地震分析中的人工边界及其在LS-DYNA中的实现

 地震分析中的局部人工边界由于具有易于实现、稳定性较好的特点，目前在时域有限元法中得到广泛应用。基于球坐标系的膨胀波(P波)和剪切波(S波)理论，引入无限介质线弹性本构关系，并采用多个平面子波和远场散射波混合透射，推导一种新的三维黏弹性人工边界方程。在有限元分析中采用边界单元作等效处理，并将地震加速度记录转化为基底边界单元上的等效节点力进行输入，建立一种新的地震反应数值模拟技术。最后以人防工程结构的地震分析为例，利用有限元软件LS-DYNA分析弹性边界、透射边界及黏弹性边界对计算结果的影响。数值模拟表明，黏弹性人工边界简单实用，可解决地震动输入和自由场响应模拟问题，能更好地模拟人工边界外半无限介质的弹性恢复性能和能量辐射作用，并验证其有效性。

ARTIFICIAL BOUNDARY FOR SEISMIC ANALYSIS AND ITS APPLICATIONS IN LS-DYNA

Local artificial boundary of seismic analysis is widely used in time-domain finite element method for its good feasibility and high numerical stability. A new equation for three-dimensional viscoelastic artificial boundary based on the theories of expansion wave(P-wave) motion and shear wave(S-wave) motion in spherical coordinate system is presented by introducing the constitutive relation of linear elastic infinite media and mixing the planar waves and the far-field scattered waves. A new numerical simulation technology for seismic responses is developed by introducing the equivalent boundary element into the finite element method and translating the seismic acceleration into the equivalent nodal force of boundary element on the bottom of the model. Finally,as a numerical example of seismic analysis for civil defense structure,the influences of elastic,transmission,viscoelastic boundary on the results are conducted by LS-DYNA. It is indicated that the viscoelastic artificial boundary is simple and can be easily used. The problems of seismic input and simulation of ground response are solved,and the elastic resume capability and energy radiation effectiveness of half infinite media outside the artificial boundary can be simulated very well. The validity of the proposed method is verified by the numerical example.