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Selected Publications:
Hubertus J. Weinitschke, “On the nonlinear theory of shallow spherical shells”, Journal of the Society for Industrial and Applied Math., Vol. 6, No. 3, September 1958
Budiansky, B., and Weinitschke, H. J., "On Axisymmetrical Buckling of Clamped, Shallow, Spherical Shells," J. Aero. Sci., 27, No. 7, (July, 1960).
H.J. Weinitschke, “On the stability problem for shallow spherical shells”, J. Math. & Phys, Vol. 38, 1960, pp. 209-231
Reissner, E. and Weinitschke, H. J. (1963): “Finite pure bending of circular cylindrical tubes”, Quarterly of Applied Mathematics, vol 10, pp.305-319.
H.J. Weinitschke, “On asymmetric buckling of shallow spherical shells”, J. Math. & Phys, Vol. 44, 1965, pp. 141-163
H.J. Weinitschke, “Zur mathematischen Theorie der endlichen Verbiegung elastischer Platten”, Habilitationsschrift, Universität Hamburg, 1965
H.J. Weinitschke, “Existenz und Eindeutigkeitssätze für die Gleichungen der kreisformigen Membran”, Meth. und Verf. d. Math. Physik, Vol. 3, 1970, pp. 117-139
H.J. Weinitschke, “On axisymmetric deformations of nonlinear elastic membranes”, Mechanics Today, Vol. 5 (E. Reissner Anniversary Volume edited by S. Nemat-Nasser), Pergamon Press, 1980, pp. 523-542
H.J. Weinitschke (Institut für Angewandte Mathematik, Universität Erlangen-Nümberg, D-8520 Erlangen, Germany), “On the calculation of limit and bifurcation points in stability problems of elastic shells”, International Journal of Solids and Structures, Vol. 21, No. 1, 1985, pp. 79-95
doi:10.1016/0020-7683(85)90106-4
ABSTRACT: Numerical methods for the computation of singular points of nonlinear equations G(u, lambda, mu) = 0 are discussed, where lambda and mu are real parameters. Simple and double limit points are treated in some detail and numerical algorithms are presented and applied to elastic shell stability problems. The case of simple symmetry breaking bifurcation points is also treated with applications to nonsymmetric bifurcation from axisymmetric states of deformation of shells of revolution.
H.J. Weinitschke, “On finite displacements of circular elastic membranes”, Math. Meth. Appl. Sci., Vol. 9, No. 1, 1987, pp. 76-98, doi: 10.1002/mma.1670090108
F.Y.M Wan and H.J. Weinitschke, “Boundary layer solutions for some nonlinear elastic membrane problems”, ZAMP, Vol. 38, 1987, pp. 79-91
H.J. Weinitschke and C.G. Lange, “Asymptotic solutions for finite deformation of thin shells of revolution with a small circular hole”, Quart. Appl. Math., Vol. 45, 1987, pp. 401-417
H. J. Weinitschke, “On uniqueness of axisymmetric deformations of elastic plates and shells”, SIAM J. Math. Anal., Vol. 18, 1988, pp. 680-692
F. Y. M. Wan (1) and H. J. Weinitschke (2)
(1) College of arts and Sciences, GN-15, University of Washington, Seattle, WA 98195, USA
(2) Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, D08520 Erlangen, Federal Republic of Germany
“On shells of revolution with the Love-Kirchhoff hypotheses”, Journal of Engineering Mathematics, Vol. 22, No. 4, 1988, pp. 285-334, Kluwer Academic publishers,
doi: 10.1007/BF00058512
ABSTRACT: On the occasion of the 100th anniversary of A.E.H. Love's fundamental paper on thin elastic shell theory, the present article summarizes a line of developments on shells of revolution related to the Love-Kirchhoff hypotheses which form the basis of Love's theory. The summary begins with the Günther-Reissner formulation of the linear theory which is shown to contain the classical first approximation shell theory as a special case. The static-geometric duality is deduced as a natural and immediate consequence of the more general theory. The repeated applications of this duality greatly simplify the solution process for boundary-value problems in shell theory, including the classical reduction of the axisymmetric bending problem and related recent reductions of shell equations for more general loadings to two simultaneous equations for a stress function and a displacement variable. In the nonlinear range, the article confines itself to Reissner's geometrically nonlinear theory of axisymmetric deformation of shells of revolution and Marguerre's shallow shell theory with special emphasis on recent results for elastic membranes, buckling of shells of revolution and applications of asymptotic methods. With fondness and appreciation, the authors dedicate this article to their teacher, collaborator and friend, Professor Eric Reissner, in the year of his seventy-fifth anniversary.
H.J. Weinitschke, “Stable and unstable membrane solutions for shells of revolution”, Proc. Pan Amer. Congr. Appl Mech. (PACAM, Rio de Janeiro, edited by A. Leissa), 1989
H. J. Weinitschke and H. Grabmüller (Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, D-8520, Erlangen, Germany), “Recent mathematical resuits in the nonlinear theory of flat and curved elastic membranes of revolution”, Journal of Engineering Mathematics, Vol. 26, No. 1, 1992, pp. 159-194,
doi: 10.1007/BF00043234
ABSTRACT: The present article reviews some recent developments in nonlinear elastic membrane theory with special emphasis on axisymmetric deformation of flat circular and annular membranes subjected to a vertical surface load and with prescribed radial stresses or radial displacements at the edges. The nonlinear Föppl membrane theory of small finite deflections as well as a simplified version of Reissner's finite-rotation theory is employed, assuming linear stress-strain relations. The main analytical techniques are reported which have been applied recently in order to determine the ranges of those boundary parameters for which solutions of the relevant nonlinear boundary value problems exist, and ranges of parameters for which the principal stresses are nonnegative everywhere. Concerning plane membranes, it is shown how the mathematical theory of existence and uniqueness was nearly completed in recent works in contrast to curved membranes where references can be given to rather few results.
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