Filters in topology optimization
In this article, a modified ('filtered') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The 'filtering' technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs. Copyright © 2001 John Wiley & Sons, Ltd.
Publication Source (Journal or Book title)
International Journal for Numerical Methods in Engineering
Bourdin, B. (2001). Filters in topology optimization. International Journal for Numerical Methods in Engineering, 50 (9), 2143-2158. https://doi.org/10.1002/nme.116