边界面法分析三维实体线弹性问题  

ANALYSIS OF 3D LINEAR ELASTICITY PROBLEMS DIRECTLY ON GEOMETRIC MODEL WITH THE BOUNDARY FACE METHOD

作　　者：覃先云[1] 张见明[1] 李光耀[1] 张正[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《固体力学学报》2011年第5期500-506,共7页Chinese Journal of Solid Mechanics

基　　金：国家973项目(2010CB328005);国家自然科学基金项目(10972074);湖南大学汽车车身先进设计制造国家重点实验室自主课题(60870003)资助

摘　　要：论文利用以边界积分方程为理论基础的边界面法分析三维实体的线弹性问题.在该方法中,边界积分和场变量插值都是在实体边界曲面的参数空间里进行.积分点的几何数据,如坐标、雅可比、外法向量都是直接由曲面算得,而不是通过单元插值近似,从而避免了几何误差.另外,该方法的实现是直接基于CAD模型中的边界表征数据结构,可以做到与CAD系统无缝集成.在分析中,避免对结构作几何上的简化,结构的所有局部细节都按照实际形状尺寸作为三维实体处理.应用实例表明,论文方法可以简单有效地模拟具有细小特征的复杂结构,可以直接基于三维弹性理论求解薄型壳体结构,可以获得比有限元法更精确的计算结果.This paper presents the boundary face method （BFM） based on boundary integral equations for solving 3D linear elasticity problems directly on geometric model. In the method, both boundary integration and variable approximation are performed in the parametric space of each boundary face. The geometric data at Gaussian integration points, such as the coordinates, the Jacobians and the outward normal, are calculated directly from the faces rather than from elements, and thus no geometric error will be introduced. The BFM has real potential to completely integrate with CAD system, because its implementation can be directly based on a CAD model through its boundary representation data. The structures with local small features are directly used for analysis,when all of geometry features are kept accurately according to their size in the real-world-coordinate system, instead of simplification for them. Numerical examples demonstrate that the proposed method effectively simulates thin shell based on 3D elastic theory and the complicated structure with detailed configurations in a simple way,and also provides more accurate results when compared with the finite element method （FEM）.

关 键 词：边界积分方程 边界面法 CAD模型 三维线弹性问题 

分 类 号：O343.2[理学—固体力学]