Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
권호 표지
DOI QR코드

DOI QR Code

Analysis for Torsion of Hollow Beam by Least Squares and Boundary Elements Method

최소자승법 및 경계요소에 의한 중공단면 보의 비틀림 해석

  • 김치경 (인천대학교 안전공학과) ;
  • 배준태 (인천대학교 안전공학과)
  • Received : 2011.12.29
  • Accepted : 2012.02.24
  • Published : 2012.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we are concerned with the performance of structural stability of torsion in square cross section of a beam with holes. The critical load is defined as the smallest load at which the equilibrium of the structure fails to be stable as the load is slowly increased from zero. The beams subjected to torsion are frequently encountered in general structures and these forces influence to the stability of structure. The boundary element method is found to be very efficient and accurate for the analysis of torsion problems including complex boundary conditions with respect to its simplicity and generality. In this paper, it is required to derive the boundary element formulation for torsion problem and integrate directly on the discrete boundary. To investigate the validity of the developed computer program, three distinctly solid cross-sections which are elliptical, rectangular and triangular one are analyzed, and comparisons are made with analytical approaches where these can also be used.

본 연구에서는 뒤틀림을 받고 있는 정사각형 단면의 중공단면 보를 최소자승법과 경계요소법을 이용하여 수치 해석하고 구조물을 해석하였다. 임계하중은 하중을 점차적으로 증가하여 구조물이 파괴가 발생하여 안정성을 상실하는 상태에서 가장 작은 하중을 의미한다. 뒤틀림을 받고 있는 beam은 일반 구조물에서 많이 발생하는 현상이며, 구조물의 안정성에 크게 영향을 미치고 있다. 최소자승법과 경계요소법은 복잡한 구조물에서도 물론, 다양한 경계조건을 포함하는 문제에 이르기까지 구조물의 안정성을 검사하는데 효과적인 수치해석 방법이다. 특히 뒤틀림의 문제에서는 단순성 및 일반성에 기인하여 매우 적합한 해석방법이다. 본 연구에서는 뒤틀림을 받고 있는 중공단면 보의 해석해를 유도하여 최소자승법으로 수치 해석하고 또한 경계요소법을 적용하여 빔의 안정성을 비교 검토하였다. 개발한 컴퓨터 프로그램의 타당성을 증명하기 위하여 삼각형, 사각형 그리고 타원형 단면에 대하여 각각 해석하여 해석해와 비교 검토하였다.

Keywords

References

  1. Boresi, A.,Sidebottom, O., Seely, F. B., Smith, J.O. (1978) Advanced Mechainics of Materials, John Wiley and Sons, New York, pp.210-252.
  2. Chen, J.T., Chen, Y.W. (2000) Dual Boundary Element Analysis using Complex Variables for Potential Problems with or Without Degenerate Boundary, Engineering Analysis with Boundary Elements, 24, pp.671-684. https://doi.org/10.1016/S0955-7997(00)00025-4
  3. Chou, S.I., Shamas-Ahmadi, M. (1992) Complex Variable Boundary Element Method for Torsion of Hollow Shafts, Nuclear Engineering and Design, 136, pp.255-263. https://doi.org/10.1016/0029-5493(92)90027-S
  4. Dorao, C.A., Tackbsen, H.A. (2007) Least-squares Spectral Method for Solving Advective Population Balance Problems, Journal of Computational and Applied Mathematics, 201, pp.247-257. https://doi.org/10.1016/j.cam.2006.02.020
  5. Dumir, P.C., Kumar, R. (1993) Complex Variable Boundary Element Method for Torsion of Anisotropic Bars, Applied Mathematical Modelling, 17, pp.80-88. https://doi.org/10.1016/0307-904X(93)90096-Y
  6. Friedman, Z., Kosmatka, J.B. (2000) Torsion and Flexure of a Prismatic Isotropic Beam using the Boundary Element Method, Computers & Structures, 74, pp.479-494. https://doi.org/10.1016/S0045-7949(99)00045-0
  7. Gaspari, D., Aristodemo, M. (2005) Torsion and Flexure of Orthotropic Beams by a Boundary Element Model, Engineering Analysis with Boundary Elements, 29, pp.850-858. https://doi.org/10.1016/j.enganabound.2005.05.002
  8. Kim, S.D., Shin, B.C. (2009) Adjoint Pseudospectral Least-Squares Methods for an Elliptic Boundary Value Problems, Applied Numerical Mathematics, 59, pp.334-348. https://doi.org/10.1016/j.apnum.2008.02.008
  9. Mokos, V.G., Sapountzakis, E.J. (2011) Secondary Torsional Moment Deformation Effect by BEM, International Journal of Mechanical Sciences, 53, pp.897-909. https://doi.org/10.1016/j.ijmecsci.2011.08.001
  10. Sapountzakis, E.J., Mokos, V.G. (2007) 3-D Beam Element of Composite Cross Section Including Warping and Shear Deformation Effect, Computers & Structures, 85, pp.102-116. https://doi.org/10.1016/j.compstruc.2006.09.003
  11. Sapountzakis, E.J. (2001) Nonuniform Torsion of Multi-Material Composite Bars by the Boundary Element Method, Computers & Structures, 79, pp.2805-2816. https://doi.org/10.1016/S0045-7949(01)00147-X
  12. Sapountzakis, E.J., Mokos, V.G. (2003) Warping Stresses in Nonuniform Torsion of Composite Bars by BEM, Computer Methods in Applied Mechanics and Engineering, 192, pp.4337-4353. https://doi.org/10.1016/S0045-7825(03)00417-1
  13. Sapountzakis, E.J. (2000) Solution of Non-Uniform Torsion of Bars by an Integral Equation Method, Computers & Structures, 77, pp.659-667. https://doi.org/10.1016/S0045-7949(00)00020-1
  14. Sapountzakis, E.J., Mokos, V.G. (2004) Nonuniform Torsion of Composite Bars of Variable Thickness by BEM, International Journal of Solids and Structures, Vol. 41, pp.1753-1771. https://doi.org/10.1016/j.ijsolstr.2003.11.025
  15. Sapountzakis, E.J., Tsipiras, V.J. (2009) Nonlinear Inelastic Uniform Torsion of Composite Bars by BEM, Computers & Structures, 87, pp.151-166.
  16. Saint Venant, B. (1885) De la Torsion des Prismes, Imprimerie periale. Paris
  17. Tan, E.L., Uy, B. (2011) Nonlinear Analysis of Composite Beams Subjected to Combined Flexure and Torsion, Journal of Constructional Steel Research, 67, pp.790-799. https://doi.org/10.1016/j.jcsr.2010.12.015
  18. Xu Rongqiao, He Jiansheng, Chen Weiqui. (2010) Saint-Venant Torsion of Orthotropic Bars with Inhomogeneous Rectangular Cross Section, Composite Structures, 92, pp.1449-1457. https://doi.org/10.1016/j.compstruct.2009.10.042
  19. Zitnan, P. (2011) Discrete Weighted Least-Squares Method for the Poisson and Biharmonic Problems on Domain Smooth Boundary, Applied Mathematics and Computation, 217, pp.8973-8982. https://doi.org/10.1016/j.amc.2011.03.103