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Boundary element method for vibration analysis of two-dimensional anisotropic elastic solids containing holes, cracks or interfaces

机译：包含孔，裂纹或界面的二维各向异性弹性固体振动分析的边界元方法

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摘要

By using the anisotropic elastostatic fundamental solutions and employing the dual reciprocity method, a special boundary element method (BEM) was developed in this paper to perform elastodynamic analysis of anisotropic elastic plates containing holes, cracks or interfaces. The system of ordinary differential equations obtained for the vibration transient analysis was solved using the Houlbolt's algorithm and modal superposition method. These equations were reduced to the standard eigenproblem for free vibration, and a purely algebraic system of equations for steady-state forced vibration. Since the fundamental solutions used in the present BEM satisfy the boundary conditions set on the holes, cracks, or interfaces, no meshes are needed along these boundaries. With this special feature, the numerical examples presented in this paper show that to get an accurate result much fewer elements were used in the present BEM comparing with those in the traditional BEM or finite element method.
机译：通过使用各向异性弹性静力学基本解并采用双重互易方法，开发了一种特殊的边界元方法（BEM）对包含孔，裂纹或界面的各向异性弹性板进行弹性力学分析。使用Houlbolt算法和模态叠加法求解了用于振动瞬态分析的常微分方程组。对于自由振动，这些方程被简化为标准本征问题，对于稳态强迫振动，这些方程被简化为纯代数方程组。由于当前BEM中使用的基本解决方案满足了在孔，裂缝或界面上设置的边界条件，因此沿这些边界不需要网格。借助此特殊功能，本文提供的数值示例表明，与传统的BEM或有限元方法相比，要获得准确的结果，本BEM中使用的元素要少得多。

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