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C~0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

机译：基于精细曲折理论的C〜0梁单元，用于多层复合材料和夹芯层板

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The paper deals with the development and computational assessment of three- and two-node beam finite elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered composite and sandwich beams. RZT is a recently proposed structural theory that accounts for the stretching, bending, and transverse shear deformations, and which provides substantial improvements over previously developed zigzag and higher-order theories. This new theory is analytically rigorous, variationally consistent, and computationally attractive. The theory is not affected by anomalies of most previous zigzag and higher-order theories, such as the vanishing of transverse shear stress and force at clamped boundaries. In contrast to Timoshenko theory, RZT does not employ shear correction factors to yield accurate results. From the computational mechanics perspective RZT requires C~0-continuous shape functions and thus enables the development of efficient displacement-type finite elements. The focus of this paper is to explore several low-order beam finite elements that offer the best compromise between computational efficiency and accuracy. The initial attention is on the choice of shape functions that do not admit shear locking effects in slender beams. For this purpose, anisoparametric (aka interdependent) interpolations are adapted to approximate the four independent kinematic variables that are necessary to model the planar beam deformations. To achieve simple two-node elements, several types of constraint conditions are examined and corresponding deflection shape-functions are derived. It is recognized that the constraint condition requiring a constant variation of the transverse shear force gives rise to a remarkably accurate two-node beam element. The proposed elements and their predictive capabilities are assessed using several elastostatic example problems, where simply supported and cantilevered beams are analyzed over a range of lamination sequences, heterogeneous material properties, and slenderness ratios.
机译：本文基于精巧之字形理论（RZT）进行三节点和两节点梁有限元的开发和计算评估，以分析多层组合梁和夹层梁。 RZT是最近提出的一种结构理论，它考虑了拉伸，弯曲和横向剪切变形，并且相对于以前开发的之字形和高阶理论提供了实质性的改进。这个新理论在分析上很严格，在变化上是一致的，并且在计算上很有吸引力。该理论不受大多数​​以前的锯齿形和高阶理论的异常影响，例如横向切应力和夹紧边界力的消失。与Timoshenko理论相反，RZT不使用剪切校正因子来产生准确的结果。从计算力学的角度来看，RZT需要C〜0连续的形状函数，因此可以开发有效的位移型有限元。本文的重点是探索几种在计算效率和精度之间取得最佳折衷的低阶光束有限元。最初的关注点是形状函数的选择，这些函数不允许细长梁中的剪切锁定效应。为此，非参数（也称为相互依赖）插值适用于近似建模平面光束变形所需的四个独立运动学变量。为了获得简单的两节点单元，检查了几种约束条件，并推导了相应的挠曲形状函数。已经认识到，要求横向剪切力恒定变化的约束条件产生了非常精确的两节点梁单元。拟议的元素及其预测能力是通过使用几个弹性示例问题进行评估的，其中在一系列层合顺序，异质材料特性和细长比上分析了简单支撑和悬臂梁。

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