Stability of Nonlinear Shells: On the Example of Spherical Shells

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.

Chapter headings. Prefaces. Introduction by the author. Basic equations of geometrically nonlinear shells. Qualitative investigations of geometrically nonlinear shells. Numerical investigations of axisymmetric loaded geometrically nonlinear shallow spherical caps and circular plates (analytical survey). Spherical caps subjected to multi-parameter loading. The deformation map. Influence of the loading path on the cap's behavior. Thermo-elastic deformations. Some special problems and the behavior of deep caps. Stability of equilibrium states of geometrically nonlinear shells. References. Index.