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Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements

机译：基于两个新的基于位移的四边形板单元的层合板几何非线性分析

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摘要

Two simple displacement-based 4-node quadrilateral elements RDKQ-NL20 and RDKQ-NL24 are developed in this paper for geometrically nonlinear analysis of thin to moderately thick laminated composite plates. The proposed quadrilateral nonlinear laminated composite plate elements are based on the first-order shear deformation theory (FSDT) and von-Karman's large deflection theory, and the total Lagrangian approach is employed to formulate the elements. The deflection and rotation functions of the element boundary are obtained from Timoshenko's laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates. The linear displacement interpolation functions of the standard 4-node quadrilateral isoparametric plane element and the in-plane displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements of elements RDKQ-NL20 and RDKQ-NL24, respectively. The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that they are accurate and efficient for large deformation, small rotation nonlinear analysis of thin to moderately thick laminated composite plates.
机译：本文开发了两个简单的基于位移的4节点四边形元素RDKQ-NL20和RDKQ-NL24，用于对薄至中厚层压复合板进行几何非线性分析。所提出的四边形非线性叠层复合板单元是基于一阶剪切变形理论（FSDT）和冯-卡尔曼的大挠度理论，并采用总拉格朗日方法来公式化。元素边界的偏转和旋转函数是从Timoshenko的叠层复合梁函数获得的，因此从理论上可以确保非常薄的叠层的会聚。将标准4节点四边形等参平面元件的线性位移插值函数和具有钻削自由度的四边形平面元素的面内位移函数视为元素RDKQ-NL20和RDKQ-NL24的面内位移，分别。开发的元件配方简单，没有剪切锁定，并且具有常规的工程自由度。数值算例表明，它们对于薄至中厚层压复合板的大变形，小旋转非线性分析是准确而有效的。

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