Evolutionary topology optimization of continuum structures with an additional displacement constraint

Evolutionary structural optimization (ESO) and its later version Bi-directional ESO (BESO) have been successfully applied to optimum material distribution problems for continuum structures. However, the existing ESO/BESO methods are limited to the topology optimization of an objective function such as mean compliance with a single constraint e.g. structural volume. The present work extends the BESO method to the stiffness optimization with a material volume constraint and a local displacement constraint. As a result, one will obtain a structure with the highest stiffness for a given volume while the displacement of a certain node does not exceed a prescribed limit. Several examples are presented to demonstrate the effectiveness of the proposed method.