Abstract
Simple and economical procedures for large-deformation elasto-plastic analysis of frames, whose members can be characterized as beams, are presented. An assumed stress approach is employed to derive the tangent stiffness of the beam, subjected in general to non-conservative type distributed loading. The beam is assumed to undergo arbitrarily large rigid rotations but small axial stretch and relative (non-rigid) point-wise rotations. It is shown that if a plastic-hinge method (with allowance being made for the formation of the hinge at an arbitrary location or locations along the beam) is employed, the tangent stiffness matrix may be derived in an explicit fashion, without numerical integration. Several examples are given to illustrate the relative economy and efficiency of the method in solving large-deformation elasto-plastic problems. The method is of considerable utility in analysing off-shore structures and large structures that are likely to be deployed in outerspace.
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References
Archer, J.S. (1965): Consistent matrix formulations for structural analysis using finite element techniques. AIAA J. 3/10, 1910–1918
Argyris, J.H.; Hilpert, O.; Malejannakis, G.A.; Scharpf, D.W. (1979): On the geometrical stiffness of a beam in space — A consistent V.W. approach. Comp. Meth. Appl. Mech. & Engg. 20, 105–131
Argyris, J.H.; Symeonidis, S. (1981): Nonlinear finite element analysis of elastic systems under nonconservative loading. Natural formulation, Part 1. Comp. Meth. Appl. Mech. & Engg. 26, 75–123
Argyris, J.H.; Boni, B.; Hindenlang, U.; Kleiver, K. (1982): Finite element analysis of two- and three-dimensional elastoplastic frames. The natural approach. Comp. Meth. Appl. Mech. & Engg. 35, 221–248
Atluri, S.N. (1975): On hybrid finite element models in solid mechanics. In: Vichnevetsky, R. (ed): Advances in computer methods for partial differential equations, pp. 346–355. AICA, Rutgers University
Atluri, S.N. (1977): On hybrid finite element models in nonlinear solid mechanics. In Bergan, P.G. et al. (eds): Finite elements in nonlinear mechanics, vol 1, pp. 3–40. Norway: Tapir Press
Atluri, S.N. (1980): On some new general and complementary energy theorems for the rate problems in finite strain, classical elastoplasticity. J. Struct. Mech. 3/1, 61–92
Atluri, S.N. (1983): Alternate stress and conjugate strain measures and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells. Theory, Comp. & Struct. 18/1, 93–106
Barten, H.J. (1944): On the deflection of a cantilever beam. Quart. Appl. Math. 2, 171
Bathe, J.J.; Ramm, E.; Wilson, W.K. (1975): Finite element formulations for large deformation dynamic analysis. Int. J. Num. Meth. Engg. 9, 353–386
Bisshop, K.E.; Drucker, D.C. (1945): Large deflections of cantilever beams. Quart. Appl. Math. 3, 272–275
Crisfield, M.A. (1981): A fast incremental/iterative solution procedure that handles snap-through. Comp. & Struct. 13, 55–62
Gallagher, R.H. (1983): Finite element method for instability analysis. In: Kardestuncer, H.; Brezzi, F.; Atluri, S.N.; Norrie, D.H.; Pilkey, W. (eds): Handbook of finite elements. London: McGraw-Hill
Hodge, P.G. (1959): Plastic analysis of structures. New York: McGraw-Hill
Karamanlidis, D.; Atluri, S.N. (1984): Mixed finite element models for plate bending analysis. Theory, Comp. & Struct. 19/3; 431–445
Kondoh, K.; Atluri, S.N. (1984): A simplified finite element method for large deformation, post-buckling analysis of large frame structures, using explicitly derived tangent stiffness matrices. Int. J. Num. Meth. Engg.
Kondoh, K.; Tanaka, K.; Atluri, S.N. (1985a) : A method for simplified nonlinear analysis of large space-trusses and -frames, using explicitly derived tangent stiffness, and accounting for local buckling. U.S. Air Force Wright Aeronautical Labs Report, AFWAL-TR-85-3079, p. 171
Kondoh, K.; Tanaka, K.; Atluri, S.N. (1985b) : An explicit expression for tangent-stiffness of a finitely deformed 3-D beam and its use in the analysis of space frames. Comp. & Struct. (submitted)
Nedergaard, H.; Pedersen, P.T. (1985): Analysis procedures for space frames with geometric and material nonlinearities, in finite element methods for nonlinear problems. Preprints Vol. 1, Proc. Europe-U.S. Symp., Trondheim, Norway, 12–16 Aug. 1985, pp. I.16-1 to I.16-20
Oden, J.T.; Childs, S.B. (1970): Finite deflections of a nonlinearly elastic bar. J. Appl. Mech. 37, 48–52
Ramm, E. (1981): Strategies for tracing the nonlinear response near limit points. In: Wunderlich, W.; Stein, E.; Bathe, K.J. (eds): Nonlinear finite element analysis in structural mechanics, pp. 63–89. Berlin, Heidelberg, New York, Tokyo: Springer
Rohde, F.U. (1953): Large deflections of a cantilever beam with uniformly distributed load. Quart. Appl. Math. 11, 337–338
Saran, M. (1984): On the influence of the discretization density in the nonlinear analysis of frames. Comp. Meth. Appl. Mech. Engg. 43, 173–180
Schmidt, R.; Dadeppo, D.A. (1970): Large deflections of heavy cantilever beams and columns. Quart. Appl. Math. 28, 441–444
Tang, S.C.; Yeung, K.S.; Chon, C.T. (1980): On the tangent stiffness matrix in a convected coordinate system. Comp. & Struct. 12, 849–856
Timoshenko, S.P.; Gere, J.M. (1961): Theory of elastic stability, 2nd Edition. London: McGraw-Hill
Ueda, Y.; Matsuishi, M.; Yamakawa, T.; Akamatsu, Y. (1968): Elasto-plastic analysis of frame structures using the matrix method. J. Soc. of Naval Arch. (Japan) 124, 183–191 (in Japanese)
Ueda, Y.; Yao, T. (1982): The plastic node method: A new method of plastic analysis. Comp. Meth. Appl. Mech. Engg. 34, 1089–1104
Wang, T.M.; Lee, S.L.; Zienkiewicz, O.C. (1961): A numerical analysis of large deflections of beams. Int. J. Mech. Sci. 3, 219–228
Yang, T.Y.; Wagner, R.J. (1973): Snap buckling of nonlinearly elastic finite element bars. Comp. & Struct. 3, 1473–1481
Yang, T.Y.; Saigal, S. (1984): A single element for static and dynamic response of beams with material and geometric nonlinearities. Int. J. Num. Meth. Engg. 20, 851–867
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Communicated by G. Yagawa, January 18, 1986
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Kondoh, K., Atluri, S.N. Large-deformation, elasto-plastic analysis of frames under nonconservative loading, using explicitly derived tangent stiffnesses based on assumed stresses. Computational Mechanics 2, 1–25 (1987). https://doi.org/10.1007/BF00282040
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DOI: https://doi.org/10.1007/BF00282040