线弹性动力场中的守恒方程及路径无关积分

CONSERVATION LAWS AND PATH-INDEPENDENT INTEGRAL IN LINEAR ELASTODYNAMICS

运用分析动力学中Ｊａｃｏｂｉ积分和循环积分概念以及Ｅｓｈｅｌｂｙ根据电磁场中能量矩概念而在弹性力学中提出的具有明确物理意义的弹性能量矩概念，推导了线弹性动力场中的各类守恒方程，并运用其得到了线弹性介质中二维裂纹等速自相似扩展中的各类路径无关积分。

Motivated by concepts of Jacobi integral and cyclic integral in analytical mechanics andEshelby's elastic energy-momentum tensor, the paper gets the conservation laws and newdual conservation laws in elastodynamics, by which the path-independent integrals are givenfor the case that crack self-similarly grows at constant speed in linear elastic media.