Summary
A tinite element method of mixed type is proposed to solve the Dirichlet problem of the von Kármán equations. Existence and convergence of the approximate solution are proved.
Similar content being viewed by others
References
Agmon, S.: TheL p approach to the Dirichlet problem. Ann. Scuola Normale Pisa13, 405–448 (1959)
Berger, M. S.: On von Kármán's equations and the buckling of a thin elastic plate. I. The clamped plate. Comm. Pure and Appl. Math.20, 687–720 (1967)
Berger, M. S., Fife, P.: On von Kármán's equations and the buckling of a thin elastic plate. II. Plate with general edge conditions. Comm. Pure and Appl. Math.21, 227–241 (1968)
Friedrichs, K. O., Stoker, J. J.: The nonlinear boundary value problem of the buckled plate. Amer. J. Math.63, 839–888 (1941)
Johnson, C.: On the convergence of a mixed finite element method for plate bending problems. Numer. Math.21, 43–62 (1973)
Kantorovich, L. V., Akilov, G. P.: Functional analysis in normed spaces. Pergamon press 1964
Keller, H. B., Reiss, E.: Iterative solutions for non-linear bending of circular plates. Comm. Pure and Appl. Math.11, 273–292 (1958)
Knightly, G. H.: An existence theorem for the von Kármán equations. Arch. Rational Mech. Anal.27, 233–242 (1967)
Krasnosel'skii, M. A. et al.: Approximate solution of operator equations: Wolters-Noordhoff 1972
Miyoshi, T.: A finite element method for the solutions of fourth order partial differential equations. Kumamoto J. Sci. (Math.)9, 87–116 (1972)
Miyoshi, T.: Finite element method of mixed type and its convergence in linear shell problems. Kumamoto J. Sci. (Math.)10, 35–58 (1973)
Morosov, N.: On the non-linear theory of thin plates. Dokl. Akad. Nauk SSSR114, 968–971 (1957)
Pian, T. H. H., Tong, P.: Basis of finite element method for solid continua. Int. J. Numerical Methods Eng.1, 3–28 (1969)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Miyoshi, T. A mixed finite element method for the solution of the von Kármán equations. Numer. Math. 26, 255–269 (1976). https://doi.org/10.1007/BF01395945
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01395945