Research Paper

Structural and Multidisciplinary Optimization

, Volume 33, Issue 4, pp 401-424

First online:

Morphology-based black and white filters for topology optimization

  • Ole SigmundAffiliated withDepartment of Mechanical Engineering, Solid Mechanics, Technical University of Denmark Email author 

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To ensure manufacturability and mesh independence in density-based topology optimization schemes, it is imperative to use restriction methods. This paper introduces a new class of morphology-based restriction schemes that work as density filters; that is, the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes, in general, provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.


Topology optimization Regularization Image processing Morphology operators Manufacturing constraints