三维固体稳态传热问题的等几何分析

Isogeometric Analysis for Steady-State Heat Transfer in Three-Dimensional Solid Problems

摘要: 在芯片微电子、增材制造等领域的机械结构设计中，设备的工作温度往往会影响整体性能，而等几何分析方法作为近年来比较热门的新型数值计算方法，在动力学以及流体力学领域已有部分应用。本文尝试发挥等几何分析不会损失几何精度的特点推展到三维稳态传热分析问题，利用多片拼接NURBS体参数化模型实现几何的多样性，并提出了对三维空间的等几何方式离散，以及对热传导及热对流两种状态下的数值分析结果。实验结果表明等几何分析法在大幅提高计算小效率的同时，在传热分析计算精度上能够等效于传统有限元方法。

Abstract: In the mechanical structure design of chip microelectronics, additive manufacturing and other fields, the working temperature of the equipment often affects the overall performance. The iso-metric analysis method, as a popular new numerical calculation method in recent years, has been partially applied in the field of dynamics and fluid mechanics. In this paper, this paper attempts to extend the characteristics of isometric analysis without loss of geometric accuracy to the three- di-mensional steady-state heat transfer analysis problem, uses multi-piece splicing NURBS body par-ametric model to achieve geometric diversity, and proposes the discretization of isogeometric methods in three-dimensional space and the numerical analysis results in heat conduction and heat convection. Experimental results show that the isometric analysis method can be equivalent to the traditional finite element method in terms of calculation accuracy of heat transfer analysis while greatly improving the calculation efficiency.