How does it work?
Design Variables
Topology optimization discretizes a domain into elements that are individually considered for inclusion in the design based on their sensitivity to an objective function. The design variables are the density values of each element.
Objective Function
If we are seeking the strongest structure possible given a set volume of material in a rough design space, and subject to specific loading conditions, then the objective function is the strain energy, which is minimized in the optimization problem.
There are an infinite number of objective functions possible, depending on the goal of the optimization. Examples are presented in the topology optimization "examples" section and in the "Redesigning MEMS" section.
Process
As shown in the graphic, the method requires a guess structure to start with. The structure is discretized, and simulated using finite elements. The objective function, constraints, and their sensitivities to changes in densities are computed on an element level. We then use those values with an optimization routine such as MMA to obtain a new density distribution, which will serve as the guess structure in the next iteration. We repeat the process until the density distribution changes only minimally between iterations.