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

The Korean Society of Mechanical Engineers (대한기계학회)
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Application of Saint-Venant's Principle to Anisotropic Beams

이방성 보 구조물 응력해석에서의 생브낭 원리

  • Kim, Jun-Sik (Dept. of Intelligent Mechanical Engineering, Kumoh Nat'l Institute of Tech.)
  • 김준식 (금오공과대학교 지능기계공학과)
  • Received : 2011.12.21
  • Accepted : 2012.02.07
  • Published : 2012.04.01
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Abstract

Asymptotic analysis is a powerful tool for the mathematically rigorous design and analysis of anisotropic beam structures. However, it has a limitation in that the asymptotic approach requires asymptotically correct boundary conditions for higher-order solutions, which are often needed for beams weak in shear. A method utilizing Saint-Venant's principle was proposed in a previous work to improve the stress state of isotropic beams and plates. In this paper, such a method is generalized for anisotropic beams, so that one does not need to consider the asymptotically correct boundary conditions for higher-order solutions. Consequently, solving the recursive system equations is not necessary, which makes the method very efficient in terms of accuracy and computational effort.

수학적 방법에 기초한 점근해석기법은 이방성 보 구조물의 설계 및 해석에 있어 강력한 도구이다. 이러한 장점에도 불구하고, 점근해석 기법은 전단 변형에 상대적으로 취약한 복합재료 보의 고차해를 구함에 있어 점근적으로 정확한 경계조건을 필요로 한다. 생브낭의 원리를 적용하여 응력상태를 개선하는 방법은 등방성 보 및 판 구조물에 대하여 개발되었고, 외팔보 등의 예제를 통해 검증되었다. 이 방법은 점근적으로 정확한 경계조건을 요구하지 않으며, 반복계산도 필요로 하지 않는다는 장점이 있다. 본 논문에서는 이 방법을 일반 이방성 보 구조물에 대하여 확장 적용하여 생브낭의 원리를 적용하는 방법을 일반화 하고자 한다.

Keywords

References

  1. Jones, R. M., 1975, Mechanics of Composite Materials, McGraw-Hill Kogakusha, Ltd.
  2. Oh, J., Cho, M., Kim, J.-S. and Grediac, M., 2008, "A Finite Element Formulation Based on an Enhanced First Order Shear Deformation Theory for Composite and Sandwich Structures," Journal of Mechanical Science and Technology, Vol. 22, No. 5, pp. 871-878. https://doi.org/10.1007/s12206-008-0103-8
  3. Kim, J.-S., Cho, M. and Smith, E. C., 2008, "An Asymptotic Analysis of Composite Beams with Kinematically Corrected End Effects," International Journal of Solids and Structures, Vol. 45, pp. 1954-1977. https://doi.org/10.1016/j.ijsolstr.2007.11.005
  4. Kim, J.-S, 2009, "An Asymptotic Analysis of Anisotropic Heterogeneous Plates with Consideration of End Effects," Journal of Mechanics of Materials and Structures, Vol. 4, No. 9, pp. 1535-1553. https://doi.org/10.2140/jomms.2009.4.1535
  5. Kim, J.-S. and Cho, M., 2011, "A Novel Methodology of Improving Stress Prediction via Saint-Venant's Principle," Journal of the COSEIK, Vol. 24, No. 2, pp. 149-156.
  6. Fung, Y. C., 1965, Foundations of Solid Mechanics, Prentice-Hall, Inc.
  7. von Mises, R., 1945, "On Saint Venant's Principle," Bulletin of the AMS, Vol.51, No. 7, pp. 555-562. https://doi.org/10.1090/S0002-9904-1945-08394-3
  8. Buannic, N. and Cartraud, P., 2001, "Higher-order Effective Modeling of Periodic Heterogeneous Beams I. Asymptotic Expansion Method," International Journal of Solids and Structures, Vol. 38, pp. 7139-7161. https://doi.org/10.1016/S0020-7683(00)00422-4
  9. Kim, J.-S. and Wang, K. W., 2011, "On the Asymptotic Boundary Conditions of an Anisotropic Beam via Virtual Work Principle," International Journal of Solids and Structures, Vol. 48, pp. 2422-2431. https://doi.org/10.1016/j.ijsolstr.2011.04.016

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  2. Improvement of Euler-Bernoulli Beam Theory for Free Vibration and Buckling Analyses via Saint-Venant's Principle vol.40, pp.4, 2016, https://doi.org/10.3795/KSME-A.2016.40.4.381