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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Embedded shell finite elements: Solid-shell interaction, surface locking, and application to image-based bio-structures
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Embedded shell finite elements: Solid-shell interaction, surface locking, and application to image-based bio-structures

机译：嵌入式壳有限元：固壳相互作用，表面锁定以及在基于图像的生物结构中的应用

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In this article, we explore an embedded shell finite element method for the unfitted discretization of solid-shell interaction problems. Its core component is a variationally consistent approach that couples a shell discretization on the surface of an embedded solid domain to its unfitted discretization with hexahedral solid elements. Derived via an augmented Lagrangian formulation and the formal elimination of interface Lagrange multipliers, our method depends only on displacement variables, facilitated by a shift of the displacement-dependent traction vector entirely to the solid structure. We demonstrate that the weighted least squares term required for stability of the formulation triggers severe surface locking due to a mismatch in the polynomial spaces of the shell element and the embedding solid element. We show that reduced quadrature of the stabilization term that evaluates the kinematic constraint at the nodes of the embedded shell elements completely mitigates surface locking. For coarse discretizations, our variationally consistent method achieves superior accuracy with respect to a locking-free nodal penalty method. We illustrate the versatility of embedded shell finite elements for image-based analysis, including patient-specific stress prediction in a vertebra and local rind buckling in a plant structure. (C) 2018 Elsevier B.V. All rights reserved.
机译：在本文中，我们探索了一种嵌入式壳有限元方法来解决固-壳相互作用问题的离散化问题。它的核心组件是一种变化一致的方法，该方法将嵌入的实体域表面上的壳离散与六面体实体元素的不适合离散耦合在一起。通过增加的拉格朗日公式和接口拉格朗日乘数的形式消除得出，我们的方法仅取决于位移变量，而位移相关的牵引向量完全移至实体结构。我们证明，由于壳单元和嵌入实体单元的多项式空间不匹配，制剂稳定性所需的加权最小二乘项会触发严重的表面锁定。我们表明，在嵌入式壳单元的节点处评估运动约束的稳定项的减小的正交完全减轻了表面锁定。对于粗略离散化，相对于无锁节点惩罚方法，我们的变分一致方法可实现更高的精度。我们说明了基于图像分析的嵌入式壳有限元的多功能性，包括椎骨中患者特定的应力预测和植物结构中的局部外皮屈曲。 （C）2018 Elsevier B.V.保留所有权利。

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