) of China (No.2006CB601205), National Natural Science Foundation of China (No.90605002, 10721062,90816025), and the Research Fund for the Doctoral Program of Higher Education of China (No.20090041110023). The financial supports are gratefully acknowledged.