A centroid-enriched strain-smoothed radial point interpolation method for nearly incompressible elastoplastic problems in solid mechanics

被引:3
作者
Zhou, Xi -Wen [1 ,2 ]
Jin, Yin -Fu [1 ]
Yin, Zhen-Yu [2 ]
Liu, Feng-Tao [3 ]
机构
[1] Shenzhen Univ, Coll Civil & Transportat Engn, Shenzhen 518060, Guangdong, Peoples R China
[2] Hong Kong Polytech Univ, Dept Civil & Environm Engn, Hung Hom, Kowloon, Hong Kong, Peoples R China
[3] Guilin Univ Technol, Coll Civil Engn & Architecture, Guilin 541004, Peoples R China
基金
中国国家自然科学基金;
关键词
Volumetric locking; Edge -based smoothed radial point interpolation; method; Strain smoothing; Incompressible material; Centroid-enriched scheme; FINITE-ELEMENT-METHOD; CONFORMING NODAL INTEGRATION; G SPACE THEORY; WEAK W-2 FORM; UNIFIED FORMULATION; VIBRATION ANALYSES; MESHLESS METHOD; RPIM; FIELDS; FEM;
D O I
10.1016/j.enganabound.2023.07.017
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
While edge-based (2D) and face-based (3D) smoothed radial point interpolation methods (ES-RPIM and FSRPIM) have demonstrated excellent performance in solid mechanics, the volumetric locking problem limits their applications in nearly incompressible problems. This paper develops a centroid-enriched edge-based/facebased smoothed RPIM (CE-ES-RPIM and CE-FS-RPIM) to address the volumetric locking problem in nearly incompressible problems. The proposed method comprises the following elements: (1) a centroid-enriched scheme is creatively used and implemented into the traditional ES-RPIM and FS-RPIM framework, in which the centroids of triangular mesh are added as spatial discretization nodes; (2) the strain-smoothing technique is performed on triangle (2D) or tetrahedron (3D) mesh to maintain the linear exactness of the radial point interpolation method; and (3) the combination of the centroid-enriched scheme and strain smoothing technique makes the ratio of the number of displacement equations to the number of incompressible constraints reach the optimal value of 2, effectively eliminating volumetric locking. The accuracy, effectiveness and efficiency of the proposed method are validated on several 2D and 3D nearly incompressible benchmark examples. All results demonstrate that the proposed method can provide accurate numerical results under an incompressible limitation and provide better performance than conventional quadratic element methods.
引用
收藏
页码:888 / 906
页数:19
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