Aim to establish the path independent integral and its dual form of energy type, and to determine the singularity order of stresses near the crack tip in plane quasicrystals.
目的建立平面准晶中能量型路径守恒积分及其对偶形式，并确定准晶裂纹体裂尖应力奇异性阶数。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
OK, so the proof, so just going to prove that the line integral is path independent; the others work the same way.
那么这个证明，只需证出线积分与路径无关的，其它的也是用同样的方法。
We say that the line integral is path independent.
我们称之为线积分与积分路径无关。
In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized.
本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。
The J integral is path-independent for the short time creep and long one, while in the transition period, it is weakly path-dependent.
积分在短时蠕变和长时间蠕变条件下是路往无关的，而在过渡蠕变时期，其与路径也只是弱相关。
A path independent of the J-integral and the stress, strain on the crack tip are discussed.
讨论了J积分的路径无关性和裂尖应力，应变奇异性。
The expression of energy release rate is deduced by means of the path-independent M-integral, and corresponding numerical results are given.
利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解。
The expression of energy release rate is deduced by means of the path-independent M-integral, and corresponding numerical results are given.
利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解。
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