最適性規準法を用いた位相最適化におけるフィルタリング法

Abstract

In the topology optimization analysis based on the homogenization design method or the density approach, the checkerboards, that is the formation of regions of altemating solid and void elements ordered in a checkerboard-like fashion, often appear in the optimum solutions. Therefore, the filtering method is necessary for these approaches. In this paper, we present an effective filteing method for the topology optimization analysis using the optimality criteria method as optimizer. In this method, the value of the gravity control function is controlled as a constrained condition. The gravity control function, which was presented by the author in the topology optimization analysis using the S LP method , is defined from the relations of the density of an element with that of its neighbor elements. This function imposes the penalty in the checkerboards and the gray scale density, that is, if the fuction is high, the checkerboards and gray scales disappear in the optimum solution. In this paper, this filtering method is applied in the topology optimization using the homogenization design method and the density approach. Several examples of 2D and 3D problems are shown to demonstrated the effectiveness of the present method.