Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions
Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions
复制标题
DOI：
10.1007/s10409-016-0570-6
复制
发表时间：
2016-06
影响因子：
3.5
通讯作者：
Bin Huang;Ji Wang;Jianke Du;Yan Guo;T. Ma;Lijun Yi
中科院分区：
文献类型：
--
作者：
Bin Huang;Ji Wang;Jianke Du;Yan Guo;T. Ma;Lijun Yi
本文采用推广的Kantorovich方法研究了多项式应力函数下对称铺层复合材料层合板在单轴拉伸载荷作用下自由边附近的局部应力集中问题。在平面应变状态下，应力场最初由Lekhnitskii应力函数假定。应用余虚功原理，得到了耦合的常微分方程组，其中的解可以通过求解广义本征值问题来获得。然后建立一个迭代过程，以实现收敛的应力分布。值得注意的是，基于应力函数的扩展Kantorovich方法在迭代过程中可以同时满足无牵引和自由边应力边界条件。计算了自由边附近和内部区域的应力分量，并与有限元法的结果进行了比较。收敛应力的计算结果与三维有限元计算结果吻合较好。一般而言，各种铺层配置被认为是数值分析。结果表明，基于多项式应力函数的扩展Kantorovich方法能够准确有效地预测复合材料层合板的局部应力，计算效率远高于三维有限元法。
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.