Abstract
Although simple finite elements as truss members and beam members in frames have been used in structural analysis for many years, the general finite element methods of analysis have been developped only recently in parallel with the development of digital computers. It is the use of general matrix methods in high speed digital computers that makes the general finite element methods feasible. At the present time the finite element methods are being used extensively in the analysis and design of flight vehicle structures as well as in other types of structures. Many large general purpose computer programs as well as many specialized programs have been developed for the analysis of structures. These computer programs use various finite elements and usually calculate and assemble the element matrices by one of the three methods of analysis described in previous chapters. Most of the general programs use the displacement method of analysis; a few general programs and many specialized programs use the force method of analysis; a few programs use the mixed method, while some programs use more than one method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.S. Przemieniecki: Theory of Matrix Structural Analysis, McGraw-Hill Book Co. (1968).
R.H. Gallagher: Finite Element Analysis, Fundamentals, Prentice-Hall, Inc. (1975).
P. Tong and J.N. Rossettos: Finite Element Method, Basic Technique and Implementation, MIT Press (1977).
H.C. Martin and G.F. Carey: Introduction to Finite Element Analysis, McGraw-Hill Book Co. (1973).
O.C. Ziepkiewicz: The Finite Element Method, Third Edition, McGraw-Hill Book Co. (1977).
T.J. Chung: Solid Mechanics and Finite Elements, McGraw-Hill Book Co. (1979).
J.H. Argyris: Energy Theorem and Structural Analysis, Butterworth Scientific Publications, London (1960).
J.H. Argyris: Recent Advances in Matrix Methods of Structural Analysis, Macmillan Co., New York (1964).
C.S. Desai and J.F. Abel: Introduction to the Finite Element Method, Van Nostrand Reinhold Co. (1972).
D.H. Norrie and G. Devries: An Introduction to Finite Element Analysis, Academic Press (1978).
G. Strang and G.J. Fix: An Analysis of the Finite Element Method, Prentice-Hall, Inc. (1973).
T.H.H. Pian: Derivation of element stiffness matrices, AIAA Journal 2, p. 576, March (1964).
T.H.H. Pian: Derivation of element stiffness matrices by assumed stress distribution, AIAA Journal 2, p. 1333, July (1964).
J.S. Przemieniecki, R.M. Bader, W.F. Bozich, J.R. Johnson and W.J. Mykytow (Editors): Proceedings of Conference on Matrix Methods in Structural Mechanics, AFFDL-TR-66–80, 1966. Various papers on finite elements, including
T.H.H. Pian: Element stiffness matrices for boundary compatibility and for prescribed boundary stresses, pp. 457–478.
R.W. Clough and J.L. Tocher: Finite element stiffnes matrices for analysis of plate bending, pp. 515–546.
L.R. Herrmann: A bending analysis of plates, pp. 577–602.
G.P. Bezeley, Y.K. Chenng, B.M. Irons and O.C. Zienkiewicz: Triangular elements in plate bending: conforming and nonconforming solutions, pp. 547–576.
F.K. Bogner, R.L. Fox, and L.A. Schmit, Jr.: The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulas, pp. 397–443.
L. Berke, R.M. Bader, W.J. Mykytow, J.S. Przemieniecki and M.H. Shirk (Editors): Proceedings of the Second Conference on Matrix Methods in Structural Mechanics, AFFDL-TR-68–150 (1968). Various papers on finite elements, including
T.H.H. Pian and Pin Tong: Rationalization of deriving element stiffness matrices by assumed stress approach, pp. 448–469.
R.S. Dunham and K.S. Pister: Finite element application of the hellinger-reissner variational theorem, pp. 471–487.
J.E. Walz, R.E. Fulton, and Nancy J. Cyrus: Accuracy and convergence of finite element approximations, pp. 995–1027.
R.H. Gallagher, Y. Yamada, and J.J. Oden (Editors): Recent Advances in Matrix Methods of Structural Analysis and Design, The University of Alabama Press, University, Alabama (1971). Various papers on finite elements.
L.R. Herrmann: Finite element boundary analysis for plates, Journal of the Engineering Mechanics Division, ASCE, 93, EM5, pp. 13–26 (1967).
R.D. Cook: Some elements for analysis of plate bending, Proc. ASCE, Journal of the Engineering Mechanics Division 98, EM6, pp. 1457–1470 (1972).
W. Visser: A Refined mixed-type plate bending element, AIAA Journal 7, pp. 1801–1802
L.S.D. Morley: The constant-moment plate bending element, Journal of Strain Analysis 6, pp. 20–24 (1971).
J. Bron and G. Khatt: Mixed quadrilateral elements for bending, AIAA Journal 10, pp. 1359–1361, Oct. (1972).
Z.M. Elias: Duality in finite element methods, Proc. of ASCE, Journal of Engineering Mechanics Division 94, pp. 931–946 (1968).
J. Robinson: Integrated Theory of Finite Element Methods, John Wiley and Sons (1973).
References for additional reading
C.A. Brebbia and J.J. Connor: Fundamentals of Finite Elements Techniques for Structural Engineers. John Wiley and Sons, New York (1974).
K.V. Rockey: The Finite Element Method: A Basic Introduction, John Wiley and Sons, New York (1975).
K.J. Bathe and E.L. Wilson: Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1976).
R.D. Cook: Concepts and Applications of Finite Element Analysis, 2nd Ed., John Wiley and Sons, New York (1981).
J.N. Reddy: An Introduction to the Finite Element Method, McGraw-Hill Book Co., New York (1984).
L.J. Segerlind: Applied Finite Element Analysis, 2nd Ed., John Wiley;and Sons, New York (1985).
I.H. Shames and C.L. Dym: Energy and Finite Element Methods in Structural Mechanics, McGraw-Hill Book Co., New York (1985).
H. Gradin Jr.: Fundamentals of the Finite Element Method, Macmillan, New York (1986).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Gatewood, B.E. (1989). Matrix structural analysis using finite elements. In: Virtual Principles in Aircraft Structures. Mechanics of Structural Systems, vol 6-7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1165-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-009-1165-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7018-8
Online ISBN: 978-94-009-1165-9
eBook Packages: Springer Book Archive