有限元计算中,板壳单元与实体单元之间的连接需要进行特殊处理,且两者在连接处的网格必须匹配。前期基于独立覆盖流形法提出了梁板壳数值分析的分区级数解。在此基础上,研究了板壳与实体单元的刚性连接。由于板壳也采用了实体计算模式,因此与实体之间通过覆盖重叠区域自然连接。基于覆盖任意连接的特性,将板壳插入到实体中形成覆盖重叠区域。实体单元和板壳单元可以各自划分网格,在连接处不必要求网格匹配,有利于前处理工作,在网格划分达到一定密度的情况下能得到高精度的计算结果。通过变截面的悬臂梁算例、球面壳与实体基座连接算例,验证了方法的有效性,并初步展示了曲壳与实体相交曲线的精确几何。此外,还修正了新方法的三维弹性矩阵。
Abstract
In Finite Element Method, the connection between plate shell elements and solid elements needs special treatment, and their meshes at the connection must be matched, which brings some inconveniences. In our previous research, the piecewise-defined series solutions for the numerical analysis of beam, plate and shell are proposed by using manifold method based on independent covers. On this basis, the rigid connection between plate shell elements and solid elements is studied in this paper. The solid calculation mode is also adopted in the analysis of plate and shell which are naturally connected with the solid element through the overlapping area of the covers. In view of the characteristic of arbitrary connection of independent covers, the plate or the shell is inserted into the solid to form the overlapping area of the covers. The solid and the shell can be meshed separately in no need of mesh matching at the connection, which is very conducive to the preprocessing work. Highly precise results can be obtained when the mesh division reaches a certain density. The effectiveness of the method is verified by examples of a cantilever beam with variable sections, and a spherical shell with a solid base. The accurate geometry of the intersection curve between the curved shell and the solid is also preliminarily demonstrated. The three-dimensional elastic matrix of the new method is also modified.
关键词
梁板壳分析 /
板壳与实体单元的连接 /
级数解 /
数值流形方法 /
独立覆盖
Key words
beam, plate and shell analysis /
connection between plate shell and solid element /
series solutions /
numerical manifold method /
independent covers
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基金
中央级公益性科研院所基本科研业务费项目(CKSF2019394/GC)
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