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

Gijun Lee; Jun-Sik Kim

doi:10.7734/COSEIK.2017.30.4.335

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2017 Vol.30, Issue 4 Preview Page Next Page

A Performance Evaluation of Beam Finite Elements with Higher-order Derivatives’ Continuity 고차미분 연속성을 가지는 유한요소 보 모델들에 대한 성능평가

2017. pp. 335-341

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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 C² and C³ 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

본 논문에서는 고차미분 연속성을 가지는 형상함수에 기초하여 오일러-베르누이 보 유한요소모델을 정식화하였으며, 다 양한 경계조건들에 대하여 그 성능을 평가하였다. 이러한 유한요소 모델들은 새로이 개발되는 고차 보 이론들과 논로컬 탄 성이론에 기초한 보 이론들의 유한요소해석에 필요하다. 그러나 고차 연속성을 가지는 유한요소에 대한 성능평가는 문헌에 서 찾아보기 어렵다. 따라서 본 연구에서는 C² 및 C³ 두 종류의 고차 유한요소들을 정식화하여 외팔보, 단순지지, 고정-힌 지 등의 경계조건들을 적용하고 정적해석을 수행하였다. 고전적인 경계조건들 이외에도 고차 경계조건들이 보의 거동에 미 치는 영향을 비교분석하였다. 경계조건에 따라서는 처짐의 미분 값들이 경계주변에서 진동하는 현상이 관찰되었으며, 이는 기하학적 경계조건들에 대하여 뚜렷이 나타난다. 특히 고정단과 같은 경계에서의 변위의 고차미분 조건은 이러한 불안정한 현상을 유발한다. 본 연구에서 얻어진 결과들은 고차 미분 연속성을 가지는 유한요소 이용에 가이드라인으로서 역할을 할 수 있을 것으로 기대된다.

키워드

고차미분 연속성 요소

오일러-베르누이 보 모델

유한요소해석

References

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 30
No :4
Pages :335-341
Received Date : 2017-06-24
Revised Date : 2017-07-18
Accepted Date : 2017-07-19
DOI :https://doi.org/10.7734/COSEIK.2017.30.4.335

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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References