Research On Multidisciplinary Topology Optimization Methods

A detailed review is firstly given of the history, the solving systems and the optimization scheme of the topology optimization in this dissertation. After discussing the influences of the corresponding parameters of SIMP method, the structural analysis methods and the programming method is summarized. On the base of this, a few shortcomings those restrict the fast development of topology optimization in engineering design is point out. To overcome these shortcomings, this dissertation discusses the multiphysics and multidisciplinary topology optimization, by which the topology optimization can be expanded to more implementations. The main work of this dissertation can be summarized as follows.(1) This dissertation presents some useful methods for solving various ordinary manufacturing constraints in the continuum topology optimization. Although some commercial software, such as OptiStruct, TOSCA etc., let the users consider some kinds of manufacturing constraints when solving topology optimizations, they can only solve a small number of structural problems just like minimizing compliance, maximizing strength and maximizing eigen-frequencies. Furthermore, the literatures on how to implement the manufacturing constraints are relative few. These limitations prevent the topology optimization to wide engineering using. This paper presents the implementation algorithms of the ordinary engineering constraints including minimal member length, symmetry, repeating features, extrusion and casting constraints. These algorithms presented not only suit for the classical structural topology optimizations, but also suit for the multiphysics topology optimizations.(2) Chamfering and rounding are the most common features of structures and mechanisms. Introducing these features is another way to make material usage more efficient by lowering or avoiding stress concentrations and making the structure even stronger. In this dissertation, a new crossing sensitivity filter is proposed for structural topology optimization with chamfering and rounding. This method also ensures the final optimal solution without checkerboard patterns or mesh-dependency. It can also partially prevent one-node hinges. Numerical examples that include both design of stiffest/strongest structures and synthesis of compliant mechanisms are provided.(3) This dissertation presents a unified modeling and solving approach for multiphysics topology optimization. A multiphysics continuum field is usually controlled by certain partial differential equations (PDE). Based on the general form of the PDE, this paper presents the mathematical model of the multi-objective multiphysics topology optimization, derives the unified solving scheme of the PDE, gets the sensitivities of the objectives and constraints, and discusses the relative mathematical programming routines. The model and methods extend the classical structural topology optimization to solving a general multiphysics topology optimization problem. After the theoretical deriving, several 2D/3D coupled multiphysics topology optimization examples are solved, and the optimal results are presented.(4)This dissertation presents an approach for solving the multidisciplinary topology optimization. To simplifying the description, a three-dimensional (3D) "heat transfer-thermal stress" coupling topology design problem is used as an instance to interpret the solving scheme. Unlike the common multiphysics topology optimization problem which usually modeled in a 3D domain or a 2D domain alternatively, the topology optimization problem mentioned in this paper has a 3D design domain (the design variable is referred asρ1) and two 2D design domains (the design variable is referred asρ2 andρ3) together in one mathematical model. Although all the model and solving method are based on a certain design instance, the solving scheme presented in this paper can be used as an efficient method for solving the boundary coupling multidisciplinary topology optimizations.(5) A prototype software system for solving the topology optimization problems of various fields including structural, heat, other alternative physics and even coupled multiphysics is developed. This prototype software system is developed by MATLAB. Although several up-to-date commercial packages have been launched for solving topology optimization, all of them are limited to solving structural problems with specific constraints and objects, such as volume, compliance, stress, eigenfrequencies and some kinds of manufacturing constraints. This prototype system pays much attention to extend these functionalities to solve the multiphysics and multidisciplinary problems. Both 2D and 3D numerical examples solved by this new prototype software are presented with engineering constraint are presented.The postprocess method of the topology optimization is also simply discussed. By the research of this dissertation, the structrual topology optimzaiton is extended to multiphysics and multidisciplinary domain in a general way. This is very helpful for the real industry design experiences.