A 10-node tetrahedral element with condensed Lagrange multipliers for the modified couple stress theory

被引：15

作者：

Choi, Jae-Hoon ^{[1
]}

Lee, Byung-Chai ^{[1
]}

Sim, Gi-Dong ^{[1
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Mech Engn, 291 Daehak Ro, Daejeon 34141, South Korea

来源：

COMPUTERS & STRUCTURES | 2021年 / 246卷

基金：

新加坡国家研究基金会;

关键词：

Modified couple stress theory; Tetrahedral element; Finite element method; Lagrange multiplier; Size effect;

D O I：

10.1016/j.compstruc.2020.106476

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, a mixed tetrahedral element based on the Lagrange multiplier is newly developed for the modified couple stress theory. The limitations of the Lagrange multiplier method are that the total number of degrees of freedom is increased and that there are zeros in the diagonal term of the stiffness matrix. We developed a method to overcome the limitations by condensing out the Lagrange multipliers in the calculation of the element stiffness. Higher-order rotation modes are introduced. As condensing out the rotation modes, the Lagrange multiplier is also condensed. The total number of degrees of freedom can be greatly reduced, maximizing computational efficiency. Through numerical examples, the convergence and efficiency of the proposed elements were validated. The developed element is expected to be used for the analysis of micro/nano-scale structures. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：16

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