基于边界面法的完整实体应力分析理论与应用

提出基于边界面法（Boundary Face Method,BFM）的完整实体应力分析方法.在该分析中,避免对结构作几何上的简化,结构的所有局部细节都按实际形状尺寸作为三维实体处理.以边界积分方程为理论基础的BFM是完整实体应力分析的自然选择.在该方法中,边界积分和场变量插值都在实体边界曲面的参数空间里实现.高斯积分点的几何数据,如坐标、雅可比和外法向量都直接由曲面算得,而不是通过单元插值近似获得,从而避免几何误差.该方法的实现直接基于边界表征的CAD模型,可做到与CAD软件的无缝连接.线弹性问题的应用实例表明,该方法可以简单有效地模拟具有细小特征的复杂结构,并且计算结果的应力精度比边界元法（Boundary Element Method,BEM）和有限元法（Finite Element Method,FEM）高.

Theory and application of stress analysis on complete solids based on boundary face method

The method of stress analysis on complete solids based on Boundary Face Method(BFM) is proposed. Without any geometric simplification of a structure, the analysis takes into account all local and small features of the structure according to their real shapes and sizes. BFM which is based on boundary integral equations is a natural choice for implementation of the complete solid stress analysis. In the BFM, both boundary integration and interpolation of field variables 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 out normals are calculated directly from the faces rather than from element interpolation, and thus the geometric errors can be avoided. The method can seamlessly interact with CAD software, because it is implemented by making direct use of a CAD model through its boundary representation data. The applications on linear elastic problem indicate that the proposed method has more accurate precision of stress and is more effective and easier to use than the traditional Boundary Element Method(BEM) and Finite Element Method(FEM) for simulation on complex structure with small features.