直接对基于FFT的计算微力学施加迪里克莱特边界条件
Lennart Risthaus1, Matti Schneider1,2
1Institute of Engineering Mathematics, University of Duisburg-Essen, Essen, Germany.
Computational mechanics
|October 28, 2024
概括
这项研究引入了一种新的方法,可以在机械问题的计算同质化中直接施加迪里克莱特边界条件. 该技术通过避免复杂的配方来提高效率,并与现有的快速里埃转换 (FFT) 代码无集成.
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
- 数字分析 数字分析
背景情况:
- 计算同质化通常使用周期边界条件与快速里埃变换 (FFT) 方法.
- 对于特定的机械和热应用,强加迪里克莱特或诺曼边界条件至关重要.
- 机械均化中的迪里克莱特边界条件的现有方法 (拉格朗日乘数,缓冲区) 损害了计算效率.
研究的目的:
- 开发一种直接方法,在基于FFT的计算均化机制中强加迪里克莱特边界条件.
- 克服现有方法的局限性,这些方法不利用FT的计算优势.
- 将新方法集成到现有的计算同质化框架中.
主要方法:
- 开发了针对矩形域上的迪里克莱特边界条件量身定制的Moulinec-Suquet离散式.
- 使用基于变形梯度和向量拉普拉斯的格林运算子的公式.
- 在边界点使用精心挑选的权重,直接施加条件.
主要成果:
- 介绍了一种新的技术,可以在没有无限系统的情况下直接施加迪里克莱特边界条件.
- 该方法被证明与离散的正弦/正弦变换兼容,使其能够与基于FFT的代码无集成.
- 数字示例验证了拟议方法的有效性和能力.
结论:
- 介绍的技术提供了一种有效和直接的方式来处理机械计算同质化中的迪里克莱特边界条件.
- 这种进步保留了基于FFT的方法的计算优势,使它们变得更加通用.
- 该方法已准备好集成到现有的计算同质化软件中.
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