时域边界元应力计算方法研究

Study of stress calculations in timedomain BEM analysis

为解决各向异性介质时域边界元方法中应力计算的问题，建立了各向异性介质时域边界元方法边界点及内点的应力计算方法，并从不同层次对其进行详细考察，其中，对边界点采取在边界上恢复应力张量的方法，对内点采取基于位移解的数值微分方法。应用所建立的应力计算方法，进行了两个算例的计算，结果表明，该计算方法具有较好的精度和稳定性，可用于各向异性介质的动态问题特别是波传播问题应力的分析计算。

This paper is to establish a scheme of stress calculations of timedomain boundary element method (BEM) for anisotropic media and to test it from different aspects. For stresses at boundary points, the conventional way that recovers the stress tensor at boundary is used. For stresses at internal points, the method of numerical differentiation based on displacement field is employed. This study demonstrates that the proposed method for stress calculations in timedomain BEM analysis is not only reliable but also accurate enough. It can be used in stress analysis of dynamic problems, especially of wave propagation problems for anisotropic media.