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TECHNICAL PAPERS

DQFEM Analyses of Static and Dynamic Nonlinear Elastic-Plastic Problems Using a GSR-Based Accelerated Constant Stiffness Equilibrium Iteration Technique

[+] Author and Article Information
Chang-New Chen

Department of Naval Architecture and Marine Engineering, National Cheng Kung University, Tainan, Taiwane-mail: cchen@mail.ncku.edu.tw

J. Pressure Vessel Technol 123(3), 310-317 (Feb 28, 2001) (8 pages) doi:10.1115/1.1374205 History: Received October 28, 1999; Revised February 28, 2001
Copyright © 2001 by ASME
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References

Chen, C. N., 1990, “Improved Constant Stiffness Algorithms for the Finite Element Analysis,” Proc., NUMETA 90, Swansea, UK, pp. 623–628.
Chen,  C. N., 1992, “Efficient and Reliable Accelerated Constant Stiffness Algorithms for the Solution of Non-linear Problems,” Int. J. Numer. Methods Eng., 35, pp. 481–490.
Ponthot, J. P. and Hogge, M., 1994, “On Relative Merits of Implicit/Explicit Algorithms for Transient Problems in Metal Forming Simulation,” Proc., International Conference on Numerical Methods for Metal Forming in Industry, Baden-Baden, GERMANY, 2 , pp. 128–148.
Chen, C. N., 1998, “The Differential Quadrature Finite Element Method,” Applied Mechanics in the Americas, D. Pamplona et al. eds., American Academy of Mechanics, 6 , pp. 309–312.
Bellman,  R. E., and Casti,  J., 1971, “Differential Quadrature and Long-term Integration,” J. Math. Anal. Appl., 34, pp. 235–238.
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Chen, C. N., 1998, “Extended Differential Quadrature,” Applied Mechanics in the Americas, D. Pamplona et al., eds., American Academy of Mechanics, 6 , pp. 309–312.
Chen, C. N., 1998, “A Differential Quadrature Finite Difference Method,” Proc., International Conference on Advanced Computational Methods in Engineering, Ghent, Belgium, pp. 713–720.
Chen, C. N., 1995, “A Differential Quadrature Element Method,” Proc., 1st International Conference on Engineering Computation and Computer Simulation, Changsha, China, 1 , pp. 25–34.
Chen, C. N., 1998, “A Generalized Differential Quadrature Element Method,” Proc., International Conference on Advanced Computational Methods in Engineering, Ghent, Belgium, pp. 721–728.
Chung,  J., and Hulbert,  G. M., 1993, “A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipations: the Generalized-α Method,” ASME J. Appl. Mech., 60, pp. 371–375.
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Hogge, M. and Ponthot, J. P., 1996, “Efficient Implicit Schemes for Transient Problems in Metal Forming Simulation,” Numerical and Physical Study of Material Forming Processes, Paris, France.
Cahill, E., 1992, “Acceleration Techniques for Functional Iteration of Non-linear Equations,” IMACS Conference on Mathematical Modelling and Scientific Computing, Bangalove, India.
Crisfield,  M. A., 1984, “Accelerated and Damping the Modified Newton-Raphson Method,” Comput. Struct., 18, pp. 267–278.
Chen, C. N., 1998, “Newton-Raphson Techniques in Finite Element Methods for Nonlinear Structural Problems,” International Series in Engineering, Technology and Applied Science, Structural Dynamic Systems Computational Techniques and Optimization, C. T. Leondes, eds., Gordon and Breach, pp. 149–242.
Saint-Georges,  P., , 1996, “High-Performance PCG Solvers for FEM Structural Analysis,” Int. J. Numer. Methods Eng., 39, pp. 1313–1340.
Chen,  C. N., 1995, “A Global Secant Relaxation (GSR) Method-Based Predictor-Corrector Procedure for the Iterative Solution of Finite Element Systems,” Comput. Struct., 54, pp. 199–205.
Stenger,  F., 1981, “Numerical Methods Based on Whittaker Cardinal, or Sinc Functions,” SIAM Review, 23, pp. 165–224.

Figures

Grahic Jump Location
A square plate with a square cutout
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Load-displacement curve of point A
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The convergence of equilibrium iteration
Grahic Jump Location
A rectangular girder framework
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Response history curves of the vertical members
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A spherical cap subjected to a step pressure
Grahic Jump Location
Dynamic response of a spherical cap subjected to a step pressure

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