使用扩展的有限元素方法来解决裂演变的改进
Yuxiao Wang1, Akbar A Javadi2, Corrado Fidelibus3
1Department of Engineering, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, United Kingdom.
Scientific reports
|November 6, 2024
概括
扩展有限元法 (XFEM) 有效地模拟了裂的生长. 这项研究通过优化元素细分和高斯点分布来提高XFEM的准确性和效率,用于裂分析.
科学领域:
- 计算力学 计算力学 计算力学
- 材料科学 材料科学 材料科学
- 断裂力学 断裂力学 断裂力学
背景情况:
- 扩展有限元法 (XFEM) 是一个强大的工具,可以模拟裂演变而无需网状精细化.
- 然而,XFEM中的近似可以导致节点位移的不准确,特别是在裂纹尖端附近.
- 提高XFEM的计算效率和准确性仍然是一个活跃的研究领域.
研究的目的:
- 在数学上研究和提高 eXtended Finite Element Method (XFEM) 的解决方案效率.
- 为了确定XFEM模拟中节点位移差异的原因.
- 建议和验证使用XFEM进行准确和高效的裂分析的改进.
主要方法:
- 对XFEM解决过程进行全面的数学分析,重点关注全球刚度矩阵.
- 开发了两种新的改进策略:基于高斯点分布和最佳高斯点确定的元素细分.
- 建议改进的应用与压力强度因子计算的相互作用积分方法.
- 对分析和标准XFEM解决方案进行数值验证.
主要成果:
- 结节位移的不一致性被确定并归因于XFEM近似.
- 提出的元素细分和最佳高斯点分配的方法显著提高了准确性.
- 增强的XFEM方法,结合交互积分方法,减少了计算时间,并消除了表面引的影响.
- 与标准XFEM相比,经验证的数值结果显示了更高的准确性和效率.
结论:
- 提议的改进有效地解决了XFEM在裂模拟中的精度限制.
- 优化元素细分和高斯点策略可以提高计算效率和解决方案精度.
- 精细的XFEM方法为破裂力学分析提供了更可靠,更快的方法.
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