Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Improvement of Euler-Bernoulli Beam Theory for Free Vibration and Buckling Analyses via Saint-Venant's Principle

생브낭 원리를 이용한 고전 보 이론의 고유진동수 및 좌굴하중 예측 개선

  • Jeong, Yong-Min (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology) ;
  • Kim, Jun-Sik (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology)
  • 정용민 (금오공과대학교 기계시스템공학과) ;
  • 김준식 (금오공과대학교 기계시스템공학과)
  • Received : 2016.01.27
  • Accepted : 2016.02.13
  • Published : 2016.04.01
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Abstract

In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.

본 논문에서는 생브낭의 원리가 근본적으로 구조물의 거동 예측에 잠재적으로 적용되어 있다는 점에 착안하여, 응력해석에 국한되어 있던 방법론을 자유진동 및 좌굴 문제 등에 적용하여 고전 보 이론의 정확도를 고차이론 수준으로 개선한다. 먼저 생브낭의 원리를 소개하고, 고전 보 이론에 의한 자유진동 그리고 좌굴해석 정식화를 진행하였다. 고전 보 이론의 변위장에 워핑함수와 섭동항을 추가하고, 합응력 등가(즉, 생브낭의 원리)를 적용하여 섭동항을 찾는다. 여기서 워핑함수들은 응력 평형방정식을 통하여 계산하였으며, 이 워핑함수들은 추가된 섭동항에 의하여 보의 응력 평형을 만족하게 된다. 제안된 방법론을 외팔보와 단순지지 보 문제에 적용하여 주파수 및 좌굴하중을 개선하였으며, 전단수정계수의 도입 없이 예측을 개선할 수 있음을 보였다.

Keywords

References

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  1. A thermo-mechanical stress prediction improvement of using the classical lamination theory via Saint-Venant’s principle for laminated composite plates vol.32, pp.2, 2018, https://doi.org/10.1007/s12206-018-0123-3