A nodal-based evolutionary optimization algorithm for frame structures

This work proposes a nodal-based evolutionary design optimization algorithm to design frame structures whose edges are the Delaunay triangulation of homogeneously distributed nodes in the design domain. The remaining nodes can freely sway in the design domain except for the loading nodes and boundary nodes. As a result, it can extend the space of admissible solutions to this optimization problem and reduce the number of design variables. Then, the sensitivity of the objective function, namely, the sum of compliance and its volume, is input into the method of moving asymptotes to update the nodal coordinates and member thickness. The most inefficient node is deleted in each iteration based on the average nodal strain energy until its number reaches a prescribed limit. 2D numerical examples for the Michell arch, L-shaped bracket, and Messerschmidt-Bolkow-Blohm beam show that the proposed algorithm can get the optimal structure within a few iterations. Compared with initial configurations in 3D, the optimal crane arm, transmission tower, and aquatic dome have less strain energy and fewer materials, showing a great potential of the proposed method to design actual space frames.