当前位置: X-MOL 学术Comput. Methods Appl. Mech. Eng. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
An implicit G1-conforming bi-cubic interpolation for the analysis of smooth and folded Kirchhoff–Love shell assemblies
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.cma.2020.113476
L. Greco , M. Cuomo

Abstract A quadrilateral bi-cubic G 1 -conforming finite element for the analysis of Kirchhoff–Love shell assemblies based on the rational Gregory interpolation is presented. The Gregory interpolation removes the symmetry of the second cross derivative at the corners of the element that allows an independent control of the side rotations of the boundaries of the element. In this way G 1 -conformity of the deformation can be implicitly obtained for any mesh of quadrilateral elements, also for not G 1 -continuous parametrizations. The interpolation is defined by means of the kinematics of the boundary ribbons. The ribbon is the differential set generated by the tangents at the boundary of the element. A new set of degrees of freedom is introduced in order to control the deformation of the boundary, and the non-linear map between this new set of degrees of freedom and the control points of the Gregory interpolation is derived. Due to the presence of rational terms, the interpolation is not consistent, so that, in order to recover consistency it is necessary to enforce the vanishing of the discontinuities of the second derivatives with additional constraints. The proposed G 1 -conforming shell element results accurate and robust as shown by several numerical investigations on benchmark problems.

中文翻译:

用于分析平滑和折叠 Kirchhoff-Love 壳组件的隐式 G1 一致性双三次插值

摘要 提出了一种基于有理 Gregory 插值法分析 Kirchhoff-Love 壳组件的符合四边形双三次 G 1 的有限元。Gregory 插值消除了单元角处二阶交叉导数的对称性,允许独立控制单元边界的侧向旋转。通过这种方式,对于任何四边形单元的网格,以及对于非 G 1 连续参数化,都可以隐式获得变形的 G 1 -一致性。插值是通过边界带的运动学定义的。带是由单元边界处的切线生成的微分集。引入了一组新的自由度以控制边界的变形,并推导出这组新的自由度与 Gregory 插值控制点之间的非线性映射。由于有理项的存在,插值是不一致的,因此,为了恢复一致性,有必要使用附加约束强制消除二阶导数的不连续性。所提出的符合 G 1 的壳单元结果准确且稳健,如对基准问题的若干数值研究所示。
更新日期:2021-01-01
down
wechat
bug