一个数值框架,在连续和并行模拟中合有限元和无网格方法
Van Dung Nguyen1, Charlotte Kirchhelle2, Amir Abdollahi1
1Department of Engineering Science, University of Oxford, Oxford, UK.
Finite elements in analysis and design : the international journal of applied finite elements and computer aided engineering
|July 22, 2025
概括
本研究介绍了一种混合的有限元方法-无网格方法 (FEM-MM) 框架,以高效地模拟工程中的大型变形. 该方法通过在关键领域选择性地使用MM来平衡准确性和计算成本,从而提高可扩展性.
科学领域:
- 计算力学 计算力学 计算力学
- 工程中的数值方法.
背景情况:
- 有限元素方法 (FEM) 在大型变形问题中面临过度元素变形的挑战.
- 动态复杂化,一个常见的解决方案,受到计算费用,数值噪声和几何限制的阻碍.
- 无网格方法 (MM) 避免了网格连接问题,但与FEM相比,它们在计算上是密集的.
研究的目的:
- 提出一个新的数字框架,将FEM和MM结合起来,以有效地解决大型变形场景.
- 通过战略性地将MM仅应用于具有显著变形的区域来保持计算效率.
- 增强MM的并行化能力,以提高计算速度.
主要方法:
- 一个混合FEM-MM方案,在一个单一问题中将这两种离散方法结合在一起.
- MM适用于敏感地区,而FEM处理较少扭曲的地区.
- 一个简化的MM并行化策略,利用最大近似和域凸化.
- 一种以正方位点为驱动的方法,用于对构成模型和组装的方法不可知论性处理.
主要成果:
- 拟议的框架显示出对大型变形问题具有出色的可扩展性.
- 在模拟准确性和计算成本之间实现了有利的平衡.
- 不依赖方法的汇编和简化的并行化有助于计算效率.
结论:
- 混合FEM-MM方法为模拟大变形提供了有效的解决方案.
- 它克服了传统的FEM和计算上昂贵的MM的局限性.
- 该框架为复杂的工程模拟提供了一个计算效率高且可扩展的工具.
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