Abstract

The dynamics of buildings and structures in an earthquake zone is studied relying on a model boundary value problem describing the dynamics of an elastic punch on an elastic half-plane under diffraction and refraction of waves generated by stress release on a crack. The problem is solved by applying an explicit difference scheme constructed using the method of bicharacteristics combined with dimensional splitting. The problems of wave diffraction and refraction by an elastic inclusion in the release of vertical and shear stresses on a horizontal crack in an elastic half-plane are considered, which model the dynamics of seismic processes in the formation of mode I and II cracks. Computer experiments are performed for media with various elastic parameters and various punch–crack distances. Their results are presented in the form of oscillograms on the ground surface and the punch, as well as diffraction displacement velocity fields and stress tensor invariants in the medium and the punch.

中文翻译：

---

具有裂纹形成的弹性半平面上的弹性冲头动力学

摘要

依靠模型边界值问题研究地震带中建筑物和结构的动力学，模型边值问题描述了弹性半平面上的弹性冲头在裂纹释放应力产生的波的衍射和折射下的动力学。通过应用使用双特征方法与维数拆分方法构造的显式差异方案来解决该问题。考虑了弹性夹杂物在弹性半平面内水平裂缝中的垂直应力和切应力释放时由弹性夹杂物引起的波衍射和折射问题，该问题模拟了模式I和II裂纹形成过程中的地震过程动力学。对具有不同弹性参数和不同穿孔裂纹距离的介质进行了计算机实验。