Methods And Software Development Of Static Topological Optimization Of Continuum Structures

Topology optimization that is one of the major subjects of optimization research up to date, usually needs to determine many more parameters than size optimization and shape optimization. However, it can be obtained more benifit so that it is more attractive for design engineer. It is well known that topology optimization of continuum structure is one of the major challenges because of difficulty to establish a good geometric model which comprising a large number of design variables, and complexity of optimization algorithm. In order to gain a reasonable structure, in the present dissertation, the ICM (Independent Continuous Mapping) method proposed by professor Y. K. Sui is used to investigate topology optimization of static structures. An optimal model with the object function of weight, stress constraints and displacement constraints is constructed. Two approximated explicit formulations of stress constraints and displacement constraints with respect to design variables are presented. Furthermore, this novel model can readily not only deal with topology optimization of continuum structures under the consideration of multiple load cases, but can be extended to three-dimensional continuum body. The corresponding numerical procedures are also developed, using the MSC.Patran & Nastran software platform. The main contents of this dissertation can be summarized as follows: 1. Establishment of Optimization Model (1) A suitable set of Filter functions of element with respect to weight, allowable stress and stiffness is introduced by means of ICM method. The discrete topology variables usually to be 0 or 1, are transformed into continuous topology ones varied from 0 to 1. Thus, the optimal model can be established using the concept of continuous variables. (2) A globalization method of stress constraints is proposed by virtue of the von Mises'yield criterion in machanics of materials. Thus, transformation of the local stress constraints of element into the global stain energy constraints of structure is obtained. The optimal model of continuum strucure subjected to strain energy of structure is constructed, under the consideration of multiple load cases. (3) An explicit formulation of displacement that is of global with related to topological variables is presented by using of unit virtual load method. Then the optimal model which refers to weight as objective and subjected to displacement constraints is suggested. In addition, the best path transmitted force in the multiple load cases is selected successfully. (4) The optimal model that normalizes with two types of dimensionless constraints, is further derived, for continuum structure with stress constraints and displacement constraints. 2. Solution of Optimization Model (1) The dual model corresponding to the optimal model of continuum structure is...