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A survey of structural and multidisciplinary continuum topology optimization: post 2000

Abstract

Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain. This paper surveys topology optimization of continuum structures from the year 2000 to 2012. It focuses on new developments, improvements, and applications of finite element-based topology optimization, which include a maturation of classical methods, a broadening in the scope of the field, and the introduction of new methods for multiphysics problems. Four different types of topology optimization are reviewed: (1) density-based methods, which include the popular Solid Isotropic Material with Penalization (SIMP) technique, (2) hard-kill methods, including Evolutionary Structural Optimization (ESO), (3) boundary variation methods (level set and phase field), and (4) a new biologically inspired method based on cellular division rules. We hope that this survey will provide an update of the recent advances and novel applications of popular methods, provide exposure to lesser known, yet promising, techniques, and serve as a resource for those new to the field. The presentation of each method’s focuses on new developments and novel applications.

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Acknowledgments

This work has been funded by the U.S. Air Force Research Laboratory (AFRL) through contract FA8650-09-2-3938, the Collaborative Center for Multidisciplinary Sciences (CCMS). The views and conclusions contained herein are those of the authors and should not be interpreted as representing official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government.

The authors would like to gratefully acknowledge the journal reviewers for their time. In addition, we would also like to thank several others for their educated review and input on this document: Dr. Bret Stanford (NASA Langley), Dr. Alicia Kim (University of Bath), Dr. Kurt Maute (University of Colorado at Boulder), Dr. Michael Y. Wang (The Chinese University of Hong Kong), Dr. Julian Norato (Caterpillar), Dr. James Guest (Johns Hopkins University), Dr. Mike Xie (RMIT University), Dr. Ha-Rok Bae (Wright State University), Dr. Ming Zhou (Altair Engineering), Dr. George Rozvany (Budapest University) and Dr. Marcelo Kobayashi (University of Hawaii). Finally, we would like to thank Christopher Fischer for helping to locate papers and Alysoun Taylor-Hall and Michelle Harr for editing.

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Deaton, J.D., Grandhi, R.V. A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidisc Optim 49, 1–38 (2014). https://doi.org/10.1007/s00158-013-0956-z

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Keywords

  • Topology optimization
  • Density methods
  • Level set
  • Evolutionary structural optimization
  • Phase field
  • Continuum topology