A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies.

翻译：一组曲线梁与壳的几何形状由某个体域中标量函数的水平集隐含定义。每种结构的力学模型基于Kirchhoff-Love理论，即考虑无剪切变形的小位移假设。这些针对单一几何的模型被推广至体模型，从而同步模拟所有水平集上的梁/壳结构整体。研究的重点在于此类模型的数值分析。本文提出了一种混合杂交且具有高阶精度的体迹有限元法，该方法支持使用与体域同维度的标准$C^0$连续Lagrange单元。由此，基于位移格式在Kirchhoff-Love理论框架下的高阶连续性要求得以成功弱化。多个数值试验验证了所提方法的精度与高阶收敛性，同时这些试验也可作为未来研究中的基准测试案例。