Engineering Transactions, 39, 1, pp. 59-74, 1991

Nonlinear Solution Methods for Fem Analysis of Concrete Structures

G. Gajer
Mc Intyre and Associates Pty. LTD., Brisbane

The essential objective of the nonlinear FEM analysis is the solution of a system of nonlinear equations. Due to strain-softening nature of fracture processes, concrete structures need a special attention in applying a suitable nonlinear solution procedure. New, sophisticated material models and the need to predict limit points and post-peak behaviour of a structure require methods capable of converging in the vicinity of such limit points. This paper reviews several nonlinear solution methods with particular reference to the usefulness in the nonlinear analysis of concrete structures exhibiting strain-softening characteristics.

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O.C.ZIENKIEWICZ, The finite element method, McGraw Hill, London 1977,

K.J.BATHE, Finite element procedures in engineering analysis, Prentice-Hall, Englewood Cliffs, New Jersey 1982.

T.H.H.PIAN AND P.TONG, Variational formulation of finite element analysis, IUTAM Symposium on High Speed Computing of Elastic Structures, pp.43-63, Liège 1970.

J.L.BATOZ and G.DHATT, Incremental displacement algorithm for nonlinear problems, Intern. J. Num. Meth. Enging., 14, pp.1262-1267, 1979.

M.A.CRISFIELD, A fast incremental/iterative solution procedure that handles "Snap Through", Comp. and Struct., 13, pp.55-62, 1981.

M.A.CRISFIELD, Overcoming limit points with material softening and strain localisation, Num. Meth. for Nonlinear Problems, [Eds.] C.TAYLOR, E.HINTON, D.R.J.OWEN, Pineridge Press, pp.244-277, Swansea 1984.

M.A.CRISFIELD, Numerical analysis of structures, Developments in Thin-Walled Structures, [Eds.] J. RHODES and A.C. WALKER, Appl. Sci. Publ., pp.235-284, London 1982.

M.A. CRISFIELD, Snap-through and snap-back response in concrete structures and the danger of under integration, Intern. J. Num. Meth. in Enging., 22, pp.751-767, 1986.

E.RIKS, Application of Newton's method to the problem of elastic stability, J. Appl.Mech., 39, pp. 1060-1066, 1972.

G.A.WEMPNER, Discrete approximations related to nonlinear theories of solids, Intern.J. Solids and Struct., 7, pp.1581-1599, 1971.

F.B.HILDEBRAND, Introduction to numerical analysis, McGraw-Hill 1974.

M.A.CRISFIELD, An arc-length method including line searches and accelerations, Intern. J. Num.Meth. in Enging., 19, pp.1269-1289, 1983.

E.RAMM, Strategies for tracing non-linear responses near limit points, Non-linear Element Anal. in Struct.Mech., [Eds.] W.WUNDERLICH, E.STEIN, K.J.BATHE, Springer­Verlag, pp.68-89, New York 1981.

R. DE BORST, Computation of post-bifurcation and post-failure behaviour of strain­softening solids, Computers and Struct., 25, 2, pp.211-224, 1987.

J.E.DENNIS and J.J.MORE, Quasi-Newton methods motivation and theory, SIAM Rev., 19, p.46, 1977.

K.J.BATHE, A.P.CIMENTO, Some practical procedures for the solution of nonlinear finite element equations, Comp. Meth. in Appl. Mech. and Enging., 22, pp.59-85, 1980.

R. DE BORST, Application of advanced solution techniques to concrete cracking and non-associated plasticity, Num. Meth. for Nonlinear Probl., [Eds.] C.TAYLOR, E.HINTON, D.R.J.OWEN, Pineridge Press, pp.314-325, Swansea 1984.

M.A.CRISFIELD, Accelerated solution techniques and Concrete cracking, Comp. Meth. in App. Mech. and Enging., 33, pp.585-607, 1982.

M.A.CRISFIELD, Incremental/iterative solution procedures for non-linear structural analysis, Num. Meth. for Nonlin. Probl., [Eds.] C.TAYLOR, E.HINTON, D.R.J.OWEN, Pineridge, 1, p.261, Swansea 1980.

G.GAJER, Finite element modelling and analysis of reinforced concrete structures, Ph. D. thesis, University of Queensland, Australia 1989.

G.GAJER and P.F.DUX, A crack band based model for FEM analysis of concrete structures, J Struct. Enging., 116, 2, pp.1696-1714, 1990.

G.GAJER and P.F.DUX, Strain-softening analysis of concrete structures, Intern. J. of Comp. and Struct.,. 33, 2, pp.575-582, 1989.

G.GAJER and P.F.DUX, A simplified non-orthogonal model for concrete, J. Struct. Enging., ASCE, to be published, 1990.

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