Abstract
Finite element methods are best known from their applications to linear elasticity theory. Dual single-field variational principles, like the principle of minimum total energy and the principle of minimum complementary energy, were shown to be advantageous in the construction of mathematical models of finite elements and in the numerical estimation of the accuracy of the approximations [1], [2], [3].
This is a preview of subscription content, log in via an institution to check access.
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
B.M. Fra,eijs de Veubeke, “Upper and lower bounds in matrix structural analysis”, AGARDograph 72, Pergamon, 1964.
B.M. Fraeijs de Veubeke, “Displacement and equilibrium models”, Chpt 9. Stress Analysis J. Wiley, 1965.
G. Sander, “Application of the dual analysis principle”, Proceedings of the IUTAM Symposium Congrès et Colloques de l’Université de Liège, 1971.
A.R.S. Ponter, “The application of dual minimum theorems to the finite element solution of potentialprob lems with special reference to seepage”, Int. Jn1 for Num. Meth. in Eng., Vol. 4, 1972.
B.M. Fraeijs deVeixbeke and M.A. Hogge, “Dual analysis for heat conduction problems by finite elements”, Int. Jn1 for Num. Meth. in Eng., Vol. 4, 1972.
O.C. Zienkiewicz and Y.K. Cheung, Chp. 10, The Finite Ele ment Method in Structural and Continuum Mechanics McGraw Hill, London, 1967.
M.A. Hogge,“ Analyse numérique des problèmes thermiques en construction aéronautiqye et spatiale”, Report SF-14, L.T.A.S., Université de Liège, 1970.
J.C. Chato and A. Shitzer, “Thermal modeling of the human body–Further solutions of the steady-state equation”, A.I.A.A. Journal, vol. 9, no 5, pp. 865–869, May 1971.
B.M. Fraeijs de Veubeke and M.A. Rogge, “Dual minimum theorems in heat conduction problems and finite element solution based on compatible temperature fields”, CISM Course on the Finite Element Method, Udine, July 1972.
B.M. Fraeijs de Veubeke and M.A. Hogge, “Dual analysis for heat conduction problems by finite elements’; Int. Jnl for Num. Meth. in Eng., Vol. 4, 1972.
M.A. Rogge,“ Analyse numérique des problemes thermiques en construction aéronautique et spatiale”, Report SF-14, L.T.A.S., Université de Liège, 1970.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1972 Springer-Verlag Wien
About this chapter
Cite this chapter
Hogge, M., Fraeijs de Veubeke, B. (1972). Heat Conduction. In: Structural Dynamics. International Centre for Mechanical Sciences, vol 126. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2957-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2957-9_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81201-3
Online ISBN: 978-3-7091-2957-9
eBook Packages: Springer Book Archive