| 豆芦镇,黄颖青,陈海波.径向多项式插值的新型非对称8节点六面体单元[J].计算力学学报,2025,42(4):589~596 |
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| 径向多项式插值的新型非对称8节点六面体单元 |
| Novel unsymmetric 8-node hexahedral element with radial polynomial interpolation |
| 投稿时间：2024-02-04 修订日期：2024-03-15 |
| DOI：10.7511/jslx20240204001 |
| 中文关键词: 径向多项式插值 有限元法 无网格法 非对称有限元 虚位移原理 |
| 英文关键词:radial polynomial interpolation finite element method meshfree method unsymmetric finite element virtual work principle |
| 基金项目:国家自然科学基金(12172350;11772322);2022年中国科学技术大学同步辐射联合基金资助项目. |
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| 中文摘要: |
| 基于虚位移原理,开发了一种新型非对称8节点六面体单元UH8-RPIM。该单元分别采用等参插值函数和径向多项式插值用于虚位移和实位移的近似假设,使得给定位移边界条件的实施以及等效节点外力的计算与传统等参元相同,同时提高了数值精度和单元间的应力平滑度。由于采用不同的位移插值函数,单元刚度矩阵呈现非对称性,但整体刚度矩阵仍是结构对称的稀疏矩阵形式。这样的设计确保了单元刚度矩阵的计算不再依赖Jacobian矩阵的行列式值,增强了单元对网格畸变的抵抗力。数值算例表明,该单元充分融合了有限元法与无网格法的优势,易于施加边界条件,具有良好的收敛性和高精度,以及出色的抗网格畸变能力。 |
| 英文摘要: |
| Based on the virtual work principle,this paper introduces a novel asymmetric 8-node hexahedral element named UH8-RPIM.The element uses isoparametric interpolation functions and radial polynomial interpolation to approximate virtual displacement and real displacement,ensuring that the imposition of prescribed displacement boundary conditions and the calculation of equivalent nodal forces are the same as the conventional isoparametric elements,while the numerical accuracy of the element is improved and stress smoothness across elements is enhanced.Due to the use of different displacement interpolation functions,the element stiffness matrix exhibits asymmetry.However,the global stiffness matrix is still structurally symmetric and sparse.Such an approach ensures that the computation of the element stiffness matrix is independent of the determinant of the Jacobian matrix and improve the immunity from mesh distortion significantly.Numerical examples demonstrate that the present element effectively combines the advantages of both the finite element method and the meshfree method with convenient imposition of boundary conditions,good convergence,high numerical accuracy,and excellent resistance to mesh distortion. |
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