Stability of NonLinear Shells is a compilation of the author's work on analyzing the behaviour of spherical caps and related shell structures under various (axisymmetric) load systems. Differing from other texts on shells of revolution, it is one of the first attempts to deal with effects of multi-parameter load systems. This extension leads to the discovery of some new, hitherto unknown phenomena exhibited by these structures. In addition, the book presents a novel way to characterize properties of solutions of the governing equations for spherical caps - a classification anchored in a theory called reciprocal systems. The author has introduced a deformation map, a projection of multi-dimensional solutions to two-dimensional graphs, to enable analysts to gain insight into the physical meaning of the results obtained.
Numerous examples illustrate the concepts introduced. This book also comes to grips with many misconceptions existing in engineering literature about the question of the stability of solutions.


For researchers and structural engineers in the aeronautical, mechanical and civil engineering disciplines.

Table of Contents

Chapter headings. Prefaces. In Memoriam. A Personal Note from the Scientific Editor. From the Rector of Ben-Gurion University of the Negev. Introduction by the author. Basic Equations of Geometrically Nonlinear Shells. Axisymmetric thermoelastic deformation of shells of revolution. Basic equations for circular plates and spherical caps. Axisymmetric thermoelastic deformation of shallow shells of revolution. Nonsymmetric shallow homogeneous isotropic caps of revolution of constant thickness. Qualitative Investigations of Geometrically Nonlinear Shells. Some important properties of shallow spherical caps and circular plates subjected to transverse loads. Reciprocal systems of shallow shells. Properties of reciprocal systems: shallow shells. Nonreciprocal shallow systems. A class of reciprocal systems based on spherical caps subjected to nonsymmetric loading. Some general remarks concerning the properties of reciprocal systems. Reduction of some thermoelastic problems of shallow shells to equivalent elastic problems. Some general properties of elastic, geometrically nonlinear, axisymmetrically deformed shallow caps of revolution. Reciprocal systems of non shallow shells. About the compatibility equations. Nonregular isometric transformations of surfaces and nonregular solutions of the theory of geometrically nonlinear shells. Numerical Investigations of Axisymmetrically Loaded Geometrically Nonlinear Shallow Spherical Caps and Circular Plates (A Survey). Introduction and short survey of numerical methods. Deformation of circular plates under transverse loading. Buckling and postbuckling behavior of circular plates under compression or under a combination of compression and bending. Clamped spherical cap subjected to uniform external pressure. Clamped spherical caps under concentrated loads at the apex, axisymmetric line loads, and miscellaneous case. Caps with a movable clamped e


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© 2001
Elsevier Science
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About the authors

D. Shilkrut

Affiliations and Expertise

Mechanical Engineering Department, Ben-Gurion University of the Negev, Israel

E. Riks

Affiliations and Expertise

Department of Aerospace Engineering, University of Delft, The Netherlands