Nonlinear Theory of Shallow Shells [1 ed.] 0387983392, 9780387983394, 9780387227764
This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideratio
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English Pages 390 [407] Year 1999
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
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
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