Structural Engineering and Mechanics

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Large displacement analysis of inelastic frame structures by convected material frame approach

  • Chiou, Yaw-Jeng (Department of Civil Engineering, National Cheng Kung University) ;
  • Wang, Yeon-Kang (Department of Civil Engineering, Chung-Cheng Institute of Technology, National Defense University) ;
  • Hsiao, Pang-An (Department of Civil Engineering, National Cheng Kung University) ;
  • Chen, Yi-Lung (Department of Civil Engineering, National Cheng Kung University)
  • Published : 2002.02.25
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Abstract

This paper presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance.

Keywords

Acknowledgement

Supported by : National Science Council of Republic of China

References

  1. ANSYS Release 5.5.1 (1998) ANSYS, Inc., Canonsburg, P. A., U. S. A.
  2. Belytschko, T., and Hsieh, B.J. (1973), "Nonlinear transient finite element analysis with convected coordinates", Int. J. Numer. Meth. Eng., 7, 255-271. https://doi.org/10.1002/nme.1620070304
  3. Belytschko, T., and Marchertas, A.H. (1974), "Nonlinear finite element method for plates and its application to dynamics response of reactor fuel subassemblies", Trans. ASME, J. Pressure Vessel Tech., 96(4), 251-257. https://doi.org/10.1115/1.3454177
  4. Belytschko, T., Schwer, L., and Klein, M.J. (1977), "Large displacement, transient analysis of space frames", Int. J. Numer. Meth. Eng., 11, 65-84. https://doi.org/10.1002/nme.1620110108
  5. Crisfield, M.A. (1990), "A consistent co-rotational formulation for non-linear, three dimensional beam elements", Compt. Meth. Appl. Mech. Eng., 81, 131-150. https://doi.org/10.1016/0045-7825(90)90106-V
  6. Dafalias, Y.F. (1987), "Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinematics", Acta Mechanica, 69, 119-138. https://doi.org/10.1007/BF01175717
  7. Dafalias, Y.F. (1988), "Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinetics", Acta Mechanica, 73, 121-146. https://doi.org/10.1007/BF01177034
  8. Hsiao, K.M., Horng, H.J., and Chen, Y.R. (1987), "A co-rotational procedure that handles large rotations of spatial beam structures", Comput. Struct., 27(6), 769-781. https://doi.org/10.1016/0045-7949(87)90290-2
  9. Hsiao, K.M., Lin, J.Y., and Lin, W.Y. (1999), "A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams", Compt. Meth. Appl. Mech. Eng., 169, 1-18. https://doi.org/10.1016/S0045-7825(98)00152-2
  10. Hughes, T.J.R., and Liu, W.K. (1978), "Implicit-explicit finite elements in transient analysis: Stability Theory", J. Appl. Mech., ASME, 45, 371-374. https://doi.org/10.1115/1.3424304
  11. Hughes, T.J.R., Pister, K.S., and Taylor, R.L. (1979), "Implicit-explicit finite elements in nonlinear transient analysis", Comput. Methods Appl. Mech, Engng. 17(18), 159-182.
  12. Mamaghani, I.H.P., Usami, T., and Mizuno, E. (1996), "Inelastic large deflection analysis of structural steel members under cyclic loading", Engng. Struct., 18(9), 659-668. https://doi.org/10.1016/0141-0296(96)00204-0
  13. Rice, D.L., and Ting, E.C. (1993), "Large displacement transient analysis of flexible structures", Int. J. Numer. Meth. Eng, 36, 1541-1562. https://doi.org/10.1002/nme.1620360908
  14. Saha, N., and Ting, E.C. (1983), Large displacement dynamic analysis of space frames, EC-SRT-83-5, School of Civil Engineering, Purdue University, IN. U. S. A.
  15. Tang, S.C., Yeung, K.S., and Chon, C.T. (1980), "On the tangent stiffness matrix in a convected coordinate system", Comput. Struct., 12, 849-856. https://doi.org/10.1016/0045-7949(80)90023-1
  16. Wang, B., Lu, G., and Yu, T.X. (1995), "A numerical analysis of the large deflection of an elastoplastic cantilever", Struct. Engng. Mech., 3(2), 163-172. https://doi.org/10.12989/sem.1995.3.2.163
  17. Wang, Y.K., Shih, C., and Ting, E.C. (1998), A general curved element for very flexible frames, CE-ST-1998- 001, Department of Civil Engineering, National Central University, Taiwan, R. O. C.
  18. Yang, T.Y., and Saigal, S. (1984), "A simple element for static and dynamic response of beams with material and geometric nonlinearities", Int. J. Num. Meth. Eng., 20, 851-867. https://doi.org/10.1002/nme.1620200506
  19. Yu, T.X., Stronge, W.J., and Liu, J.H. (1989), "Large deflections of an elastoplastic strain-hardening cantilever", J. Appl. Mech., ASME, 56, 737-743. https://doi.org/10.1115/1.3176166

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