In the context of a nonlinear stability theory of elastic structures, the geometrically nonlinear formulation of a spatial beam element (recently introduced by several authors) is reviewed for application to a perturbative approach of the post-buckling analysis of space beam grids or frames.
The implementation aspects of the procedure in an iterative-incremental algorithm are discussed, and the performances of several implemented iteration strategies are brought out, with the aim of improving the usual known ones. The adopted strategy to detect and trace post-buckling equilibrium paths is then discussed. Finally, some numerical examples are used to demonstrate the characteristics and capabilities of the analytical model.
Get full access to this article
View all access options for this article.
References
1.
SchockH.J., Untersuchungen zur Tragfaehigkeit von seilverspannten Druckstaeben, Diss., Inst. fuer Tragkonstruktionen u. konst. Entwerfen. Univ. Stuttgart, 4, 1976, pp. 1–21.
2.
BatheK.J.BolourchiS., Large Displacement Analysis of Three Dimensional Beam Structures, Int. J. for Num. Methods in Engrg., 14, 1979.
3.
BorriC., Non linearita' geometrica di travature spaziali; il caso dei grigliati a guscio, Note e Pubbl. di Ing. Strutturale, 1st. di Ing. Civile, Univ. di Firenze, No. 11. 1982, pp. 1–31.
4.
BorriC.HufendiekH.W., Geometrically Nonlinear Behaviour of Space Beam Structures, J. of Struct. Mech., 13, 1985, pp. 1–25.
5.
AugustiG.BorriC.ChiostriniS.SpinelliP., Analisi di Stabilita' di Gusci Grigliati – Proc. of IX Nat. Congr. AIMETAII, 1988, pp. 505–508.
6.
ChiostriniS., Analisi Non Lineare e Stabilita' di Grigliati Spaziali di Travi – Doct. Thesis – Dept. of Civil Engrg. Univ. of Florence, Jan. 1989.
7.
SmartW.M., Textbook on Spherical Astronomy, Cambridge University Press, 1977, sixth edition.
8.
SpainB., Tensor Calculus, Oliver and Boyd, Edinburgh1960, third edition.
9.
SeeT., Large Displacement Elastic Buckling of Space Structures – Ph. D. Thesis, Univ. of Cambridge – Dec. 1983.
10.
ArgyrisJ.H., Continua and Discontinua, Proc. of the 1st Conf. on Matrix Meth. in Struct. Mech., Wright-Patterson AFB Ohio, 1965, 11–189.
11.
PianT.H.H.TongP., Variational Formulation of Finite Displacement Analysis – High Speed Computing of Elastic structures – IUTAM Symposium, Liege, 1970, pp. 43–63.
12.
ZienkiewiczO.C., Incremental Displacements in Finite Elements Analysis, Int. J. Num. Meth. Eng., 3, 1971, pp. 587–588.
13.
TesarA., Postbuckling Resonance Analysis of Thin Shells, Int. J. Num. Meth. Eng., 20, pp. 2221–2234, 1984.
14.
BerganP.G.HorrigmoeG.KrakelandB.SoreideT.H., Solution Techniques for Non-linear Finite Element Problems, Int. J. Num. Meth. Eng.12, 1677–1696, 1978.
15.
BerganP.G.SoreideT., Solution of Large Displacement and Instability Problems Using the Current Stiffness Parameter, Finite Elements in Non-linear Mechanics, Tapir Press 3 (1978), pp. 647–669.
16.
HaislerW.H.StricklinJ.A.KeyE., Displacement Incrementation in Non-linear Structural Analysis by the Self Correcting Method. Int. J. Num. Meth. Eng.11, 3–10, 1977.
17.
LockA.C.SabirA.B., Algorithm for Large Deflection Geometrically Non-linear Plane and Curved Structures, Mathematics of Finite Elements and Applications, ed WhitemanJ.R., Academic Press, New York, 1973, 483–494.
18.
RiksE., The Applications of Newton's Method to the Problem of Elastic Stability, J. Appl. Mech.39, 1060–1066, 1972.
19.
RiksE., An Incremental Approach to the Solution of Snapping and Buckling Problems, Int. J. Solids Structures, 15, pp. 529–531, 1979.
20.
WempnerG.A., Discrete Approximations Related to Non-linear Theories of Solids, Int. J. Solid Struct. 7, 1581–1599, 1971.
21.
WesselsM., Das statische und dynamische Durchschlags-problem der imperfekten flachen Kugelschale bei elastischer rotations-symmetrischer Verformung - Diss., Tu Hannover, 1980.
22.
BatozJ.L.DhattG., Incremental Displacement Algorithms for Non-linear Problems, Int. J. Num. Meth. Eng.14, 1262–1267, 1979.
23.
RammE., Strategies for Tracing Nonlinear Response Near Limit Points, Workshop: Nonlinear finite element analysis in structural mechanics, Bochum Springer Verlag, July 1980.
24.
BorriC.ZahltenW., Unpublished Communication.
25.
CrisfieldM.A., A Fast Incremental-Iterative Solution Procedure that Handles Snap-Through, Computers & Structures, 13, 55–62, 1981.
26.
ThompsonJ.M.T.HuntG.W., A General Theory of Elastic Stability, J. Wiley & Sons, 1972.
27.
MalletR.H.MarcalP.V., Finite Element Analysis of Nonlinear Structures, Proc. ASCE. J. Struct. Div., ST/94, 1968, 2081–2105.
RammE., Geometrisch-nichtlineare Elastostatik und finite Elemente - Bericht. No. 2, Inst. fuer Baustatik, Universitaet Stuttgart, 1976.
30.
BorriC., Sul Comportamento Post-critico di Gusci Reticolari Monostrato presenze di imperfezioni. Proc. of VIII Nat. Congr. AIMETA, II, 623–629. 1986.
31.
BorriC.SpinelliP., Buckling and Post-buckling Behaviour of Single-layer Reticulated Shells Affected by Random Imperfections, Comp. & Struct., 30, 4, 1988, 937–943.
32.
WittrickW.H.WilliamsF.W., An Algorithm for Computing Critical Buckling Loads of Elastic Structures, J. of Struct. Mech., 1, 4, 1973, pp. 497–518.
33.
ButterworthJ.W., Nonlinear Analysis and Stability of Elastic Skeletal Systems, Ph. D. Thesis, Dept. of Civil Eng., University of Surrey, 1975.
