The Nonlinear Theory of Shells Through Variational Principles: From Elementary Algebra to Differential Geometry

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9780471954941: The Nonlinear Theory of Shells Through Variational Principles: From Elementary Algebra to Differential Geometry

The Nonlinear Theory of Shells through Variational Principles From Elementary Algebra to Differential Geometry R. Valid Ecole Centrale de Paris, Laboratoire de Mécanique et Technologie, Ecole Normale Supérieure de Cachan, CNRS, Paris, France Ex-Scientific Advisor at Office National d’Etudes et Recherches Aerospatiales (ONERA), France This book provides new nonlinear variational principles of shells in statics and dynamics in an intrinsic, compact and coordinate-free method. The first part deals with primal displacements formulation, classical mixed principles, and new static and dynamic formulations devoted to dual principles. The second part addresses static and dynamic stability where classical theories are completed by some new methods, among which are some original developments relative to mixed or dual principles. Finally, besides various computational strategies among which are some original proposals, a large number of results from numerous practical researches in all ranges of elastic, plastic and composite nonlinear shell structures are given. Every chapter contains similar three-dimensional presentations of the used methods in linear spaces. An intrinsic geometrical and coordinate-free method which essentially utilises linear mappings defined on tangent pianes of a bidimensional manifold is developed in an introduction to differential geometry. It is presented as an appendix, in text-book style, called ‘From Elementary Algebra to Differential Geometry’ and provides all the mathematics and notations needed in a new intrinsic presentation.

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This book provides new nonlinear variational principles of shells in statics and dynamics in an intrinsic, compact and coordinate-free method. Primal displacements formulation, classical mixed principles and new static and dynamic formulations devoted to dual principles are addressed in the first part. The second part deals with static and dynamic stability, including some original developments relative to mixed or dual principles. Finally, new computational strategies are given. An appendix, in text-book style, called "From Elementary Algebra to Differential Geometry," provides all the mathematics and notations needed in a new intrinsic presentation.

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