Topology Optimization

Abstract

Topology optimization is a computational approach to systematically optimize the conceptual layout and the geometry of a body on the basis of a basic description of a design problem. In contrast to other design optimization methods, the outer shape of the body and the geometry of the material interfaces within the body may undergo radical changes in the optimization process, including both shape and topological changes. This unique feature reduces significantly the dependence of the optimized design on the initial guess from which the optimization process is started and allows finding nonintuitive solutions for complex design problems. Formulating optimization problems that yield meaningful, practical designs requires a solid understanding of the physical phenomena that dominate the body's functionality, as well as insight into the mathematical characteristics of the high‐dimensional design spaces used in topology optimization. Topology optimization methods involve a broad variety of computational techniques for describing the geometry of the body, predicting the physical phenomena of interest, and searching for the optimum design. This chapter provides an introduction to modern topology optimization. Instead of providing a comprehensive overview, the most important and widely used approaches are discussed in sufficient detail to provide the reader with a basic understanding of the state of the art of topology optimization.

Adaptive level set topology optimization using hierarchical B-splines

“…The shape of the new hole is then optimized along with existing domain boundaries. The reader is referred to Sigmund and Maute (2013) or Maute (2017) for further details. Although proven useful, topological derivatives only provide information about where to place an infinitesimal hole and it remains unclear what the size and shape of a finite sized hole should be.…”