Review Article

Structural and Multidisciplinary Optimization

, Volume 49, Issue 1, pp 1-38

First online:

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

  • Joshua D. DeatonAffiliated withDepartment of Mechanical and Materials Engineering, Wright State University Email author 
  • , Ramana V. GrandhiAffiliated withDepartment of Mechanical and Materials Engineering, Wright State University

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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.


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