Sensitivity filtering from the non-local perspective

We present a mathematical model of topology optimization for non-local linear diffusion equation. The model provides a rigorous and constructive answer to the challenge of interpreting sensitivity filtering as an internal feature of a specific continuum mechanics model, which has been raised in Sigmund and Maute (Struct Multidiscip Optim 46(4):471–475, 2012).

Our model enjoys two very interesting properties. On the one hand, the governing non-local integral equations of this model approximate the well-known local generalized Laplace equation with diffusion coefficient obeying SIMP (Solid Isotropic Material with Penalization) law. On the other hand, the topology optimization problem admits optimal solutions for a range of penalization parameters of practical interest without the need for any external regularization techniques, something which is well known to be false in the case of topology optimization with SIMP for classical local description of continuum mechanics.