Lagrangian Formulation of a Geometrically Exact Nonlinear Frame-Cable Element

기하 비선형성을 엄밀히 고려한 비선형 프레임-케이블요소의 정식화

  • 정명락 (성균관대학교 건설환경시스템공학과) ;
  • 민동주 (성균관대학교 건설환경시스템공학과) ;
  • 김문영 (성균관대학교 건설환경시스템공학과)
  • Received : 2011.11.25
  • Accepted : 2012.05.29
  • Published : 2012.06.30


Two nonlinear frame elements taking into account geometric nonlinearity is presented and compared based on the Lagrangian co-rotational formulation. The first frame element is believed to be geometrically-exact because not only tangent stiffness matrices is exactly evaluated including stiffness matrices due to initial deformation but also total member forces are directly determined from total deformations in the deformed state. Particularly two exact tangent stiffness matrices based on total Lagrangian and updated Lagrangian formulation, respectively, are verified to be identical. In the second frame element, the deformed curved shape is regarded as the polygon and current flexural deformations in iteration process are neglected in evaluating tangent stiffness matrices and total member forces. Two numerical examples are given to demonstrate the accuracy and the good performance of the first frame element compared with the second element. Furthermore it is shown that the first frame element can be used in tracing nonlinear behaviors of cable members.


Supported by : 건설교통기술평가원


  1. 김문영, 장승필 (1990) 보존력과 비보존력을 받는 평면뼈대 구조물의 기하적 비선형 해석, 대한토목학회 논문집, 10(1), pp.17-26.
  2. Battini, J.M. (2008) A Rotation-free Corotational Plane Beam Element for Non-linear Analyses, Int. J. Numer. Meth. Engng. 75, pp.672-689.
  3. Irvine, H.M. (1981) Cable Structures, MIT Press.
  4. Meek, J.L., Xue, Q. (1996) A Study on the Instability Problem for 2D-frames, Comput. Methods Appl. Mech. Engrg. 136, pp.347-361.
  5. Saafan, S.A. (1963) Nonlinear Behavior of Structural Plane Frames, Journal of the Structural Division, ASCE V. 89, p.557.
  6. Santos, H.A.F.A., Moitinho de Almeida, J.P. (2010) Equilibrium-based Finite-element Formulation for the Geometrically Exact Analysis of Planar Framed Structures, J. Engineering Mechanics, 136(12).
  7. Souza, R. (2000) Forced-based Finite Element for Large Displacement Inelastic Analysis of Frames, Ph.D., University of California at Berkeley, Berkeley, CA, pp.40-54.
  8. Timoshenko, S.P., Gere, J.M. (1970) Mechanics of Materials, McGraw-Hill, New York.