Geometric method for stability of non-linear elastic thin shells (Q2756537)

This book is a treatise on extensions of the work of A. V. Pogorelov who studied the problem of nonlinear stability for thin elastic isotropic shells. It is not possible to linearize the governing equations because after a critical value of the load, kinky patterns (ribs) occur on the surface. A. V. Pogorelov's approach consists in using a geometric description of the shell (isometric transformations) in a variational formulation of the problem.NEWLINENEWLINENEWLINEThe extensions here are: Chapter one: The case of anisotropic shells (convex shells under external pressure, cylindrical shells under axial compression). Chapter two: The case of chapter one, but one supposes additionally a linear memory (cylindrical shells under external pressure). Chapter three: The case of elasto-plastic shells (cylindrical shells under axial compression). Chapter four: The case of static as well as dynamic impulse loads (cylindrical and convex shells under external pressure or axial compression). Chapter five: The case of a cylindrical rigid-plastic shell subject to axial impact. The last chapter six is an appendix with descriptive information on the theory of surfaces.NEWLINENEWLINENEWLINEMany of the analytical results are checked favourably with experiments. A bibliography contains 261 references, mainly from the authors from the ``former' East-block. An index ends this book.NEWLINENEWLINENEWLINEThis volume will be of interest to researchers in structural mechanics.