Large displacement analysis of space-frame structures. (English) Zbl 0675.73034

Summary: The current research is mainly concerned with the geometrically nonlinear static analysis of three-dimensional space-frame structures. The elastic analysis of frame structures by means of the finite element method in the post-buckling range inevitably involves the solution of large systems of nonlinear equations. The most satisfactory way of solving such problems is to combine the arc-length method [M. A. Crisfield, Comput. Struct. 13, 55-62 (1981; Zbl 0479.73031)] within each increment with the Newton-Raphson method (NR method) as the iteration strategy. For large joint rotations, the joint orientation matrix suggested by C. Oran [ASCE J. Structural Div. 99, 987-1001 (1973)] has been used to update the rotational displacement of a joint. The present study deals with the “imperfect” approach to trace the secondary paths of three-dimensional frame structures, the particular examples studied being a two-hinged deep arch and a shallow geodesic dome. Eigenvectors are calculated at bifurcation points to force the structure on to the secondary path by introducing a small perturbation either in load or in geometry.


74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)


Zbl 0479.73031
Full Text: DOI


[1] Wood, R.D.; Zienkiewicz, O.C., Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells, Comput. & structures, 7, 725-735, (1977) · Zbl 0372.73062
[2] Rensedi, S.N., Nonlinear static and dynamic analysis of framed structures, Comput. & structures, 10, 879-897, (1979) · Zbl 0417.73071
[3] Powell, G.H., Theory of nonlinear elastic structures, ASCE J. structural div., 94, 2687-2701, (1969)
[4] Mallett, R.H.; Marcal, P.V., Finite element analysis of nonlinear structures, ASCE J. structural div., 94, 2081-2105, (1968)
[5] Williams, F.W., An approach to the nonlinear behaviour of the members of a rigid jointed plane frame work with finite deflections, Quart. J. mech. appl. math., 7, 451-469, (1964) · Zbl 0129.18803
[6] Jennings, A., Frame analysis including change of geometry, ASCE J. structural div., 94, 627-644, (1968)
[7] Papadrakakis, M., Post-buckling analysis of spatial structures by vector iteration methods, Comput. & structures, 14, 393-402, (1981) · Zbl 0467.73052
[8] Chu, K.H.; Rampetsreiter, R.H., Large deflection buckling of space frames, ASCE J. structural div., 98, 2701-2722, (1972)
[9] Oran, C., Tangent stiffness in plane frames, ASCE J. structural div., 99, 973-985, (1973)
[10] Oran, C., Tangent stiffness in space frames, ASCE J. structural div., 99, 987-1001, (1973)
[11] Bathe, K.J.; Ozdemir, H., Elastic-plastic large deformation static and dynamic analysis, Comput. & structures, 6, 81-92, (1976) · Zbl 0347.73034
[12] Murray, D.W.; Wilson, E.L., Finite element large deflection analysis of plates, ASCE J. engrg. mech. div., 95, 143-165, (1969) · Zbl 0185.52705
[13] Yang, T.Y., Matrix displacement solution to elastic problems of beams and frames, Internat. J. solids and structures, 9, 829-842, (1973)
[14] Sharifi, P.; Popov, E.P., Nonlinear buckling of sandwich arches, ASCE J. engrg. mech. div., 97, 1397-1412, (1971)
[15] Felippa, C.A., Solution of linear equations with skyline stored symmetric matrix, Comput. & structures, 5, 13-29, (1975) · Zbl 0319.65026
[16] Ramm, E., Strategies for tracing the nonlinear response near limit points, (), 63-69 · Zbl 0474.73043
[17] J.L. Meek and H.S. Tan, Large deflection and post buckling analysis of two and three dimensional elastic spatial frames, Res. Rept. CE49, Department of Civil Engineering, University of Queensland, Australia.
[18] Meek, J.L.; Tan, H.S., A stiffness matrix extrapolation strategy for nonlinear analysis, Comput. meths. appl. mech. engrg., 43, 181-194, (1984) · Zbl 0542.73108
[19] Meek, J.L.; Tan, H.S., Geometrically nonlinear analysis of space frames by an incremental iterative technique, Comput. meths. appl. mech. engrg., 47, 261-282, (1984) · Zbl 0552.73071
[20] Bergan, P.G.; Clough, R.W., Convergence criteria for iterative process, Aiaa j., 10, 1107-1108, (1972)
[21] Crisfield, M.A., A fast incremental/iterative solution procedure that handles snap-through, Comput. & structures, 13, 55-62, (1981) · Zbl 0479.73031
[22] Greenstadt, J., The determination of the characteristic roots of a matrix by the Jacobi method, (), 84-91
[23] H.S. Tan, Finite element analysis of the elastic, nonlinear response of frames, plates and arbitrary shells to static loads, Ph.D. Thesis, University of Queensland, Australia.
[24] Haisler, W.E.; Stricklin, J.H.; Key, J.E., Displacement incrementation in nonlinear structural analysis by the self-correcting method, Internat. J. numer. meths. engrg., 11, 3-10, (1977) · Zbl 0347.73056
[25] Batoz, J.L.; Dhatt, G., Incremental displacement algorithms for nonlinear problems, Internat. J. numer. meths. engrg., 14, 1262-1267, (1979) · Zbl 0423.73061
[26] Powell, G.; Simons, J., Improved iteration strategy for nonlinear structures, Internat. J. numer. meths. engrg., 17, 1455-1467, (1981) · Zbl 0462.73065
[27] Riks, E., An incremental approach to the solution of snapping and buckling problems, Internat. J. solids and structures, 15, 529-551, (1979) · Zbl 0408.73040
[28] Wempner, G.A., Discrete approximations related to nonlinear theories of solids, Internat. J. solids and structures, 7, 1581-1599, (1971) · Zbl 0222.73054
[29] Kani, I.M.; McConnel, R.E.; See, T., The analysis and testing of a single layer shallow braced dome, (), 613-618
[30] Crisfield, M.A., Accelerated solution techniques and concrete cracking, Comput. meths. appl. mech. engrg., 33, 585-607, (1982) · Zbl 0478.73088
[31] Meek, J.L.; Loganathan, S., Geometrically nonlinear analysis of space frame structures, (), 324-329 · Zbl 0675.73034
[32] Meek, J.L.; Tan, H.S., Large deflection analysis of space frames, (), 142-146
[33] Meek, J.L.; Tan, H.S., Geometrical nonlinear analysis of space frames by an incremental iterative technique, (), 569-579
[34] Huddleston, J.V., Finite deflection and snap through of high circular arches, J. appl. mech., 35, 763-769, (1968)
[35] Da Deppo, D.A.; Schmidt, R., Side sway buckling of deep circular arches under a concentrated load, J. appl. mech., 36, 325-327, (1969)
[36] Noor, A.K.; Peters, J.M., Instability analysis of space trusses, Comput. meths. appl. mech. engrg., 40, 199-218, (1983) · Zbl 0505.73051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.