Nonlinear Theory of Shallow Shells

I. I. Vorovich (auth.)0387983392, 9780387983394, 9780387227764

This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.

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Table of contents :
The Main Boundary Value Problems in the Nonlinear Theory of Shallow Shells….Pages 1-59
General Mathematical Questions….Pages 60-106
Topological Methods Applied to Solvability of the Main Boundary Value Problems of the Nonlinear Theory of Shallow Sells in Displacements….Pages 107-144
The Tolopological Method in the Problem of Solvability of the Main Boundary Value Problems in the Nonlinear Theory of Shallow Shells with an Airy Stress Function….Pages 145-180
The Variational Approach to the Problem of Solvability of Boundary Value Problems of Nonlinear Shallow Shell Theory….Pages 181-205
Numerical-Analytical Methods in the Nonlinear Theory of Shallow Shells….Pages 206-228
Direct Methods in the Nonlinear Theory of Shallow Shells….Pages 229-262
Formulation of the Problem of Stability. Global Uniqueness of Solutions. Stiffness of Shells. Well-Posedness Classes….Pages 263-295
Stability in the Large of the Membrane State of a Shallow Shell. Existence of the Lower Critical Value….Pages 296-342
A Probabilistic Approach to the Problem of Stability of Shallow Shells….Pages 343-351