A 10-node tetrahedral element with condensed Lagrange multipliers for the modified couple stress theory. (1st April 2021) - Choi, Jae-Hoon; Lee, Byung-Chai; Sim, Gi-Dong
Highlights: We developed a novel 10-node tetrahedral element for the modified couple stress theory. Higher-order rotation modes are introduced to condense out the Lagrange multiplier DOFs. Since the Lagrange multipliers are condensed out, the computational efficiency is dramatically increased. The structural behavior with size effect can be predicted efficiently using the developed element. Abstract: 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.