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http://dx.doi.org/10.7734/COSEIK.2017.30.4.335

A Performance Evaluation of Beam Finite Elements with Higher-order Derivatives' Continuity  

Lee, Gijun (Department of Mechanical System Engineering, Kumoh National Institute of Technology)
Kim, Jun-Sik (Department of Mechanical System Engineering, Kumoh National Institute of Technology)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.30, no.4, 2017 , pp. 335-341 More about this Journal
Abstract
In this paper, beam finite elements with higher-order derivatives' continuity are formulated and evaluated for various boundary conditions. All the beam elements are based on Euler-Bernoulli beam theory. These higher-order beam elements are often required to analyze structures by using newly developed higher-order beam theories and/or non-classical beam theories based on nonlocal elasticity. It is however rare to assess the performance of such elements in terms of boundary and loading conditions. To this end, two higher-order beam elements are formulated, in which $C^2$ and $C^3$ continuities of the deflection are enforced, respectively. Three different boundary conditions are then applied to solve beam structures, such as cantilever, simply-support and clamped-hinge conditions. In addition to conventional Euler-Bernoulli beam boundary conditions, the effect of higher-order boundary conditions is investigated. Depending on the boundary conditions, the oscillatory behavior of deflections is observed. Especially the geometric boundary conditions are problematic, which trigger unstable solutions when higher-order deflections are prescribed. It is expected that the results obtained herein serve as a guideline for higher-order derivatives' continuous finite elements.
Keywords
higher-order derivatives' continuity; euler-bernoulli beam theory; finite element method;
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Times Cited By KSCI : 5  (Citation Analysis)
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