|
|
瞬态常系数热传导问题的等几何边界元法研究
|
Abstract:
等几何边界元法(IGABEM)在温度场方面的应用研究是边界元法的重要应用之一，相比于传统边界元法，等几何边界元通过样条函数进行几何与物理场的插值近似，可有效降低传统边界元中的离散误差，提高计算精度，因而被广泛应用于数值分析中。采用径向基方法将含有时间梯度域积分项转化成边界积分，并采用NURBS进行几何插值，保持结构外形的精确。通过算例，对比传统BEM与IGABEM的计算结果，验证该算法的正确性与有效性。
The application of isogeometric boundary element method (IGABEM) in the temperature field is one of the important applications of the boundary element method. Compared with the traditional boundary element method, the isogeometric boundary element uses the spline function to perform geometric and physical field interpolation approximation. It can effectively reduce the discrete error in the traditional boundary element and improve the calculation accuracy, so it is widely used in numerical analysis. Radial basis method was used to transform the integral term with time gradient domain into boundary integral, and NURBS was used for geometric interpolation to maintain the precise shape of the structure. Through numerical example, the calculation results of traditional BEM and IGABEM are compared to verify the correctness and effectiveness of the algorithm.
| [1] | 公颜鹏. 等几何边界元法的基础性研究及其应用[C]. 北京: 北京理工大学, 2019. |
| [2] | 刘程. 等几何边界元在声学结构敏感度分析及其形状优化设计中的应用[D]: [硕士学位论文]. 合肥: 中国科学技术大学, 2017: 2-3. |
| [3] | 高效伟, 王静, 等. 高等边界元法理论与程序[M]. 北京: 科学出版社, 2015: 18-22. |
| [4] | 王静. 飞行器热防护系统典型热结构热分析边界元算法研究[D]: [博士学位论文]. 南京: 东南大学, 2011: 28-29, 128-129. |
| [5] | 陈磊磊, 卢闯, 徐延明, 赵文畅, 陈海波. 细分曲面边界元法的黏附吸声材料结构拓扑优化分析[J]. 力学学报, 2019, 51(3): 884-893. |
| [6] | Gao, X.W. and Davies, T.G. (2002) Boundary Element Programming in Mechanics. Cambridge University Press, Cambridge. |
| [7] | Chen, L.L., Liu, C., Zhao, W.C. and Liu, L.C. (2018) An Isogeometric Approach of Two Dimensional Acoustic Design Sensitivity Analysis and Topology Optimization Analysis for Absorbing Material Distribution. Computer Methods in Applied Mechanics and Engineering, 336, 507-532. https://doi.org/10.1016/j.cma.2018.03.025 |
