A mathematical programming approach is proposed for the large displacement elastoplastic analysis of space trusses. Features of the general methodology include the preservation of static-kinematic duality through the concept of fictitious forces and deformations, exact descriptions of equilibrium and compatibility for arbitrarily large displacements, albeit small strain, that can be specialized to any order of geometrical nonlinearity, and a complementarity description of the elastoplastic constitutive laws. The finite incremental formulation developed takes the form of a special mathematical programming problem known as a nonlinear complementarity problem for which a predictor-corrector type numerical scheme is proposed.
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References
1.
GioncuV., Buckling of reticulated shells: state-of-the-art, International Journal of Space Structures, 10, 1995, 1–46.
MaierG.SmithD. Lloyd, Update to “Mathematical programming applications to engineering plastic analysis”, Applied Mechanics Update, ASME, New York, 1986, pp. 377–383.
4.
SmithD. Lloyd, Large-displacement elastic-plastic analysis of frames, in: Engineering Plasticity by Mathematical Programming, eds. CohnM.Z.MaierG., Pergamon Press, New York, 1979, pp. 536–547.
5.
De FreitasJ.A.T., The elastoplastic analysis of planar frames for large displacements by mathematical programming, Ph.D. thesis, University of London, 1979.
6.
De FreitasJ.A.T.SmithD. Lloyd, Elastoplastic analysis of planar structures for large displacements, Journal of Structural Mechanics, 12, 1984–85, 419–445.
7.
De FreitasJ.A.T.SmithD. Lloyd, Existence, uniqueness and stability of elastoplastic solutions in the presence of large displacements, Solid Mechanics Archives, 9, 1984, 433–450.
8.
De FreitasJ.A.T.De AlmeidaJ.P.B.M.VirtuosoF.B.E., Nonlinear analysis of elastic space trusses, Meccanica, 20, 1985, 144–150.
9.
DirkseS.P.FerrisM.C., MCPLIB: a collection of nonlinear mixed complementarity problems, Optimization Methods and Software, 5, 1995, 319–345.
10.
DenkeP.H., Nonlinear and thermal effects on elastic vibrations, Technical Report SM-30426, Douglas Aircraft Company, 1960.
11.
Tin-LoiF.VimonsatitV., Nonlinear analysis of semirigid frames: a parametric complementarity approach, Engineering Structures, 18, 1996, 115–124.
12.
BallioG.PetriniV.UrbanoC., The effect of loading process and imperfections on the load bearing capacity of beam columns, Meccanica, 8, 1973, 56–67.
13.
MadiU.R., Idealising the members behaviour in the analysis of pin-jointed spatial structures, in: Space Structures, ed. NooshinH., Elsevier Science Publishers, London, 1984, pp. 462–467.
14.
MadiU.R.SmithD. Lloyd, A finite element model for determining the constitutive relation of a compression member, in: Space Structures, ed. NooshinH., Elsevier Science Publishers, London, 1984, pp. 625–629.
15.
CorradiL., On compatible finite element models for elastic plastic analysis, Meccanica, 13, 1978, 133–150.
16.
MaierG., A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes, Meccanica, 5, 1970, 121–130.
17.
De FreitasJ.A.T.SmithD. Lloyd, Finite element elastic beam-column, Journal of Engineering Mechanics, ASCE, 109, 1983, 1247–1269.
18.
Tin-LoiF.MisaJ.S., Large displacement elastoplastic analysis of semirigid steel frames, International Journal for Numerical Methods in Engineering, 39, 1996, 741–762.
FordeB.W.R.StiemerS.F., Improved arc length orthogonality methods for nonlinear finite element analysis, Computers & Structures, 27, 1987, 625–630.
21.
ComiC.MaierG.Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening, European Journal of Mechanics, A/Solids, 9, 1990, 563–585.
22.
YangY.B.LeuL.J., Constitutive laws and force recovery procedures in non-linear analysis of trusses, Computer Methods in Applied Mechanics and Engineering, 92, 1991, 121–131.
23.
KrenkS.HededalO., A dual orthogonality procedure for non-linear finite element equations, Computer Methods in Applied Mechanics and Engineering, 123, 1995, 95–107.
24.
HangaiY.KawamataS., Analysis of geometrically nonlinear and stability problems by static perturbation method, Report of the Institute of Industrial Science, Vol. 22, No. 5, The University of Tokyo, 1973.
