Evolutionary topology and shape design for general physical field problems

As a practical tool for design engineers, evolutionary techniques for structural topology, shape and size optimisation have successfully resolved the whole range of structural problems from frames to 2D and 3D continuums with design criteria of stress, stiffness, frequency and buckling. In view of the generality of the finite element formulation using either a variational calculus or weighted residual approach, it is logical to extend its applications to other steady state field problems in mathematical physics governed by partial differential equations. The range of physical problems falling to this category includes heat conduction, incompressible fluid flow, elastic torsion, electrostatics and magnetostatics, etc. This paper discusses the general principles involved in setting up the adaptive evolutionary algorithms that have finite element techniques as the analysis engines. To avoid the complexity of classical solutions, the proposed method develops a simple outer loop procedure consisting of finite element analysis and design modifications. Illustrative examples are presented to demonstrate the capability in solving the above-mentioned physical field situations.