A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis
A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis
复制标题
DOI：
10.1007/s00707-015-1547-4
复制
发表时间：
2016-01
期刊：
影响因子：
2.7
通讯作者：
Chien H. Thai;A. Ferreira;M. Abdel Wahab;H. Nguyen-Xuan
中科院分区：
文献类型：
--
作者：
Chien H. Thai;A. Ferreira;M. Abdel Wahab;H. Nguyen-Xuan
本文提出了复合材料层合板和夹层板的广义分层高阶剪切变形理论。我们利用高阶剪切变形理论，在每一层，这样的连续性的位移和横向剪应力层界面处的保证。由于加强了位移和横向剪应力的连续性，在一个内部层流层，最小数量的变量被保留从本理论与其他分层理论相比。该方法只需要五个变量，从一阶和高阶剪切变形理论得到的相同。与基于等效单层的剪切变形理论相比，本理论能够得到更高精度的层内剪应力。板的上下表面满足横向剪应力自由边界条件，不需要任何剪切修正系数。从Galerkin弱形式导出离散的系统方程，并通过等几何分析（伊加）得到解。离散形式要求横向位移的C1连续性，因此伊加中的NURBS基函数自然保证了这一条件。研究了不同几何形状、纵横比、刚度比和边界条件的复合材料层合板和夹层板。所得到的结果进行了比较与三维弹性解，解析解以及基于各种板理论的数值解。
This paper presents a generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates. We exploit a higher-order shear deformation theory in each layer such that the continuity of the displacement and transverse shear stresses at the layer interfaces is ensured. Thanks for enforcing the continuity of the displacement and transverse shear stresses at an inner-laminar layer, the minimum number of variables is retained from the present theory in comparison with other layerwise theories. The method requires only five variables, the same as what obtained from the first- and higher-order shear deformation theories. In comparison with the shear deformation theories based on the equivalent single layer, the present theory is capable of producing a higher accuracy for inner-laminar layer shear stresses. The free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate are fulfilled without any shear correction factors. The discrete system equations are derived from the Galerkin weak form, and the solution is obtained by isogeometric analysis (IGA). The discrete form requires the C1continuity of the transverse displacement, and hence NURBS basis functions in IGA naturally ensure this condition. The laminated composite and sandwich plates with various geometries, aspect ratios, stiffness ratios and boundary conditions are studied. The obtained results are compared with the 3D elasticity solution, the analytical as well as numerical solutions based on various plate theories.