固定边半平面体裂纹问题的超奇异积分方程法

对固定边半平面含平行于边界裂纹的问题进行研究,由固定边半平面弹性体的弹性力学基本解,利用换功定律、位移-应变关系、胡克定律及裂纹岸应力边界条件,得到描述该问题的超奇异积分方程组,并通过适当的积分变换,在有限部积分的意义下建立了相应的数值方法。对裂纹面上作用均布力情况的算例表明,固定边对应力强度因子的大小起削弱作用。

Hyper-singular integral equation method on crack in half-plane body with fixed boundary

We considered the problem of the crack parallel to the fixed boundary in a half-plane body, with the distributed loads only at the crack surface. Based on the fundamental solution of the elastic mechanics on the half-plane body with free boundary,and using Bitt's low, the stress-displacement relation, Hooke's low, and the stress boundary condition of the crack, the hyper-singular integral equations to describe this problem was \{derived\}; through suitable integral transforms, we established the corresponding numerical method, in the sense of the finite-part integral of the hyper-singular integral. Moreover, by this method, the non-dimensional stress intensity factors of the crack under the uniformly distributed loads were calculated. The result shows that the stress intensity factors are weakened close to the fixed boundary.