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结构性能反馈驱动的壳体变厚度参数化设计

Parametric Variable-Thickness Design of Shell Structures Driven by Structural Performance Feedback

  • 摘要: 针对壳体结构设计中厚度取值依赖经验、结构事后合理化等问题,提出结构力学性能和参数化设计协同的壳体厚度设计方法,构建涵盖“形态参数化定义—性能数据提取—厚度决策算法—几何模型重构”的闭环工作流。将曲面控制点与曲面网格点的参数关联,通过有限元分析提取节点等效应力,并通过映射函数将应力值转换为变截面厚度,最终生成变厚度双层壳体。选取自由曲面壳与双曲抛物面壳两类典型壳体进行对比试验,在自重荷载与四边简支边界条件下,自由曲面壳的变厚度壳较薄壳等效应力峰值降低33.9%、变形位移降低21.1%,材料用量仅为均质厚壳的65.6%;双曲抛物面壳的变厚度壳较薄壳等效应力峰值降低65.2%、变形位移降低44.5%,材料用量仅为均质厚壳的50.9%。结果表明:变厚度壳体以接近薄壳的材料用量实现接近厚壳的力学性能,验证了“按力赋厚”的可行性,为壳体厚度设计提供可计算的数字化路径。

     

    Abstract: In the design of shell structures, challenges such as experience-dependent thickness determination and post-hoc structural rationalization are prevalent. To address these issues, this study proposes a shell thickness design method that integrates structural mechanical performance with parametric design, establishing a closed-loop workflow encompassing "parametric form definition, performance data extraction, thickness decision algorithm, and geometric model reconstruction." By correlating the control points of the surface with the mesh nodes of the surface, equivalent nodal stresses are extracted via finite element analysis, and stress values are converted into variable cross-sectional thicknesses through a mapping function, ultimately generating a variable-thickness double-layer shell. Comparative experiments were conducted on two typical shell types—free-form shells and hyperbolic paraboloid shells—under self-weight loading and simply supported boundary conditions. For free-form shells, the variable-thickness design reduced the peak equivalent stress by 33.9% and the deformation displacement by 21.1% compared to the thin-shell design, while the material consumption was only 65.6% of that of the homogeneous thick shell. For hyperbolic paraboloid shells, the variable-thickness design reduced the peak equivalent stress by 65.2% and the deformation displacement by 44.5%, with the material usage being merely 50.9% of that of the homogeneous thick shell. The results indicate that variable-thickness shells achieve mechanical performance comparable to that of thick shells while using a material quantity close to that of thin shells, verifying the feasibility of "thickness assignment based on force" and providing a computable digital approach for shell thickness design.

     

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