Sensitivity filtering from a continuum mechanics perspective

In topology optimization filtering is a popular approach for preventing numerical instabilities. This short note shows that the well‐known sensitivity filtering technique, that prevents checkerboards and ensures mesh‐independent designs in density‐based topology optimization, is equivalent to minimizing compliance for nonlocal elasticity problems known from continuum mechanics. Hence, the note resolves the long‐standing quest for finding an explanation and physical motivation for the sensitivity filter.