On the Example of Spherical Shells To order this title, and for more information, click here
By D. Shilkrut, Mechanical Engineering Department, Ben-Gurion University of the Negev, Israel E. Riks, Department of Aerospace Engineering, University of Delft, The Netherlands
Description 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.
Audience
For researchers and structural engineers in the aeronautical, mechanical and civil engineering disciplines.
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 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 and
geometrically 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 by
the 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
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