Xiaoming Wang

A level set method for structural topology optimization

This paper presents a new approach to structural topology optimization. We represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension. Such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure. Furthermore, a well-founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints. The result is a 3D topology optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation. We have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods. The benefit and the advantages of the proposed method are illustrated with several 2D examples that are widely used in the recent literature of topology optimization, especially in the homogenization based methods.

Design of Multimaterial Compliant Mechanisms Using Level-Set Methods

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthetics of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

A level-set based variational method for design and optimization of heterogeneous objects

Abstract A heterogeneous object is referred to as a solid object made of different constituent materials. The object is of a finite collection of regions of a set of prescribed material classes of continuously varying material properties. These properties have a discontinuous change across the interface of the material regions. In this paper, we propose a level-set based variational approach for the design of this class of heterogeneous objects. Central to the approach is a variational framework for a well-posed formulation of the design problem. In particular, we adapt the Mumford–Shah model which specifies that any point of the object belongs to either of two types: inside a material region of a well-defined gradient or on the boundary edges and surfaces of discontinuities. Furthermore, the set of discontinuities is represented implicitly, using a multi-phase level set model. This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations. Promising features of the proposed method include strong regularity in the problem formulation and inherent capabilities of geometric and material modeling, yielding a common framework for optimization of the heterogeneous objects that incorporates dimension, shape, topology, and material properties. The proposed method is illustrated with several 2D examples of optimal design of multi-material structures and materials.

A feature-based topological optimization for structure design

The feature-based modeling technology in computer aided design (CAD) has been widely studied, which greatly facilitates the manufacture of the design. We have incorporated the standard idea into topology optimization, and developed a feature-based structure topology optimization method. The method applies a real valued function to implicitly represent complex material interfaces of a design structure, and employs constructive solid geometry (CSG) to describe the design structure based on a set of simple geometric primitives during the topological optimization process. Meanwhile, the topological derivative analysis is adopted to determine where a simple geometric primitive is inserted in the current structure, and the morphing technology is used to determine which is chosen among the given geometric primitives by combining with the sensitivity analysis. In addition, Boolean operations on the geometric primitives are implemented by R-function method, which guarantees the regularity of the structure representation function, and which meets the need of the structure boundary smoothness for finite element analysis in the fixed Euler meshes. Finally, in order to further simplify the design structure, the shape matching technique is applied to merge the given geometric primitives so that each connected perforation is only constructed by one based geometric primitive.

A Feature-Based Structural Topology Optimization Method

Feature-based modeling has been widely studied in Computer Aided Design (CAD) and greatly facilitates mechanical design and manufacture. This paper incorporates the standard technology into topology optimization, and develops a feature-based structural topology optimization method. The method employs implicit models or level set models to represent complex structural boundaries; adopts R-function theory to handle set-theoretic operations; applies topological derivative analysis to determine the insertion position of geometric primitives; uses morphing technology and sensitivity analysis to choose the geometric primitives; employs the shape matching to merge the given geometric primitives for the further simplification of the final design.

Incorporating Topological Derivatives into Level Set Methods for Structural Topology Optimization

The aim of this paper is to investigate the use of topological derivatives in combination with the level set method for topology optimization of solid structures. We present a topological derivative analysis and a technique of combining it with the level set model. The success of this combined approach is demonstrated in numerical examples, with a significantly high rate of convergence of the optimization process.

Damping Characteristic of Composite Material with Periodic Micro-Tetrahedron Structures

Research on damping characteristic of structures and materials is always one of the studies of international grand issue. Here, we addressed the damping characteristic of composite material with periodic micro-tetrahedron structures. We estabLished two computational models: one is a composite material model with periodic micro-tetrahedron structure, and another is the mass point model with periodic micro-tetrahedron structures. The unit cell of the first model is the micro-tetrahedron structure, in which the six edges are made of steel, and all the other areas are filled with a kind of high damping material such as rubber. In order to improve the damping characteristic of the first model, we transform the first model into the second model by applying a centraLized mass to the center of every parallelepiped, which consist of six micro-tetrahedron structures. By analyzing and comparing the damping characteristic of the two models, it can be concluded that the damping characteristic of the mass point model is better, and properly choosing the weight of the centraLized mass can improve the damping characteristic of the structure.