稜線の生成を含むシェル構造体の形状最適設計

抄録

Optimized smooth shells resist the external force efficiently through membrane stiffness. However, the smooth optimal shapes aren’t always fabricated because of some shape restrictions. In this case, ridges need to be designed properly to increase the stiffness. Their anisotropic mechanical characteristics increase local bending stiffness and influence on load transfer and deformation. In this paper, we propose a shape optimization method for designing ridges on a shell structure by modifying the H¹ gradient method. In the proposed method, fictitious shell elements are connected with the rotational springs and the spring constants are set up manually to adjust the local stiffness. In addition, the bending stiffness of the fictitious shell is increased to assist in the creation of ridges. The proposed method was applied to the shape optimization problem for minimizing the mean compliance, where the total volume is constrained. Case studies were performed with different rotational spring distribution and stiffness of shell elements. For proper conditions, ridges were created according to the rotational spring distribution and the mean compliance decreased by 99%. We confirmed the proposed method is effective for optimizing shell structure with ridges.