An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms

A method is developed to systematically remove and reintroduce low density elements from and into the nite element mesh on which the structural topology optimization problem is de ned. The material density eld which de nes the topology and the local ‘sti ness’ of the structure is optimally distributed via non-linear programming techniques. To prevent elements from having zero sti ness, an arbitrarily small lower bound on the material density is typically imposed to ensure that the global sti ness matrix does not become singular. While this approach works well for most minimum compliance problems, the presence of low density elements can cause computational problems, particularly in structures that exhibit geometric non-linearities, e.g. in compliant mechanisms. To resolve this problem, a systematic approach for removing and reintroducing low density elements is presented, and the substantial performance improvements both in design and computational e ciency of the method over current methods are discussed. Several structures and compliant mechanisms are designed to demonstrate the method