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Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates

机译：用于多层复合板静，自由振动分析的分层混合最小二乘有限元模型

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摘要

Layerwise finite element models are developed based on a mixed least-squares formulation for both static and free vibration analysis of multilayered composite plates. The models assume a layerwise variable description of displacements, transverse stresses and in-plane strains, taken as independent variables. Altogether, the benefits of this finite element formulation are twofold. First, the layerwise mixed formulation enables the fulfilment of the so-called C_z~0 requirements, completely and a priori. Specifically, the interlaminar continuity of displacements and transverse stresses, due to compatibility and equilibrium conditions, are both in the form of C~0 continuous functions in the thickness z-direction. Second, the least-squares formulation leads to a variational unconstrained minimization problem, where the finite element approximating spaces can be chosen independently. Therefore, contrary to mixed weak form models, the mixed least-squares models are able to by-pass stability conditions, also known as inf-sup conditions. Ultimately, the model for static analysis yields a symmetric positive definite system of linear equations, whereas the model for free vibration analysis yields a symmetric quadratic eigenvalue problem. The numerical examples show that the models predictive capabilities are in excellent agreement with three-dimensional exact solutions, from very thick to very thin plates, and are shown to be insensitive to shear locking.
机译：基于混合最小二乘公式开发了分层有限元模型，用于多层复合板的静态和自由振动分析。这些模型假定位移，横向应力和面内应变为分层变量描述，并作为独立变量。总而言之，这种有限元公式化的好处是双重的。首先，逐层混合的配方能够完全先验地满足所谓的C_z〜0要求。具体地，由于相容性和平衡条件，位移和横向应力的层间连续性在厚度z方向上均为C〜0连续函数的形式。其次，最小二乘公式会导致变分的无约束最小化问题，其中可以独立选择有限元近似空间。因此，与混合弱形式模型相反，混合最小二乘模型能够绕过稳定性条件，也称为inf-sup条件。最终，用于静态分析的模型产生一个对称的线性方程组的正定系统，而用于自由振动分析的模型产生一个对称的二次特征值问题。数值示例表明，该模型的预测能力与从极厚​​板到极薄板的三维精确解非常吻合，并且对剪切锁定不敏感。

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  • 来源
    《Composite Structures》 |2010年第9期|2328-2338|共11页
  • 作者

    F. Moleiro; C.M. Mota Soares; C.A. Mota Soares; J.N. Reddy;

  • 作者单位

    Department of Mechanical Engineering, IDMEC/IST - Institute Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;

    rnDepartment of Mechanical Engineering, IDMEC/IST - Institute Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;

    rnDepartment of Mechanical Engineering, IDMEC/IST - Institute Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;

    Department of Mechanical Engineering, Texas A&M University, College Station, TX 77483-3123, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    layerwise theory; mixed formulation; least-squares formulation; finite element model; multilayered composite plates;

    机译：分层理论混合配方最小二乘公式;有限元模型多层复合板;

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