History of the stiffness method

International Journal for Numerical Methods in Engineering

Volumn 67, Issue 2, 2006, Pages 149-157

  Samuelsson, Alf ^a   Zienkiewicz, O C ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Computational mechanics; History; Stiffness method

Indexed keywords

COMPUTATIONAL METHODS; CONTINUUM MECHANICS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING; STRUCTURAL MEMBERS;

COMPUTATIONAL MECHANICS; CONTINUUM PROBLEMS; DISCRETE-TYPE PROBLEMS; STIFFNESS METHOD;

STIFFNESS;

COMPUTATIONAL METHODS; CONTINUUM MECHANICS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING; STIFFNESS; STRUCTURAL MEMBERS;

EID: 33745907272     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1510     Document Type: Review

References (41)

1. Timoshenko SP. History of the Strength of Materials. McGraw-Hill: New York, 1953.
2. Ramm E. Entwicklung der Baustatik von 1920 bis 2000. Bauingenieur 2000; 75(7/8):7-29.
3. Kupper K-E. Die Geschichte der Baustatik. W. Ernst and Sohn: 2002.
4. Zienkiewicz OC. The birth of the finite element method and of computational mechanics. International Journal for Numerical Methods in Engineering 2004; 60:3-10.
5. Clebsch A. Theorie der Elasticität fester Körper. 1862.
6. Clebsch A. Theorie der Elasticität fester Körper (French translation by Barré de Saint-Venant, with annotated footnotes). 1883.
7. Manderla H. Die Berechnung der Sekunärspannungen, Allgem: Bauzeitung, 1880; 45:34.
8. Berry A. Transactions of Royal Aeronautical Society 1919.
9. Mohr O, Ziviling. 1892; 38.
10. Wilson WM, Maney GA. University of Illinois Engineering Experiment Station, Bulletin 80, 1915.
11. Matheson JAL. Hyperstatic Structures, vol. VI. 1959.
12. Bendixsen A. Die Methode der Alpha-Gleichungen zur Berechnung von Rahmenkonstruktionen. 1914.
13. Ostenfeld A. Die Deformationsmethode. 1926.
14. Čališev KA. Tehnički List. 1922; 1-2; 1923; 17-21.
15. Cross H. Analysis of continuous frames by distributing fixed moments. Proceedings of the ASCE 1930; 57:919-928.
16. Cross H. Analysis of continuous frames by distributing fixed moments. Transactions of the ASCE 1932; 96:1-10.
17. Grinter LE. Discussion to paper by H. Cross. Transactions of the ASCE 1932; 96:11-20.
18. Grinter LE. Wind stress analysis simplified. Proceedings of the ASCE 1933; 59:3-27.
19. Southwell RV. Stress calculation in frameworks by the method of 'systematic relaxation of constraints'. Part I & II. Proceedings of the Royal Society of London, Series A 1935; 151:56-95.
20. Southwell RV. Relaxation Methods in Engineering Science. Oxford University Press: Oxford, 1940.
21. Duncan WJ, Collar AR. A method for the solution of oscillation problems by matrices. Philosophical Magazine 1934; 17(Series 7):865.
22. Duncan WJ, Collar AR. Matrices applied to the motions of damped systems. Philosophical Magazine 1934; 19(Series 7):197.
23. Frazer RR, Duncan WJ, Collar AR. Elementary Matrices. Cambridge University Press: Cambridge, MA, 1960.
24. Kron G. Tensorial analysis of elastic structures. Journal of the Franklin Institute 1944; 238:399-442.
25. Argyris JH. Energy theorems and structural analysis. Aircraft Engineering 1954; 26:347-356, 383-394; 1955; 27:42-58, 80-94, 125-134, 145-158.
26. Levy S. Computation of influence coefficients for aircraft structures with discontinuities and sweepback. Journal of the Aeronautical Sciences 1937; 14:547.
27. Falkenheiner H. Calcul systématique des caracteristiques elastic des systémes hyperstatiques. La Recherche Aéronatique 1950; 17:17.
28. Lang AL, Bisplinghoff RL. Some results of sweptback wing structural studies. Journal of the Aeronautical Sciences 1951; 18:751.
29. Langefors B. Analysis of elastic structures by matrix transformations with special regard to semimonocoque structures. Journal of the Aeronautical Sciences 1952; 19:45.
30. Hrenikoff A. Solution of problems of elasticity by the framework method. Journal of Applied Mechanics 1941; A8(1):169-175.
31. McHenry D. A lattice analogy for the solution of stress problems. Journal of the Institute of Civil Engineer 1943; 21:59-82.
32. Richardson LF. The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stresses in a masonry dam. Transactions of the Royal Society of London, Series A 1910; 210:307-357.
33. Southwell RV. Relaxation Methods in Theoretical Physics. Oxford University Press: Oxford, 1946.
34. Zienkiewicz OC. Doctoral Thesis, Imperial College, 1945.
35. Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Society 1943; 49:1-61.
36. Clough RW. The finite element method - a personal view of its original formulation. In From Finite Elements to the Troll Platform, Bell K (ed.). Tapir: Trondheim, 1994.
37. Turner MJ, Clough RW, Martin HC, Topp LJ. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences 1956; 23:805-823.
38. Pian THH, Tong P. Basis of finite element methods for solid continua. International Journal for Numerical Methods in Engineering 1969; 1:3-28.
39. Wilson EL, Taylor RL, Doherty WP, Ghaboussi J. Incompatible displacement models. In Numerical and Computer Methods in Structural Mechanics, Fenves ST et al. (eds). Academic Press: New York, 1973.
40. Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973.
41. Zienkiewicz OC, Cheung YK. The Finite Element Method in Structural Mechanics. McGraw-Hill: New York, 1967.