Development of high-performance general-purpose 10-node tetrahedral element using smoothed finite element method

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K12000
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60100:Computational science-related
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: ONISHI Yuki 東京工業大学, 工学院, 助教 (20543747)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 平滑化有限要素法 / 四面体メッシュ / 微圧縮大変形 / ロッキング / 圧力チェッカーボーディング / 偏差応力振動

Outline of Final Research Achievements

The formulation of a high-performance smoothed finite element method (S-FEM) for solving large deformation nearly incompressible problems accurately and robustly is studied. In order to target real problems with complex geometry, the study was conducted on 10-node tetrahedral (T10) meshes. The proposed method avoids shear locking by radially subdividing a T10 element into a 4-node tetrahedral (T4) meshes and applying the existing S-FEM within each element. Volume locking and pressure checkerboarding were avoided by applying selective reduced integration with a constant pressure at each T10 element. However, a new issue arose in which spatial oscillations occurred in the deviatoric stress, and this issue remains unsolved to date.

Free Research Field

計算工学

Academic Significance and Societal Importance of the Research Achievements

有限要素法（FEM）は近年の製品設計に欠かせない技術となっているが，未だに精度を確保することが難しい課題が山積している．特に複雑形状を対象とする実問題では高精度な六面体メッシュが生成出来ないため，やむを得ず低精度な四面体メッシュを使用しているのが現状である．本研究は四面体メッシュを用いても実用上充分な精度を確保することを目的としており，その成果が実用化されれば社会的意義は大きい．また，本研究は平滑化有限要素法(S-FEM)という次世代技術をいち早く取り入れた研究であり，適用範囲が固体力学に限らない普遍性を持つことから，その学術的意義も大きい．