DOI QR코드

DOI QR Code

Numerical Evaluation of Fundamental Finite Element Models in Bar and Beam Structures

Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석

  • Ryu, Yong-Hee (Department of Civil Engineering, North Carolina State University) ;
  • Ju, Bu-Seog (Department of Civil Engineering, North Carolina State University) ;
  • Jung, Woo-Young (Department of Civil Engineering, Gangneung-WonJu National University) ;
  • Limkatanyu, Suchart (Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University)
  • 류용희 (노스캐롤라이나주립대학교 토목공학과) ;
  • 주부석 (노스캐롤라이나주립대학교 토목공학과) ;
  • 정우영 (강릉원주대학교 토목공학과) ;
  • Received : 2013.01.10
  • Accepted : 2013.02.28
  • Published : 2013.03.31

Abstract

The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

References

  1. Cook, R. D. (2002). Concepts and applications of finite element analysis. 4th ed., Wiley, NewYork, USA.
  2. Courant, R. L. (1943). "Vibrational Methods for the Solutionof Problems of Equilibrium and Vibration.", Bulletin of the American Mathematical Society, Vol. 49, pp. 1-23.
  3. Iqbal, R. (2007). "Development of a finiteelement program incorporating advanced element types." M.S. Thesis, Osmania University Hyderabad, India
  4. Kassimali, A. (2011). Matrix Analysis of Structures, Pacific Grove, Cengage Learning, CA, USA.
  5. Kattan, P. I. (2007). MATLAB guide to finite elements: an interactive approach. 2nd ed. NewYork :Springer.
  6. Melosh, R. J. (1985). "Self-qualification of finite element analysis results by polynomial extrapolation." Finite Elements in Analysis and Design, Vol. 1, pp. 49-60. https://doi.org/10.1016/0168-874X(85)90007-1
  7. Olson, M. D. and Bearden, T. W. (1979). A simple flat triangular shell element revisited, Int. J. Numer. Meth. Engng., Vol. 2, pp. 51-68.
  8. Robinson, J. (1980). Four-node quadrilateral stress membrane element with rotational stiffness, Int. J. Numer. Meth. Engng., Vol. 3, pp. 1567-1569.
  9. Sze, K. Y., Wanji, C., and Cheung, Y. K. (1992). "An efficient quadrilateral plane element with drilling degrees of freedom using orthogonal stress modes." Comp. Struct., Vol. 42, No. 5, pp. 695-705. https://doi.org/10.1016/0045-7949(92)90181-X
  10. Timoshenko, S. P. (1953). History of Strength of Materials, McGraw-Hill Book Co. New York.