Advanced Steel Construction

Vol. 5, No. 4, pp. 500-514 (2009)



Fawu Wang 1,* and Yaopeng Liu 2

1Department of Civil Engineering, Nanjing University of Aeronautics and Astronautics Yudao Street, Nanjing, China

2Department of Civil and Structural Engineering, The Hong Kong Polytechnic University Hunghom, Kowloon, Hong Kong

*(Corresponding author: E-mail:This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 22 May 2008; Revised: 6 August 2008; Accepted: 20 August 2008




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Co-rotational formulation is suitable for the incremental-iterative nonlinear analysis of framed structure which can be divided into three stages: the predictor, corrector and error-checking phases. The corrector or force recovery procedure determines the accuracy of the solution while the predictor affects only the convergence speed and direction of iteration. This paper details the formulation of the incremental-iterative nonlinear analysis of framed structure with PEP element and reviews the present existing force recovery procedures. A new force recovery method is proposed and compared with total secant iteration method and pure incremental method. It is found through three numerical examples that this incremental iteration force recovery procedure has a convergence rate comparable to total secant iteration method and it is recommended for path-dependent analysis.



Nonlinear analysis; framed structures; force recovery procedure; steel frame


[1] Yang, Y.B., Lin, S.P. and Leu, L.J., "Solution Strategy and Rigid Element for Nonlinear Analysis of Elastically Structures Based on Updated Lagrangian Formulation", Engineering Structures, 2007, Vol. 29, pp. 1189-1200.

[2] Chan, S.L., "Large Deflection Kinematic Formulations for Three-Dimensional Framed Structures", Computer Methods in Applied Mechanics and Engineering, 1992, Vol. 95, pp. 17-36.

[3] Oran, C., "Tangent Stiffness in Space Frames" , 1973, Vol. 99, pp. 987-1001.

[4] Izzuddin, B.A. and Elnashai, A.S., "Eulerian Formulation for Large-Displacement Analysis of Space Frames", Journal of Engineering Mechanics, 1993, Vol. 119, pp. 549-569.

[5] Felippa, C.A. and Haugen, B., "A Unified Formulation of Small-Strain Co-Rotational Finite Elements: I. Theory", Computer Methods in Applied Mechanics and Engineering, 2005, Vol. 194, pp. 2285-335.

[6] Chan, S.L. and Kitipornchai, S., "Geometric Nonlinear Analysis of Asymmetric Thin-Walled Beam-Columns", 1987, Vol. 9, pp. 243-254.

[7] Papadrakakis, M., "Post-Buckling Analysis of Spatial Structures by Vector Iteration Methods", Computers and Structures, 1981, Vol. 14, pp. 393-403.

[8] Chin, C.K., Al-Bermani, F.G.A. and Kitipornchai, S., "Non-Linear Analysis of Thin-Walled Structures Using Plate Elements", International Journal for Numerical Methods in Engineering, 1994, Vol. 37, pp. 1697-1711.

[9] Chan, S.L. and Zhou, Z.H., "Pointwise Equilibrating Polynomial Element for Nonlinear Analysis of Frames", Journal of Structural Engineering, 1994, Vol. 120, pp. 1703-1717.