Abstract
Topology design involves working with multiple fields. The primary information are the quantities defining the design, and one can argue that for practical purposes this is the only information of real interest. In topology optimization the design variables define the density distribution of material and the optimization problem makes a certain objective function minimal while other objectives are satisfied as constraints in a mathematical programming statement. The evaluation of the objective and constraint functions will involve state variables that relate the design variables to physical behavior, and various physical responses may be involved; these fields will typically be coupled in multi-physics applications. Computational procedures for topology design (and for design optimization as a whole) thus encompass discretization schemes for design and state fields together with algorithms for optimization and for analysis. The prevailing computational approach to structural design and topology design in particular is to view the optimization procedure as a problem in the design variables only. This means that analysis is treated as a function call that provides information on function values and derivatives as a function of design. In optimization terms this is a nested format. Computational challenges are thus by the nature of the problem two-fold and successful implementations rely on both efficient analysis (and the associated sensitivity analysis) and on the efficiency of optimization algorithms. The basic concept of topology optimization and how to apply the methodology to multi-physics devices will be illustrated by considering some recent work on design of structural parts of aircraft and cars, of channel fluid-flow problems, and of waveguides. One of the issues that will be discussed is how simpler models may be used if they still give good designs that can be validated.
