接触与大变形问题的光滑有限元分析

范亚杰; 李燕; 李中潘; 陈荟键; 冯志强

doi:10.21656/1000-0887.440251

接触与大变形问题的光滑有限元分析

doi: 10.21656/1000-0887.440251

西南交通大学力学与航空航天学院，成都 610031

(我刊编委冯志强来稿)

基金项目:

国家自然科学基金 12002290

详细信息

作者简介:
范亚杰(1999—)，男，硕士生(E-mail: fanyajie@my.swjtu.edu.cn)

李中潘(1997—), 男，博士生(E-mail: 2017114420@my.swjty.edu.cn)

陈荟键(1991—), 男，博士生(E-mail: huijianc@foxmail.com)

冯志强(1963—)，男，教授，博士生导师(E-mail: zhiqiang.feng@univ-evry.fr)

通讯作者:
李燕(1990—)，女，副教授，硕士生导师(通讯作者. E-mail: yanli@swjtu.edu.cn)

中图分类号: O343.3
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出版历程
- 收稿日期: 2023-08-17
- 修回日期: 2023-11-29
- 刊出日期: 2024-02-01

Smoothed Finite Element Analysis of Contact and Large Deformation Problems

School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

(Contributed by FENG Zhiqiang, M. AMM Editorial Board)

摘要

摘要: 橡胶材料因具有良好的抗震、吸能作用，在实际工程中应用广泛.然而橡胶超弹性材料的碰撞属于强非线性问题，分析橡胶材料的接触碰撞和大变形问题对于提高装置的缓冲性能具有重要意义.光滑有限元法(smoothed finite element method，S-FEM)是一种弱形式的数值计算方法，相比于传统的有限元方法，光滑有限元法对网格的质量要求不高，允许单元在计算过程中发生较大的变形，且光滑域的构造比较灵活，在不增加自由度的前提下，可以达到较高的精度.在光滑有限元法的基础上，采用双势方法进行接触计算，以充分利用光滑有限元法计算大变形问题的优点和双势方法求解接触力的优势.通过与有限元软件MSC.Marc的数值结果对比，验证了该算法的准确性和能量守恒性，并且分析了摩擦因数对碰撞体的影响.
- 接触 /
- 大变形 /
- 超弹性材料 /
- 光滑有限元法 /
- 双势方法
Abstract: Rubber material is widely used in practical engineering due to its good seismic and energy absorption effect. However, the collision of hyperelastic materials is a strong nonlinear problem. It is of great significance to analyze the contact collision and large deformation of hyperelastic materials to improve the buffering performance of the device. The smoothed finite element method (S-FEM) is a weak form of numerical calculation method. Compared with the traditional finite element method, the smoothed finite element method has low requirements on the mesh quality, allows the element to undergo large deformation during the calculation process, where the construction of the smooth domain is more flexible. The S-FEM has high accuracy without additional degrees of freedom. Based on the S-FEM, the double potential method was applied to contact calculation, with both advantages of the S-FEM in calculating large deformation problems and advantages of the double potential method in solving contact force fully used. In comparison with the numerical results of finite element software MSC. Marc, the results of the proposed algorithm were verified with high accuracy and good energy conservation, and the effects of the friction coefficient on the collision body were analyzed.
- contact /
- large deformation /
- hyperelastic material /
- smoothed finite element method /
- bi-potential theory
edited-by

edited-by
注释:

1) (我刊编委冯志强来稿)

HTML全文

图 1 碰撞模型示意图

Figure 1. Schematic diagram of the collision model

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图 2 Coulomb摩擦锥

Figure 2. Coulomb's frictional cone

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图 3 四边形单元划分光滑域个数

Figure 3. Numbers of smooth domains to be divided

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图 4 有限元背景网格被划分为4个光滑域

Figure 4. The finite element background mesh divided into 4 smooth domains

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图 5 超弹性体的碰撞模型

Figure 5. The collision model for hyperelastic bodies

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图 6 3种工况下的von Mises应力图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. The von Mises stress contours for 3 conditions

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图 7 与MSC.Marc的一致性对比

Figure 7. Conformity comparison with MSC.Marc

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图 8 摩擦因数对点O位移、速度的影响

Figure 8. Effects of the friction coefficient on displacements and velocities of point O

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图 9 超弹性体碰撞模型

Figure 9. The collision model for hyperelastic bodies

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图 10 各个时刻下的von Mises应力图

Figure 10. The von Mises stress diagrams at various moments

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图 11 接触带1的节点位移-时间历程图

Figure 11. Nodal displacement-time histories for contact zone 1

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图 12 与MSC.Marc的一致性对比

Figure 12. Conformity comparison with MSC.Marc

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图 13 两个小球碰撞模型图

Figure 13. The model for 2 colliding balls

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图 14 接触带1-2的节点位移-时间历程图(V_{y0, L}=-20 m/s，V_{y0, R}=-20 m/s)

Figure 14. Nodal displacement-time histories of contact zones 1-2 (V_{y0, L}=-20 m/s, V_{y0, R}=-20 m/s)

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图 15 Von Mises应力图(V_{y0, L}=-20 m/s，V_{y0, R}=-20 m/s)

Figure 15. The von Mises stress contour (V_{y0, L}=-20 m/s, V_{y0, R}=-20 m/s)

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图 16 与MSC.Marc的一致性对比(V_{y0, L}=-20 m/s，V_{y0, R}=-20 m/s)

Figure 16. Conformity comparison with MSC.Marc(V_{y0, L}=-20 m/s, V_{y0, R}=-20 m/s)

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图 17 接触带1-2的节点位移-时间历程图(V_{y0, L}=-20 m/s，V_{y0, R}=-10 m/s)

Figure 17. Nodal displacement-time histories for contact zones 1-2(V_{y0, L}=-20 m/s, V_{y0, R}=-10 m/s)

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图 18 Von Mises应力图(V_{y0, L}=-20 m/s，V_{y0, R}=-10 m/s)

Figure 18. The von Mises stress contour (V_{y0, L}=-20 m/s, V_{y0, R}=-10 m/s)

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图 19 与MSC.Marc的一致性对比(V_{y0, L}=-20 m/s，V_{y0, R}=-10 m/s)

Figure 19. Conformity comparison with MSC.Marc(V_{y0, L}=-20 m/s, V_{y0, R}=-10 m/s)

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表 1 不同摩擦因数不同时刻下的3种工况

Table 1. Three conditions at different moments with different friction coefficients

condition	the moment the ball reaches the lowest point T/ms	σ_max/Pa
① μ=0.0	0.87	8.32E6
② μ=0.2	0.70	4.37E6
③ μ=0.4	0.61	4.22E6

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表 2 计算效率对比结果

Table 2. Comparison results of calculation efficiency

	time integration method	contact algorithm	total CPU T_CPU/s
MSC.Marc	Newmark implicit	penalty	9.48
FEM	1st-order implicit	bi-potential	20.1
CSFEM-1SD	1st-order implicit	bi-potential	9.887
CSFEM-2SD	1st-order implicit	bi-potential	11.058
CSFEM-3SD	1st-order implicit	bi-potential	12.415
CSFEM-4SD	1st-order implicit	bi-potential	13.495
CSFEM-8SD	1st-order implicit	bi-potential	17.627
CSFEM-16SD	1st-order implicit	bi-potential	26.314

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