Pseudoforce Method for Nonlinear Analysis and Reanalysis of Structural Systems
Publication: Journal of Structural Engineering
Volume 127, Issue 5
Abstract
This paper develops a new solver to enhance the computational efficiency of finite-element programs for the nonlinear analysis and reanalysis of structural systems. The proposed solver does not require the reassembly of the global stiffness matrix and can be easily implemented in present-day finite-element packages. It is particularly well suited to those situations where a limited number of members are changed at each step of an iterative optimization algorithm or reliability analysis. It is also applicable to a nonlinear analysis where the plastic zone spreads throughout the structure due to incremental loading. This solver is based on an extension of the Sherman-Morrison-Woodburg formula and is applicable to a variety of structural systems including 2D and 3D trusses, frames, grids, plates, and shells. The solver defines the response of the modified structure as the difference between the response of the original structure to a set of applied loads and the response of the original structure to a set of pseudoforces. The proposed algorithm requires O(mn) operations, as compared with traditional solvers that need O(m2n) operations, where m = bandwidth of the global stiffness matrix and n = number of degrees of freedom. Thus, the pseudoforce method provides a dramatic improvement of computational efficiency for structural redesign and optimization problems, since it can perform a nonlinear incremental analysis no harder than the inversion of the global stiffness matrix. The proposed method's efficiency and accuracy are demonstrated in this paper through the nonlinear analysis of an example bridge and a frame redesign problem.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abu Kassim, A. M., and Topping, B. H. V. (1987). “Static reanalysis: A review.”J. Struct. Engrg., ASCE, 113(5), 1029–1045.
2.
Arora, J. S. (1976). “Survey of structural reanalysis techniques.”J. Struct. Div., ASCE, 102(4), 783–802.
3.
Argyris, J. H. ( 1956). “The matrix analysis of structures with cut-outs and modifications.” Communication to 9th Int. Congr. of Theoretical and Appl. Mech., University of Brussels, Brussels, 131–142.
4.
Bathe, K. J. ( 1996). Finite element procedures, Prentice-Hall, Upper Saddle River, N.J.
5.
Deng, L. ( 2000). “Reliability analysis of highway bridge systems.” PhD thesis, City University of New York, New York.
6.
Foley, C. M., and Vinnakota, S. (1999). “Inelastic behavior of multistory partially restrained steel frames: Part I.”J. Struct. Engrg., ASCE, 125(8), 854–861.
7.
Ghosn, M., Deng, L., Xu, J. M., Liu, Y., and Moses, F. ( 1997). “Documentation of program NONBAN.” NCHRP 12-36, National Cooperative Highway Research Program, Washington, D.C.
8.
Gierlinski, J. T., Sears, R. J., and Shetty, N. K. ( 1993). “Integrity assessment of fixed offshore structures: A case study using RASOS software.” Proc., 12th Int. Conf., American Society of Mechanical Engineers, New York, 399–408.
9.
Golub, G. H., and Van Loan, C. F. ( 1996). Matrix computation, 3rd Ed., John Hopkins University Press, Baltimore.
10.
Hirai, I., Wang, B. P., and Pilkey, W. D. ( 1984). “An efficient zooming method for finite element analysis.” Int. J. Numer. Methods in Engrg., 20, 1671–1683.
11.
Holnicki-Szulc, J. ( 1989). “Optimal structural remodeling: Simulation by virtual distortion.” Communication in Appl. Numer. Methods, 5, 289–298.
12.
Holnicki-Szulc, J. ( 1991). Virtual distortion method, Springer, Berlin.
13.
Kirsh, U., and Moses, F. ( 1995). “An improved reanalysis method for grillage-type structures.” Computers & Structures, 68, 79–88.
14.
Kirsh, U., and Rubinstein, M. F. ( 1970). “Modification of structural analysis by the solution of a reduced set of equations.” UCLA Paper Eng-0570, University of California, Los Angeles.
15.
Kirsh, U., and Rubinstein, M. F. (1972). “Reanalysis of limited structural design modifications.”J. Engrg. Mech. Div., ASCE, 98(1), 61–70.
16.
Kohnke, P. ( 1997). Ansys user's manual, theory, Ansys, Inc., Canonsburg, Pa.
17.
Liew, J. Y., White, D. W., and Chen, W. F. (1993a). “Second-order refined plastic-hinge analysis for frame design: Part I.”J. Struct. Engrg., ASCE, 119(11), 3196–3216.
18.
Liew, J. Y., White, D. W., and Chen, W. F. (1993b). “Second-order refined plastic hinge analysis for frame design: Part II.”J. Struct. Engrg., ASCE, 119(11), 3217–3237.
19.
MaGuire, W., and Gallagher, R. H. ( 1979). Matrix structural analysis, Wiley, New York.
20.
Makode, P. V., Corotis, R. B., and Ramirez, M. R. (1999). “Nonlinear analysis of frame structures by pseudo distortions.”J. Struct. Engrg., ASCE, 125(11), 1309–1317.
21.
Mohraz, B., and Wright, R. N. ( 1973). “Solving topologically modified structures.” Comp. and Struct., 3, 341–353.
22.
Pail, G. H., and Buckle, I. G. ( 1970). “Computer program for bridge deck analysis.” Rep. No. UC SESM 70-26, University of California, Berkeley, Calif.
23.
Sack, R. L., Carpenter, W. C., and Hatch, G. L. ( 1967). “Modification of elements in the displacement method.” AIAA J., 5(9), 1708–1710.
24.
Sherman, J., and Morrison, W. J. ( 1949). “Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a giving row of the original matrix.” Annals of Mathematical Statistics, 20, 621.
25.
Sherman, J., and Morrison, W. J. ( 1950). “Adjustment of an inverse matrix corresponding to a change in one element of a given matrix.” Annals of Mathematical Statistics, 21, 124–126.
26.
Wang, B. P., and Pilkey, W. D. ( 1980). Efficient reanalysis of locally modified structures, Dept. of Mech. and Aerospace Engrg., Virginia University, Charlottesville, Va.
27.
Wang, B. P., and Pilkey, W. D. ( 1981). “Parameterization in finite element analysis.” Proc., Int. Symp. on Optimum Struct. Des., Tuscon, Ariz., 7.1–7.7.
28.
Wang, B. P., Pilkey, W. D., and Palazzola, A. R. ( 1983). “Reanalysis, modal synthesis and dynamic design.” State-of-the-art surveys on finite element technology, A. K. Noor and W. D. Pilkey, eds., American Society of Mechanical Engineers, New York, 225–295.
29.
Yang, Y. B. ( 1984). “Linear and nonlinear analysis of space frames with nonuniform torsion using interactive computer graphics.” PhD thesis, Cornell University, Ithaca, N.Y.
30.
Ziemian, R. D. ( 1990). “Advanced methods of inelastic analysis in the limit state of steel structures.” PhD thesis, Cornell University, Ithaca, N.Y.
31.
Znidaric, A., and Moses, F. ( 1997). “Structural safety of existing road bridges.” Proc., 7th Int. Conf. on Struct. Safety and Reliability, Balkema, Rotterdam, The Netherlands, 1843–1850.
32.
Znidaric, A., and Moses, F. ( 1998). “Resistance of deteriorated post-tensioned concrete beams—An ongoing research.” Proc., 8th IFIP WG 7.5 Working Conf. on Reliability and Optimization of Struct. Sys., International Federation for Information Processing, 339–346.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 127 • Issue 5 • May 2001
Pages: 570 - 578
History
Received: May 26, 2000
Published online: May 1, 2001
Published in print: May 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.