We present six thin plate/shell models, derived from three distinct types of curvature operators formulated within the corotational frame, for simulating both rest-flat and rest-curved triangular meshes. Each curvature operator derives a curvature expression corresponding to both a plate model and a shell model. The corotational edge-based hinge model uses an edge-based stencil to compute directional curvature, while the corotational FVM hinge model utilizes a triangle-centered stencil, applying the finite volume method (FVM) to superposition directional curvatures across edges, yielding a generalized curvature. The corotational smoothed hinge model also employs a triangle-centered stencil but transforms directional curvatures into a generalized curvature based on a quadratic surface fit. All models assume small strain and small curvature, leading to constant bending energy Hessians, which benefit implicit integrators. Through quantitative benchmarks and qualitative elastodynamic simulations with large time steps, we demonstrate the accuracy, efficiency, and stability of these models. Our contributions enhance the thin plate/shell library for use in both computer graphics and engineering applications.

翻译：本文提出了六种薄板/壳模型，它们源自三种在共旋框架内构建的不同类型曲率算子，用于模拟既可以是平坦静止状态也可以是弯曲静止状态的三角形网格。每种曲率算子分别推导出一个对应于板模型和一个对应于壳模型的曲率表达式。基于共旋的边铰链模型采用基于边的模板来计算方向曲率，而基于共旋的FVM铰链模型则利用三角形中心模板，应用有限体积法（FVM）对跨越各边的方向曲率进行叠加，从而得到一个广义曲率。基于共旋的平滑铰链模型同样采用三角形中心模板，但基于二次曲面拟合将方向曲率转换为广义曲率。所有模型均假设小应变和小曲率，从而得到恒定的弯曲能量Hessian矩阵，这有利于隐式积分器的应用。通过定量基准测试以及采用大时间步长的定性弹性动力学模拟，我们证明了这些模型的准确性、高效性和稳定性。我们的工作丰富了薄板/壳模型库，可同时应用于计算机图形学和工程领域。