Optimal design of material microstructures and optimization of structural topology for design -dependent loads.

Abstract

A strategic challenge for technology is the development of advanced composite materials to meet growing functional demands. Traditional parametric-based composite material design methods are not general enough to accommodate novel materials with unusual properties. In this dissertation, a non-parametric design method is proposed to design materials with unique properties. This method, which is a combination of topology optimization and homogenization, is especially geared to design topologies of material microstructures. As is often the case in research, in the course of the work with microstructure topology optimizations, it became apparent that the mathematical features of homogenization responded to the unanswered problem of optimizing structural topology for design-dependent loads. With respect to the design of material microstructures, we tackled design of thermoelastic material with unusual properties and the design of extremal microstructure corresponding to optimal material conductivity bounds. Among other things, we designed and fabricated negative thermal expansion microstructures. Experimental results confirmed the designed properties. Regarding the problem of topology optimization for design-dependent loads, it requires a simple and efficient algorithm to simulate design-dependent loads which may change directions and location as the shape of the given structure changes. The issue of design-dependent load is critical to many engineering disciplines. In fact, all structures involving solid and fluid interaction, including darns, pipes, and airfoils, carry such design-dependent loads. Of the two main contributions of this work on design-dependent loads, the first is the development of a new algorithm using fictitious thermal loads to simulate design-dependent loads due to mismatch of thermal expansion coefficients among constituent phases. The second contribution is the extension to compliant mechanism design which was motivated by the desire to use topology optimization to design multiple physics actuators in Micro Electro Mechanical Systems. To address a fundamental issue of modeling the design-dependent coupling forces between two physics domains, this research presents formulations combining compliant mechanisms and design-dependent loads to design compliant mechanisms actuated by hydrostatic pressure. In addition, numerical results of structures and pressure actuated compliant mechanisms are presented to demonstrate the performance of the proposed algorithms.