A variational method for analysis of laminates with parallel arrays of intralaminar cracks
A variational method for analysis of laminates with parallel arrays of intralaminar cracks
复制标题
分析具有平行层内裂纹阵列的层合板的变分法
DOI：
10.1002/nme.6152
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
V. Vinogradov
中科院分区：
文献类型：
--
作者：
V. Vinogradov
本文提出了一种鲁棒变分方法，用于预测具有平行但不一定共面层内裂纹的层合板的有效热弹性性能。任意层压板铺设，裂纹模式，任何平面内力和弯矩，以及温度变化都可以同时处理。该方法基于最小互补能量原理。假定允许的平面内应力分量随厚度呈线性关系。导出了裂纹层合板的有效柔度矩阵、热膨胀和曲率以及比热的简单矩阵表达式。杨氏模量、泊松比、剪切模量、弯曲刚度和热膨胀作为各种对称和非对称层合板裂纹密度的函数的预测与七项独立发表的研究的实验结果非常吻合。该方法的准确性和鲁棒性得到了不需要实验拟合参数的补充。结果表明，同样的形式可以应用于分析闭合的层内裂缝，以及裂缝的非均匀和非对称分布。
This paper presents a robust variational method for prediction of the effective thermoelastic properties of laminates with parallel, but not necessarily coplanar intralaminar cracks. Arbitrary laminate layup, crack patterns, and any in‐plane forces and bending moments, and temperature change can be treated simultaneously. The method is based on the principle of minimum complementary energy. The admissible in‐plane stress components are assumed to be linear through the ply thickness. Simple matrix expressions are derived for the effective compliance matrix, thermal expansions and curvatures, and specific heat of a cracked laminate. Predictions for the Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of crack density for various laminates of symmetric and nonsymmetric layups demonstrated excellent agreement with experimental results of seven independently published studies. Accuracy and robustness of the method are complemented by the fact that no experimentally fitted parameters are required. It is shown that the same formalism can be applied to analysis of closed intralaminar cracks, as well as nonuniform and nonsymmetrical distributions of cracks.