Lagrangian Description Based Topology Optimization-A Revival of Shape Optimization

Unlike in the previous treatment where shape and topology optimization were carried out essentially in an Eulerian framework, the aim of the present work is to show how to perform topology optimization based on a Lagrangian framework, which is seamlessly consistent with classical shape optimization approaches, with use of a set of moving morphable components (MMCs). It is hoped that the present work may light up the revival of classical shape optimization in structural design and optimization and inspire some subsequent works along this direction. Some representative examples are also provided to illustrate the effectiveness of the proposed solution framework.