Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics

Topology optimization of structures and composite continua has two main subfields: Layout Optimization (LO) deals with grid-like structures having very low volume fractions and Generalized Shape Optimization (GSO) is concerned with higher volume fractions, optimizing simultaneously the topology and shape of internal boundaries of porous or composite continua. The solutions for both problem classes can be exact/analytical or discretized/FE-based. This review article discusses FE-based generalized shape optimization, which can be classified with respect to the types of topologies involved, namely Isotropic-Solid/ Empty (ISE), Anisotropic-Solid/Empty (ASE), and Isotropic-Solid/Empty/Porous (ISEP) topologies. Considering in detail the most important class of (i.e. ISE) topologies, the computational efficiency of various solution strategies, such as SIMP (Solid Isotropic Microstructure with Penalization), OMP (Optimal Microstructure with Penalization) and NOM (NonOptimal Microstructures) are compared. The SIMP method was proposed under the terms direct approach or artificial density approach by Bendsoe over a decade ago; it was derived independently, used extensively and promoted by the author's research group since 1990. The term SIMP was introducted by the author in 1992. After being out of favour with most other research schools until recently, SIMP is becoming generally accepted in topology optimization as a technique of considerable advantages. It seems, therefore, useful to review in greater detail the origins, theoretical background, history, range of validity and major advantages of this method.