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为有效模拟和准确重构复合材料层合板三维应力/应变/变形场,基于变分渐近方法构建单斜对称的复合材料层合板渐近修正理论和重构关系。主要内容包括:基于旋转张量分解概念用一维广义应变和翘曲表示板的三维应变场,以考虑包括板翘曲变形在内的所有变形;基于变分渐近法将原三维问题分析严格拆分为非线性二维板分析(等效单层板模型)和沿法线方向的一维线性分析;通过层合板厚跨比和二维应变量阶数2个较小参数将应变能渐近修正到第二阶,并转换为Reissner形式以便于实际应用;利用生成的二维板变形和翘曲函数精确重构三维场。通过一具有20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一阶剪切变形理论和古典层合理论更好,与三维有限元精确解相一致。
In order to effectively simulate and accurately reconstruct the three-dimensional stress / strain / deformation field of composite laminates, the asymptotic correction theory and reconstruction relationship of monolayer symmetric composite laminates are established based on the variational asymptotic method. The main contents include: Based on the concept of rotational tensor decomposition, the one-dimensional generalized strain and warpage are used to represent the three-dimensional strain field of the plate to consider all the deformations including the plate warpage deformation; the original three-dimensional problem is analyzed strictly based on the variational asymptotic method Which is divided into nonlinear two-dimensional plate analysis (equivalent single-layer plate model) and one-dimensional linear analysis along the normal direction; through the laminate thickness ratio and two-dimensional strain order of 2 smaller parameters will strain gradually Nearly revised to the second order, and converted to Reissner form for practical application; using the generated two-dimensional plate deformation and warping function to accurately reconstruct the three-dimensional field. An example of cylindrical bending with 20-layer composite laminates shows that the accuracy of the 3D stress field generated by VAPAS reconstruction based on the asymptotic variational procedure developed by this theory and reconstruction process is more accurate than the first-order shear deformation theory and the classical layer Theory of rationality is better, consistent with the exact solution of the three-dimensional finite element.