TOPOLOGY DESCRIPTION FUNCTION BASED METHOD FOR MATERIAL DESIGN

The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the ＇Hamilton-Jacobi-type＇ equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson＇s ratio, the other with negative Poisson＇s ratio. The examples show the method based on TDF is effective for material design.

The Spatiotemporal Evolution of Wave Packets under Chaotic Condition

Using the minimum uncertainty state of quantum integrable system as initial state, the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechanics. Due to the existence of the avoided energy level crossing in the spectrum there exist nonlinear resonances between some pairs of neighboring components of the wave packet, the deterministic dynamical evolution becomes very complicated and appears to be chaotic. It is proposed to use expectation values for the whole set of basic dynamical variables and the corresponding spreading widths to describe the topological features concisely such that the quantum chaotic motion can be studied in contrast with the quantum regular motion and well characterized with the asymptotic behaviors. It has been demonstrated with numerical results that such a wave packet has indeed quantum behaviors of ergodicity as in corresponding classical case.

GENERALIZED BOCHNER THEOREM ON LOCALLY CONVEX SPACES

The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with other topological descriptions of characteristic functionals of probability measures on other infinite dimensional spaces.

Bi-material Topology Optimization Using Analysis Mesh-Independent Point-Wise Density Interpolation

This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-based topology optimization approaches,this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain.To be specific,the density design variable points can be freely positioned,independently of the field points used for discretization of the displacement field.By this means,a material interface description of relatively high quality can be achieved,even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain.Numerical examples,regarding the minimum static compliance design and the maximum fundamental eigen-frequency design,are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques.It is shown that this method is free of numerical difficulties such as checkerboard patterns and the“islanding”phenomenon.