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Hybrid equilibrium finite element formulation for composite beams with partial interaction

机译：部分相互作用的复合梁混合平衡有限元公式

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摘要

Thanks to their various benefits, composite beams have been increasingly used in various applications. This study will focus on two-layer composite beams with a flexible shear interface between layers. The finite element method, in particular its displacement-based formulation, has been recognized as the most popular method for numerical analysis of composite beams. However, when applied to Timoshenko beams with partial interaction, the displacement-based formulation may suffer from the so-called shear-locking and slip-locking phenomena, leading to erroneous solutions. Hybrid and mixed finite element formulations have been viewed as competitive alternatives, since they naturally avoid locking effects. Special types of these formulations are the so-called equilibrium-based formulations, producing statically admissible solutions. This work introduces for the first time an equilibrium-based finite element formulation for the analysis of Timoshenko composite beams with partial interaction. The formulation relies on a variational principle of complementary energy involving only force/moment-like variables as fundamental unknown fields. The approximate field variables are selected such that all equilibrium equations hold in strong form. The inter-element equilibrium is enforced by resorting to the Lagrangian multiplier method. Unlike traditional displacement-based finite element formulations, the proposed scheme is naturally free from both shear-and slip-locking phenomena. The accuracy and effectiveness of the new formulation is numerically assessed through the analysis of several numerical examples. In particular, the ability of the formulation to model accurately both very flexible and very stiff shear connections is numerically shown.
机译：由于它们的各种优点，复合梁已越来越多地用于各种应用中。这项研究将集中于两层复合梁，各层之间具有灵活的剪切界面。有限元法，特别是其基于位移的公式化，已经被认为是用于复合梁数值分析的最流行方法。但是，当应用于具有部分相互作用的季莫申科梁时，基于位移的公式可能会遭受所谓的剪切锁定和滑动锁定现象，从而导致错误的解决方案。混合和混合有限元公式化已被视为竞争性替代方案，因为它们自然可以避免锁定效应。这些配方的特殊类型是所谓的基于平衡的配方，可产生静态允许的溶液。这项工作首次引入了基于平衡的有限元公式，用于分析具有部分相互作用的Timoshenko复合梁。该表述依赖于互补能量的变分原理，该互补能量仅涉及力/矩样变量作为基本未知场。选择近似场变量，以使所有平衡方程均保持强形式。通过使用拉格朗日乘数法可以强制元素间平衡。与传统的基于位移的有限元公式不同，所提出的方案自然没有剪切和滑移现象。通过分析几个数值示例，对新配方的准确性和有效性进行了数值评估。特别地，数值显示了该制剂对非常柔性和非常刚性的剪切连接两者进行精确建模的能力。

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