中文摘要：

扩大 Kantorovich 方法被采用在免费的边的附近学习本地压力集中在相称性地分层合成把压成薄片在多项式压力功能之上使遭到了到单轴的张力的负担。压力领域开始在飞机紧张状态下面借助于 Lekhnitskii 压力功能被假定。使用互补虚拟工作的原则，联合平常的微分方程在答案能被解决一个概括特征值问题在哪个获得被获得。然后，一个反复的过程被建立完成会聚的压力分布。压力函数基于扩大 Kantorovich，这应该被注意方法能两个都在反复的进程期间满足没有拖拉、免费的边压力边界条件。免费的边附近并且在内部区域的压力部件被计算并且由有限元素方法与那些相比获得了结果(女性) 。会聚的压力有好协议，那些结果获得了由三维(3D ) 女性。为概论，各种各样的 layup 配置为数字分析被考虑。建议多项式压力功能基于的结果表演扩大了 Kantorovich 方法在预言本地压力在精确、有效合成把压成薄片并且计算地比 3D 更有效女性。

英文摘要：

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.