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提出粘弹性三维轴辐射8结点无限元模型,以坐标系的z轴为极轴,以圆柱面为人工边界,用边界点的坐标和位移表示无限元内部任意点的坐标和位移。坐标映射函数和位移函数简单明了,能够方便地反映无限域内位移场的衰减特点。推导了轴辐射无限元的辐射阻尼矩阵。该模型能较好地模拟成层无限弹性体的弹性恢复力和辐射阻尼,数值计算时只需对边界进行无限元的单元划分,无需基本解。算例结果表明,文中方法具有良好的精度。
The 8-node finite element model of viscoelastic 3D-axis radiation is proposed. The z-axis of the coordinate system is the polar axis and the cylindrical surface is the artificial boundary. The coordinates and displacements of the boundary points are used to represent the coordinates and displacements of arbitrary points inside the infinite element. The coordinate mapping function and the displacement function are simple and clear, which can easily reflect the attenuation characteristics of the displacement field in the infinite domain. The radiation damping matrix of axis radiation is derived. The model can well simulate the elastic restoring force and radiation damping of infinitely elastic layered bodies. In the numerical calculation, the boundary elements need only be divided into units without any basic solution. The results show that the method in this paper has good accuracy.