THE VARIATIONAL THEORY OF A CIRCULAR ARCH WITH TORSIONAL SPRINGS AT BOTH EDGES

Title & Authors
THE VARIATIONAL THEORY OF A CIRCULAR ARCH WITH TORSIONAL SPRINGS AT BOTH EDGES
Go, Jae-Gwi;

Abstract
Arches are constrained with rotational resistance at both edges. An energy method is used to derive variational formulation which is used to prove the existence of equilibrium states of elastic circular arches for the torsional spring constants ${\rho}-\;{\geq}\;0,\;{\rho}+\;{\geq}\;0,\;and\;{\rho}-\;+\;{\rho}+\;>\;0$. The boundary conditions are searched using the existence of minimum potential energy.
Keywords
arches;buckling;equilibrium state;rotational resistance;
Language
English
Cited by
References
1.
F. E. Browder, Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965), 176-183

2.
D. A. Dadeppo, Nonlinear analysis of buckling and postbuckling behavior of circular arches, J. Appl. Math. and Phys. 20 (1969), 847-857

3.
R. W. Dickey and P. Broughton, Stability criteria for shallow arches, J. Engineering Mechanics Division ASCE 97 (EM3), 1971

4.
M. Miklavcic, Applied functional analysis and partial differential equations, World Scientific Publishing Co., 1998

5.
G. J. Simitses, Elastic stability of structures, Prentice-Hall, New Jersey, 1976

6.
I. Tadjbakhsh and F. Odeh, Equilibrium states of elastic rings, J. Math. Anal. Appl. 18 (1967), 59-74

7.
S. P. Timoshenko and J. M. Gere, Theory of elastic stability, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961

8.
E. Zeidler, Applied functional analysis: Main principal and their applications, Applied Mathematical Sciences, 109, Springer-Verlag, New York, 1995