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基于一阶剪切变形理论(FSDT),本文构造一种新型的20自由度(每结点5个自由度),四边形复合材料层合板单元,适合于任意铺设情形的层合板的计算。它是按如下方式构造的:(1) 单元每边的转角和剪应变由Timoshenko层合厚梁理论来确定;(2) 对单元域内的转角场和剪应变场进行合理的插值;(3) 引入平面内双线性位移场来体现层合板面内与弯曲的耦合作用。本文单元,记为TMQ20,不存在剪切闭锁现象,在计算单层的各向同性板时可以退化为文[1]中优质的中厚板单元TMQ。在文[2]中将给出本文单元对于层合板问题的详细数值算例。
Based on the first-order shear deformation theory (FSDT), a new type of 20-DOF (5-DOF per node) quadrilateral composite laminate unit is constructed in this paper. It is suitable for the calculation of any laid-up laminate. It is constructed as follows: (1) The corner and shear strain on each side of the unit is determined by the Timoshenko-laminated thick beam theory; (2) a reasonable interpolation of the angular and shear strain fields within the unit domain; (3) The in-plane bilinear displacement field is introduced to reflect the coupling effect between the in-plane and the bending of the laminate. The element in this paper, denoted as TMQ20, has no shear-locking phenomenon and can be degenerated into the high-quality plate element TMQ in [1] when calculating the monolayer isotropic plate. In [2], a detailed numerical example of the laminated element problem is given in this paper.