Beam p-version finite element for geometrically non-linear vibrations in space

J.R. Fonseca; P. Ribeiro

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Beam p-version finite element for geometrically non-linear vibrations in space

机译：空间中几何非线性振动的梁p型有限元

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摘要

A beam p-version, hierarchical finite element for geometrically non-linear vibrations in space is presented. Stresses are obtained by adding the effects of traction, torsion and bending. A simplified version of Green's strain tensor and the generalised Hooke's law are used. The mass and stiffness matrices are obtained by the principle of the virtual work, and the ensuing non-linear equations of motion are solved by Newmark's method. Some examples of linear spacial motion and non-linear planar motion are tested, in order to verify the element derived, and it is demonstrated that this element requires a small number of degrees of freedom for accuracy. Non-linear vibrations in space are then studied.

机译：提出了一种用于空间中几何非线性振动的梁式p版本分层有限元。应力是通过增加牵引力，扭转力和弯曲力来获得的。使用格林应变张量的简化版本和广义的胡克定律。通过虚拟功的原理获得质量和刚度矩阵，并通过纽马克方法求解随之产生的非线性运动方程。为了验证派生的元素，测试了线性空间运动和非线性平面运动的一些示例，并证明了此元素需要少量的自由度以确保准确性。然后研究空间中的非线性振动。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2006年第12期|p.905-924|共20页
作者
J.R. Fonseca; P. Ribeiro;
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作者单位

Department of Mechanical Engineering, University of Wales Swansea, Swansea SA2 8PP, United Kingdom;

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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
中图分类自动化基础理论;工程基础科学;
关键词
p-version; hierarchical finite element; 3D beam; non-linear; vibrations;

机译：p版本;分层有限元;3D梁;非线性;振动;

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专利

1. A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams [J] . Ribeiro P International Journal for Numerical Methods in Engineering . 2004,第15期

机译：用于弯曲梁几何非线性振动的p版本一阶剪切变形有限元
2. Flexural and torsional non-linear free vibrations of beams using a p-version finite element [J] . R. Lopes Alonso, P. Ribeiro Computers & Structures . 2008,第11a12期

机译：使用p型有限元的梁的挠曲和扭转非线性自由振动
3. Elasto-plastic and geometrically nonlinear vibrations of beams by the p-version finite element method [J] . Ribeiro P., van der Heijden G.H.M. Journal of Sound and Vibration . 2009,第1a2期

机译：p型有限元方法对梁的弹塑性和几何非线性振动
4. NATURAL FREQUENCIES OF ROTATING CANTILEVER FLEXIBLE BEAMS BY USING THE p-VERSION OF THE FINITE ELEMENT METHOD [C] . . 2004

机译：有限元法的p版本旋转悬臂柔性梁的固有频率
5. Free vibration analysis of tapered composite beams using hierarchical finite element method. [D] . Chen, Lin. 2005

机译：渐进式组合梁的自由振动分析，采用层次有限元法。
6. A Co-Rotational Based Anisotropic Elasto–Plastic Model for Geometrically Non-Linear Analysis of Fibre Reinforced Polymer Composites: Formulation and Finite Element Implementation [O] . Aamir Dean, Nabeel Safdar, Raimund Rolfes 2019

机译：基于比例关系的各向异性弹塑性模型用于纤维增强聚合物复合材料的几何非线性分析：配方和有限元实现
7. Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces Part II : Optimal rate of convergence of the p-version finite element solutions [O] . I. Babuska, Benqi Guo 1999

机译：加权Besov空间框架中有限元方法的p-版本的正反逼近定理第二部分：p-型有限元解的最优收敛速度
8. Solution of geometrically nonlinear statics problems by the p-version of the finite element method [R] . Szabo, Barna A. 1991

机译：用有限元方法求解几何非线性静力学问题

Beam p-version finite element for geometrically non-linear vibrations in space

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