Extension of MITC to higher‐order beam models and shear locking analysis for compact, thin‐walled, and composite structures
Extension of MITC to higher‐order beam models and shear locking analysis for compact, thin‐walled, and composite structures
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DOI：
10.1002/nme.5588
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发表时间：
2017-05
影响因子：
2.9
通讯作者：
E. Carrera;A. G. D. Miguel;A. Pagani
中科院分区：
文献类型：
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作者：
E. Carrera;A. G. D. Miguel;A. Pagani
本文在Carrera统一列式的框架下引入了一类混合内插梁单元，以消除剪切锁定的不利影响。采用张量分量混合插值法(MITC)，利用一般的一维有限元建立了基于位移的无锁模型。采用假定的横向剪应变分布来推导虚功，并用全高斯-勒让德求积法对刚度矩阵的所有分量进行数值计算。线性、二次和三次梁单元采用统一的形式，并应用于包括紧凑结构、层合结构和薄壁结构在内的线性静力问题。对不同经典积分格式下剪切锁定对一般梁单元的影响进行了全面的研究，证明了MITC方法在解决这一数值问题方面的突出能力。利用拉格朗日和勒让德多项式实现了基于纯位移变量和广义位移变量展开的精细化梁理论，使得人们能够以类似3D的精度捕捉复杂的应力状态。在可能的情况下，将数值算例与文献中的解析解、数值解和商业软件解进行比较。结果表明，MITC单元是避免剪切闭锁的自然选择，在梁的横向剪应力计算中表现出前所未有的精度。
A class of mixed interpolated beam elements is introduced in this paper under the framework of the Carrera Unified Formulation to eliminate the detrimental effects due to shear locking. The Mixed Interpolation of Tensorial Components (MITC) method is adopted to generate locking‐free displacement‐based beam models using general 1D finite elements. An assumed distribution of the transverse shear strains is used for the derivation of the virtual work, and the full Gauss‐Legendre quadrature is used for the numerical computation of all the components of the stiffness matrix. Linear, quadratic, and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact, laminated, and thin‐walled structures. A comprehensive study of how shear locking affects general beam elements when different classical integration schemes are used is presented, evidencing the outstanding capabilities of the MITC method to overcome this numerical issue. Refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of Lagrange and Legendre polynomials over the cross‐sectional domain, allowing one to capture complex states of stress with a 3D‐like accuracy. The numerical examples are compared to analytic, numerical solutions from the literature, and commercial software solutions, whenever it is possible. The efficiency and robustness of the proposed method demonstrated throughout all the assessments, illustrating that MITC elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations.