求解含裂纹各向异性板与单向复合材料板应力强度因子的变分解法

THE VARIATIONAL METHOD TO DETERMINE THE SIF OF ANISOTROPIC PLATES AND UNIDIRECTIONAL FIBROUS COMPOSITE PLATES WITH CRACKS

  • 摘要: 本文推导了含边缘裂纹各向异性板与单向复合材料板的应力与位移的函数项级数表达式。该级数每一项均满足平衡方程、协调方程与裂纹表面静力边界条件。通过最小势能原理的变分方程来满足其余静力边界条件以确定级数中的待定系数,从而求得应力强度因子。最后,本文给出了长条板拉伸试件、紧凑拉伸试件与三点弯曲试件的计算结果。收敛是迅速的,几乎所有算例都能满足两位收敛。

     

    Abstract: The serves expressions of stresses and displace ments of both anisotropic and unidirectional fiber-reinforced com posite plates with cracks are derived.Each term of the series can satisfy the equilibrium equations,the equation of compatibility and boundary conditions of forces on the crack suifaces and other boundary conditions of forces can be satisfied by the variationat method to deter mine the stress intensity factors. Finally, the computational results about strip tension,compact tension and three point bending specimens are presented.

     

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