Abstract This paper introduces a novel hybrid finite element (FE) formulation of shell element to enable assembly process simulation of compliant sheet-metal parts with higher efficiency and flexibility. Efficiency was achieved by developing both new hybrid quadrilateral and triangular elements. Quadrilateral element (QUAD+) was formulated by combining area geometric quadrilateral 6 (AGQ6) nodes and mixed interpolated tensorial components (MITC) to model membrane and bending/shear component respectively. Triangular element (TRIA+) was formulated by merging assumed natural deviatoric strain (ANDES) for membrane and MITC for bending/shear component. Flexibility was addressed by developing an open-source C++ code, enhanced by the OpenMP interface for multiprocessing programming. Tests and benchmarks were compiled and executed within Matlab using the MEX API interface. Extensive benchmark studies were accomplished to evaluate the performance of the proposed hybrid formulation and the shell formulations used in three FEM packages - ABAQUS, ANSYS and COMSOL- under static linear elastic condition with small strain assumption. It was observed that the proposed QUAD+ and TRIA+ elements performed better amongst the FE packages, especially when there was in-plane mesh distortion, with errors below 3%. It was also identified that the best efficiency is obtained by adopting dominant QUAD+ elements compared to the TRIA+ when working on complex geometries. This paper also contributes to present a wide set of benchmark studies required to verify new release of FE packages using shell element or evaluate the performance of new shell formulations.

中文翻译：

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一种新型混合壳单元公式（QUAD+ 和 TRIA+）：基准和比较研究

摘要 本文介绍了壳单元的一种新颖的混合有限元 (FE) 公式，能够以更高的效率和灵活性对柔性钣金零件进行装配过程仿真。效率是通过开发新的混合四边形和三角形元素来实现的。四边形单元 (QUAD+) 是通过组合面积几何四边形 6 (AGQ6) 节点和混合插值张量分量 (MITC) 分别对膜和弯曲/剪切分量进行建模来制定的。三角形单元 (TRIA+) 是通过合并膜的假定自然偏应变 (ANDES) 和弯曲/剪切分量的 MITC 来制定的。通过开发开源 C++ 代码解决了灵活性问题，并通过用于多处理编程的 OpenMP 接口进行了增强。使用 MEX API 接口在 Matlab 中编译和执行测试和基准测试。完成了广泛的基准研究，以评估在具有小应变假设的静态线性弹性条件下，所提出的混合公式和在三个 FEM 包（ABAQUS、ANSYS 和 COMSOL）中使用的壳公式的性能。据观察，提议的 QUAD+ 和 TRIA+ 元件在 FE 封装中表现更好，尤其是当存在面内网格失真时，误差低于 3%。还发现，在处理复杂几何形状时，与 TRIA+ 相比，通过采用占主导地位的 QUAD+ 元素可以获得最佳效率。