边界元法中对称面条件处理的场点映射法

本文充分利用了格林函数本身的对称性和互易性,建立了更完善、更有效的对称面条件处理的场点映射法.它用对称面把物体分成基本体和非基本体,通过作场点 p 关于对表面的映射,来正确反映非基本体的影响,计算仅需离散基本体的原有物体表面(不包含对称面).与其他方法相比,本方法不受无限域的影响,不会带来附加的奇异性和新的棱边角点;仅与场点有关而与单元特性无关,因此,完全适合在高阶边界元中使用.

Field Point Reflection Approach for Utilizing Symmetry Conditons in Boundary Element Methods

Compared with other approahes,a bettes approach,the field point reflection approah,which makes full use of the symmetric and reciprocal properties of the Green's functions is proposed.In this appro- ach the structure is divided into a pasic part and a complementary part by the symmetry planes.By reflecting the field points on the basic part about the symmetry planes,the effect or the behavior of the complementary part of the structure can be examined exactly.Therefore,only the surface of the basic part excluding the symmetry planes needs to be discretized.Different from other approaches,there are no additional singularities,edges and corners being introduced.This new approach is not restraind by infinite domains,and it allows an easy implementation of higher order boundary elements.