This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Survey of Solution Procedures for Nonlinear Static and Dynamic Analyses
Annotation ability available
Sector:
Language:
English
Abstract
This paper presents a review of the solution techniques most widely used for solving the governing equations for static and dynamic, large deflection, elastic-plastic response of structures. For the transient response, one explicit direct integration method (central differences) and three implicit methods (Houbolt, Newmark Beta, and Wilson) are compared with respect to accuracy and stability. A modal superposition technique is developed and compared to the direct integration methods. It is concluded that the choice of a suitable method depends on the structure and loading involved and on the frequency response desired. For the static response, the available techniques are grouped according to whether they yield exact or approximate solutions to the nonlinear equations. The convergence characteristics for each method are summarized. Although it is concluded that the choice of methods depends on which type of nonlinearity (geometric or material) is most significant, the first-order self-correcting method is recommended as the best method overall for static problems.
Authors
Topic
Citation
Stricklin, J. and Haisler, W., "Survey of Solution Procedures for Nonlinear Static and Dynamic Analyses," SAE Technical Paper 740317, 1974, https://doi.org/10.4271/740317.Also In
References
- Balmer H. A. “Improved Computer Programs-DEPROSS 1, 2, and 3 to Calculate the Dynamic Elastic-Plastic Two-Dimensional Responses of Impulsively-Loaded Beams, Rings, Plates, and Shells of Revolution.” Massachusetts Institute of Technology ASRL TR 128-3 August 1965
- Huffington, N. J. Jr. “Numerical-Analysis of Elasto-plastic Stress.” U.S. Army Ballistic Research Laboratory Memorandum Report No. 2006 September 1969
- Krieg R. D. Duffey T. A. “UNIVALVE II: A Code to Calculate the Large Deflection Dynamic Response of Beams, Rings, Plates, and Cylinders.” Sandia Corporation Report SC-RR-68-303 October 1968
- Stricklin J. A. Martinez J. E. Tillerson J. R. Hong J. H. Haisler W. E. “Nonlinear Dynamic Analysis of Shells of Revolution by the Matrix Displacement Method.” NASA CR 110406 National Aeronautics and Space Administration Washington, D.C.
- Farhoomand I. Wilson E. L. “A Nonlinear Finite Element Code for Analyzing the Blast Response of Underground Structure.” Contract Report No. N-70-1 U.S. Army Engineer Waterways Experiment Station Vicksburg, Miss. January 1970
- McNamara J. F. Marcal P. V. “Incremental Stiffness Method for Finite Element Analysis of Nonlinear Dynamic Problems.” International Symposium of Numerical and Computer Methods in Structural Mechanics Urbana, Illinois September 1971
- Stricklin J. A. Haisler W. E. Von Riesemann W. E. “Geometrically Nonlinear Structural Analysis by the Direct Stiffness Method.” J. of Struct. Div., ASCE, ST9 Sept. 1971 2299 2314
- Wu R. W. H. Witmer E. A. “Finite-Element Analysis of Large Transient Elastic-Plastic Deformations of Simple Structures, With Application to the Engine Rotor Fragment Containment/Deflection Problem.” NASA-CR-120886 National Aeronautics and Space Administration Washington, D.C. January 1972
- Key S. W. Beisinger Zelma E. “The Transient Dynamic Analysis of Thin Shells by the Finite Element Method.” Air Force Third Conference on Matrix Methods in Structural Mechanics Wright-Patterson Air Force Base Ohio October 19-21 1971
- Krieg R. D. Key S. W. “Transient Shell Response by Numerical Time Integration.” Proceedings of 2nd U.S.-Japan Seminar on Matrix Methods of Structural Analysis University of Alabama Press Huntsville, Alabama 1972
- Stricklin J. A. Martinez J. E. Tillerson J. R. Hong J. H. Haisler W. E. “Nonlinear Dynamic Analysis of Shells of Revolution by the Matrix Displacement Method.” AIAA Journal 9 4 April 1971 629 636
- Houbolt J. C. “A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft.” Journal of the Aero. Sciences 17 1950 540 550
- Newmark N. M. “A Method of Computation for Structural Dynamics.” Journal of the Engineering Mechanics, Div. Proceedings of the Am. Soc. of Civil Engr. 85 July 1959 67 94
- Bathe K. J. Wilson E. L. “Stability and Accuracy Analysis of Direct Integration Methods.” International Journal of Earthquake Engineering and Structural Dynamics 1 1973 283 291
- Tillerson J. R. Stricklin J. A. “Numerical Methods of Integration Applied in the Nonlinear Dynamic Analyses of Shells of Revolution.” NASA-CR-108639 National Aeronautics and Space Administration Washington, D.C. August 1970
- Chan S. P. Cox H. L. Benfield W. A. “Transient Analysis of Forced Vibrations of Complex Structural-Mechanical Systems.” Journal of Royal Aero. Soc. 66 619 July 1962 457 460
- Weeks G. “Temporal Operators for Nonlinear Structural Dynamics Problems.” Journal of Engineering Mechanics Division ASCE October 1972 1087 1104
- Wu R. W. H. Witmer E. A. “Nonlinear Transient Responses of Structures by the Spatial Finite-Element Method.” AIAA Journal 11 8 August 1973 1110 1117
- Nickell R. E. “A Survey of Direct Integration Methods in Structural Dynamics.” Department of the Navy, Office of Naval Research, Tech. Report No. 9 Brown University Providence, R.I. April 1972
- Dunham R. S. Nickell R. E. Stickler D. C. “Integration Operators for Transient Structural Response.” Computers and Structures 2 1972 1 15
- Goudreau G. L. Taylor R. L. “Evaluation of Numerical Integration Methods in Elastodynamics.” Computer Methods in Applied Mechanics and Engineering 2 1 1972 65 68
- Harii K. Kawahara M. “A Numerical Analysis on the Dynamic Response of Structures.” Proceedings, 19th Japan National Congress for Applied Mechanics 1969 17 22
- Nickell R. E. Second U.S.-Japan Symposium on Computational Method Berkeley, California August 1972
- Bathe K. J. Wilson E. L. “Solution Methods for Eigenvalue Problems in Structural Mechanics.” International Journal for Numerical Methods in Engineering 6 1973 213 226
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Large Deflection Elastic-Plastic Dynamic Response of Stiffened Shells of Revolution.” 1974 Pressure Vessels and Piping-Materials-Nuclear Conference Miami, Florida June 1974 SLA-73-0128 Sandia Corporation Albuquerque, New Mexico December 1972
- Haisler W. E. Stricklin J. A. Stebbins F. J. “Development and Evaluation of Solution Procedures for Geometrically Nonlinear Structural Analysis.” AIAA Journal 10 3 March 1972 264 272
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Evaluation of Solution Procedures for Material and/or Geometrically Nonlinear Structural Analysis.” AIAA Journal 11 3 March 1973 292 299
- Tillerson J. R. Stricklin J. A. Haisler W. E. “Numerical Methods for the Solution of Nonlinear Problems in Structural Analysis.” Symposium on Numerical Solution of Nonlinear Structural Problems, ASME 1973 Annual Winter Meeting Detroit, Michigan November 11-15 1973
- Haisler W. E. “Development and Evaluation of Solution Procedures for Nonlinear Structural Analysis.” Ph.D. dissertation 1970 Texas A&M University College Station, Texas
- Stricklin J. A. Haisler W. E. MacDougall H. R. Stebbins F. J. “Nonlinear Analysis of Shells of Revolution by the Matrix Displacement Method.” AIAA Journal 6 12 December 1968 2306 2312
- Perrone N. Kao R. “Large Deflection Response and Buckling of Partially and Fully Loaded Spherical Caps.” AIAA Journal 8 12 December 1970 2130 2136
- Kawai T. Yoshimura N. “Analysis of Large Deflection of Plates by the Finite Element Method.” International Journal for Numerical Methods in Engineering 1 1969 123 133
- De Donato O. “Iterative Solution of the Incremental Problem for Elastic-Plastic Structures With Associated Flow Laws.” International Journal of Solids and Structures 5 1969 81 95
- Marcal P. V. “A Comparative Study of Numerical Methods of Elastic-Plastic Analysis.” AIAA Journal 6 1 January 1968 157
- Witmer E. A. Kotanchik J. J. “Progress Report on Discrete-Element Elastic and Elastic-Plastic Analysis of Shells of Revolution Subjected to Axisymmetric and Asymmetric Loading.” Proceedings of the Second Conference on Matrix Methods in Structural Mechanics Wright-Patterson Air Force Base, Ohio October 15-17 1968 December 1969 1341 1453
- Connor J. J. Logcher R. D. Chan S. “Nonlinear Analysis of Elastic Framed Structures.” Journal of the Structural Division, ASCE 94 ST6 June 1968 1525 1547
- Mallet R. H. Marcal P. V. “Finite Element Analysis of Nonlinear Structure.” Journal of the Structural Division, ASCE 94 ST9 September 1968 2081 2105
- Oden J. T. Key J. E. “Numerical Analysis of Finite Axisymmetric Deformations of Incompressible Elastic Solids of Revolution.” International Journal of Solids and Structures 6 5 May 1970 497 518
- Oden J. T. Sato T. “Finite Strains and Displacements of Elastic Membranes by the Finite Element Method.” International Journal of Solids and Structures 3 1967 471 488
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Geometrically Nonlinear Analysis by the Direct Stiffness Method.” Report 70-16 August 1970 Aerospace Engineering Dept., Texas A&M University College Station, Texas
- Tezcan S. S. Mahapatra B. C. “Tangent Stiffness Matrix for Space Frame Members.” Journal of the Structural Division, ASCE 95 ST6 June 1969 1257 1270
- Walker A. C. Hall D. G. “An Analysis of the Large Deflections of Beams Using the Rayleigh-Ritz Finite Element Method.” Aeronautical Quarterly November 1968 357 367
- Bushnell D. Almroth B. O. “Finite-Difference Energy Method for Nonlinear Shell Analysis.” Proceedings of the Conference on Computer Oriented Analysis of Shell Structures Lockheed Company Palo Alto, California Aug. 10-14 1970 337 394
- Mescall J. R. “On the Numerical Analysis of the Nonlinear Axisymmetric Equations for Shells of Revolution.” TR 64-20 U.S. Army Materials Research Agency 1964
- Brogan F. Almroth B. “Buckling of Cylinders With Cutouts.” AIAA 7th Aerospace Sciences Meeting New York Jan. 20-22 1969 Paper No. 6992
- Bushnell D. “Bifurcation Phenomena in Spherical Shells Under Concentrated and Ring Loads.” AIAA Journal 5 11 November 1967 2034 2040
- Bushnell D. “Nonlinear Analysis for Axisymmetric Elastic Stresses in Ring-Stiffened, Segmented Shells of Revolution.” Proceedings of the AIAA/ASME 10th Structures Structural Dynamics and Materials Conferences New Orleans April 14-16 1969
- Bushnell D. “Analysis of Ring-Stiffened Shells of Revolution Under Combined Thermal and Mechanical Loading.” Proceedings of the AIAA/ASME 11th Structures Structural Dynamics and Materials Conference April 22-24 1970 196 210
- Greenbaum G. A. Conroy D. C. “Postwrinkling Behavior of a Conical Shell of Revolution Subjected to Bending Loads.” AIAA Journal 8 4 April 1970 700 707
- Kalnins A. Lestingi J. F. “On Nonlinear Analysis of Elastic Shells of Revolution.” Journal of Applied Mechanics March 1967 59 64
- Mescall J. F. “Large Deflections of Spherical Shells Under Concentrated Loads.” Journal of Applied Mechanics December 1965 936 938
- Stephens W. B. Fulton R. E. “Axisymmetric Static and Dynamic Buckling of Spherical Caps Due to Centrally Distributed Pressures.” AIAA Journal 7 11 November 1969 2120 2126
- Thurston G. A. “Continuation of Newton's Method Through Bifurcation Points.” Journal of Applied Mechanics 36 September 1969 425 430
- Oden J. T. “Finite Element Applications in Nonlinear Structural Analysis.” Proceedings of the Conference on Finite Element Methods Vanderbilt University Tennessee 1969 419 456
- Brebbia C. Connor J. “Geometrically Nonlinear Finite Element Analysis.” Journal of the Engineering Mechanics Division ASCE 95 EM2 April 1969 463 483
- Poskitt T. J. “Numerical Solution of Nonlinear Structures.” Journal of the Structural Division ASCE 93 ST4 August 1967 69 94
- Oden J. T. Kubitza W. K. “Numerical Analysis of Nonlinear Pneumatic Structures.” Proceedings of the International Colloquium on Pneumatic Structures Stuttgart, Germany 1967
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Formulation, Computation, and Solution Procedures for Material and/or Geometric Nonlinear Structural Analysis by the Finite Element Method.” Sandia Corporation Report, SC-CR-72-3102 July 1972
- Hofmeister L. D. Greenbaum G. A. Evenson D. A. “Large Strain, Elasto-Plastic Finite Element Analysis.” Proceedings of AIAA/ASME 11th Structures Structural Dynamics and Materials Conference Denver, Colorado April 1970 250 259
- Bushnell D. “Large Deflection Elastic-Plastic Creep Analysis of Axisymmetric Shells.” Symposium on Numerical Solution of Nonlinear Structural Problems, ASME 1973 Annual Winter Meeting Detroit, Michigan November 11-15 1973
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Self-Correcting Initial Value Formulations in Nonlinear Structural Mechanics.” AIAA Journal 9 10 October 1971 2066 2067
- Stricklin J. A. Haisler W. E. Von Riesemann W. A. “Evaluation of Solution Procedures for Material and/or Geometrically Nonlinear Structural Analysis by the Direct Stiffness Method.” AIAA/ASME 13th Structures, Structural Dynamics, and Materials Conference San Antonio, Texas April 1972 13
- Armen H. Levine H. S. Pifko A. B. “Plasticity-Theory and Finite Element Applications.” Proceedings of 2nd U.S.-Japan Seminar on Matrix Methods of Structural Analysis and Design August 1972 393 437
- Armen H. Levine H. Pifko A. Levy A. “Nonlinear Analysis of Structures.” Grumman Research Department Report RE-454 May 1973