An automatically connected graph representation based on B-splines for structural topology optimization

This paper introduces an automatically connected graph representation for structural topology optimization. Structural members of optimal topologies are constructed based on a graph whose each edge is represented by a B-spline curve with varying thickness. A square matrix including connective coefficients with either 0 or 1 is first proposed to automatically determine the way of linking two vertices of an edge. This significantly improves the flexibility of searching optimal topologies. Additionally, resulting designs are completely free from the checkerboard effect and grayscale without any filtering techniques. Control point coordinates of B-spline curves are considered as continuous design variables, while connective coefficients and thickness parameters are taken as discrete ones. Accordingly, this approach helps to reduce the total number of design variables considerably. Modified differential evolution (mDE), which is modified from original differential evolution (DE) to reduce computational cost but still guarantee the quality of solution, is proposed. mDE with the possibility of easily handling such variables and the capability of finding a global solution is utilized as an optimizer. The proposed method is essentially an intuitive method without a strong mathematical or theoretical background. Gained results are compared with other studies to verify the effectiveness of the present method.