Stability of Nonlinear Shells
On the Example of Spherical ShellsBy
- D. Shilkrut
- E. Riks
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.
Studies in Applied Mechanics
Hardbound, 480 Pages
Published: June 2002
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 revolutionof 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 edge subjected to different types of loading. The hinged cap in pure bending. Axisymmetric deformation states and the phenomena of bifurcation in compression and tension. Deformation of hinged spherical caps under various types of loading. A comparison of the behavior of hinged and clamped caps: Returning to the role of membrane stresses in the buckling process. Shallow spherical caps with flanges. A model for imperfect support conditions.
Spherical Caps Subjected to Multi-Parameter Loading. The Deformation Map. Influence of the Loading Path on the Cap's Behavior. Thermo-Elastic Deformations. Axisymmetric deformation of hinged spherical caps under a two-parameter load system (q and M). Nonsymmetric bifurcation phenomena in the case of a two-parameter loading. The deformation map - The analysis tool for systems under multi-parameter external loads. Three-parametric loading systems and the manifestation of chaos-like phenomena in statics. The influence of the loading procedure in the case of a multi-parameter load system. Multi-parametric thermo-elastic problems: Their analogy with pure elastic problems and some additional numerical results. Some Special Problems and the Behavior of Deep Caps. Deformation of circular plates on elastic foundation. A model of crack formation and delamination in layered composites. Stability phenomena in a spherical cap loaded by means of a rigid plate with unilateral contact between them. Bifurcation phenomena in a truncated spherical cap in tension. Deformation and stability of deep spherical caps. Axisymmetric deformation of deep hemispheric shells. The Stability of Equilibrium States of Geometrically Nonlinear Shells. Some remarks on the stability of equilibrium states of shells andgeometrically nonlinear conservative structures in general. Formulation of the stability criterion as a test for the axisymmetric equilibrium states of spherical caps. Investigating stability of equilibrium states of shallow spherical shells bythe method of small oscillations. Alternative tests for stability for shallow caps of revolution in the subspace of axisymmetric deformations. Total potential energy of equilibrium states and a physical explanation of snap-through process. Stability of axisymmetric equilibrium states of non-shallow spherical caps subjected to one-parametric systems of loading. Comparison of reported numerical results and data of other authors about eigenfrequencies of nonlinear shells. Concluding remarks on the stability of single parametric loading systems. References. Index