While shape optimization using isogeometric shells exhibits appealing features by integrating design geometries and analysis models, challenges arise when addressing computer-aided design (CAD) geometries comprised of multiple non-uniform rational B-splines (NURBS) patches, which are common in practice. The intractability stems from surface intersections within these CAD models. In this paper, we develop an approach for shape optimization of non-matching isogeometric shells incorporating intersection movement. Separately parametrized NURBS surfaces are modeled using Kirchhoff–Love shell theory and coupled using a penalty-based formulation. The optimization scheme allows shell patches to move without preserving relative location with other members during the shape optimization. This flexibility is achieved through an implicit state function, and analytical sensitivities are derived for the relative movement of shell patches. The introduction of differentiable intersections expands the design space and overcomes challenges associated with large mesh distortion, particularly when optimal shapes involve significant movement of patch intersections in physical space. Throughout optimization iterations, all members within the shell structures maintain the NURBS geometry representation, enabling efficient integration of analysis and design models. The optimization approach leverages the multilevel design concept by selecting a refined model for accurate analysis from a coarse design model while maintaining the same geometry. We adopt several example problems to verify the effectiveness of the proposed scheme and demonstrate its applicability to the optimization of the internal stiffeners of an aircraft wing.

中文翻译：

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具有移动交叉点的不匹配等几何壳的形状优化


虽然使用等几何壳的形状优化通过集成设计几何图形和分析模型展现出吸引人的功能，但在处理由多个非均匀有理 B 样条 (NURBS) 面片组成的计算机辅助设计 (CAD) 几何图形时会出现挑战，这在实践中很常见。棘手之处源于这些 CAD 模型内的表面交叉点。在本文中，我们开发了一种结合相交运动的不匹配等几何壳的形状优化方法。使用 Kirchhoff-Love 壳理论对单独参数化的 NURBS 曲面进行建模，并使用基于惩罚的公式进行耦合。该优化方案允许壳片在形状优化期间移动而不保留与其他成员的相对位置。这种灵活性是通过隐式状态函数实现的，并且针对壳补丁的相对运动导出分析灵敏度。可微交点的引入扩展了设计空间并克服了与大网格变形相关的挑战，特别是当最佳形状涉及物理空间中面片交点的显着移动时。在整个优化迭代过程中，壳结构内的所有成员都保持 NURBS 几何表示，从而实现分析和设计模型的高效集成。该优化方法利用多级设计概念，从粗略设计模型中选择精炼模型进行精确分析，同时保持相同的几何形状。我们采用几个示例问题来验证所提出方案的有效性，并证明其在飞机机翼内部加强筋优化中的适用性。