用渐近变分法对复合材料层合板简化数值建模及仿真

Simplified numerical modeling and simulation of composite laminated plates by the variational asymptotic method

为有效分析三维复合材料层合板非线性、单向耦合弹性问题,基于渐近变分方法构建单斜对称的复合材料层合板的简化模型。推导了基于旋转张量分解概念的复合材料层合板能量表达式;利用渐近变分法将三维层合板严格拆分为二维板分析和沿法线方向的一维非线性分析;进行了降维后近似能量推导及reissner形式转换;提供了三维场重构关系以得到沿厚度方向的准确应力分布。通过对一具有四层复合层合板的柱形弯曲算例表明:基于该理论和重构过程开发的渐近变分程序VAPAS重构生成的三维应力场精确性较古典层合理论更好,与三维有限元精确解相一致。

This paper develops a simplified model for composite laminated plates by the variational asymptotic method（VAM） in order to efficiently analyze the nonlinear,one-way couples problem.It deduced the 3D energy expressions based on the decomposition of rotation tensor（DRT）.The 3D laminated plate model is decomposed into a 2D plate analysis and a non-linear 1D analysis along the normal direction.The approximate energy after dimensionality reduction was deduced and converted to a form of reissner model.The 3D field recovery relations are provided to obtain accurate stress distribution through the thickness direction.The cylindrical bending example of 4-layer composite plate shows that the 3D stress fields recovered by this theory have better accuracy than those by the classic laminated theory（CLT）,which indicates the validity of this model.