NONLINEAR FINITE ELEMENT ANALYSIS OF BENDING OF STRAIGHT BEAMS USING HP-SPECTRAL APPROXIMATIONS
NONLINEAR FINITE ELEMENT ANALYSIS OF BENDING OF STRAIGHT BEAMS USING HP-SPECTRAL APPROXIMATIONS
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发表时间：
2011-03
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通讯作者：
R. Ranjan
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作者：
R. Ranjan
用传统的有限元插值法(即Hermite三次或等间距拉格朗日函数)建立了各种梁理论的位移有限元模型。各种梁的有限元模型在用于横向挠度w、总转动φ和/或剪切应变γXz的内插函数的选择或用于建立有限元模型的积分形式(例如，弱形式或最小二乘法)方面彼此不同。本文研究了利用超谱节点展开来消除剪切和膜锁定的交替梁有限元的发展。对所研究的梁理论分别采用位移有限元模型和混合有限元模型进行了线性和非线性分析。将所得结果与文献中的解析(级数)解和非线性有限元解进行了比较，发现它们在所有情况下都有很好的一致性。©2011 IAU，阿拉克分会。版权所有。
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form used (e.g., weak form or least-squares) to develop the finite element model. The present study is concerned with the development of alternative beam finite elements using hpspectral nodal expansions to eliminate shear and membrane locking. Both linear and non-linear analysis are carried out using both displacement and mixed finite element models of the beam theories studied. Results obtained are compared with both analytical (series) solutions and nonlinear finite element solutions from literature, and excellent agreement is found for all cases. © 2011 IAU, Arak Branch. All rights reserved.