It is of great importance for the development of new products to find the best possible topology or layout for given design objectives and constraints at a very early stage of the design process (the conceptual and project definition phase). Thus, over the last decade, substantial efforts of fundamental research have been devoted to the development of efficient and reliable procedures for solution of such problems. During this period, the researchers have been mainly occupied with two different kinds of topology design processes; the Material or Microstructure Technique and the Geometrical or Macrostructure Technique. It is the objective of this review paper to present an overview of the developments within these two types of techniques with special emphasis on optimum topology and layout design of linearly elastic 2D and 3D continuum structures. Starting from the mathematical-physical concepts of topology and layout optimization, several methods are presented and the applicability is illustrated by a number of examples. New areas of application of topology optimization are discussed at the end of the article. This review article includes 425 references.
Issue Section:
Review Articles
Keywords:
continuum mechanics,
topology,
optimisation,
design engineering,
materials,
Mathematical-Physical Fundamentals,
Definitions,
Formulations,
Material Models—Microstructure Techniques,
Homogenization,
Perimeter, and Filtering Techniques—Macrostructure Techniques,
Approach by Growing and Degenerating a Structure (Material Removal),
Approach by Inserting Holes—New Applications of Topology Optimization
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