Advances In The Theory Of Plates And Shells (studies In Applied Mechanics, 24)

Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations. Content: Introduction / G.Z. Voyiadjis and D. Karamanlidis -- Theory and finite-element formulation for shell structures undergoing finite rotations / Y. Başar and Y. Ding -- A refined theory of anisotropic thick plates / S. Igarashi and K. Shibukawa -- Generalized theory for bending of thick plates / A.K. Muhammad, M.H. Baluch, and A.K. Azad -- Postbuckling of long thick plates in compression including higher order transverse shearing effects / M. Stein, P.D. Sydow, and L. Librescu -- Bending of thick plates on an elastic foundation / G.Z. Voyiadjis and P.I. Kattan -- Higher-order constitutive equations for thick cylindrical shells / G.Z. Voyiadjis and G. Shi -- Boundary layers and Saint-Venant's principle for slender and thin elastic bodies / F.Y.M. Wan -- Dynamic analysis of plates and shallow shells by the D-BEM / D.E. Beskos -- Nonlinear analysis of imperfect cylindrical angle-ply panels / C.-Y. Chia -- Nonlinear local-global static analysis of shells of revolution / P.L. Gould and H. Harintho -- Recent studies on buckling, vibration and static response of anisotropic shear-flexible plates / D. Karamanlidis [and others] -- The effects of time-dependent excitation on the oscillatory motion of viscously damped laminated composite flat panels / A. Nosier, L. Librescu, and D. Frederick -- Effect of soil-structure interaction on the vibrations of stretched circular plates / B.A. Ovunc -- The internal loading of a fibre reinforced composite plate / A.P.S. Selvaduarai and N. Moutafis. Plates and shells play an important role in structural, mechanical, aerospace and manufacturing applications. The theory of plates and shells have advanced in the past two decades to handle more complicated problems that were previously beyond reach. In this book, the most recent advances in this area of research are documented. These include topics such as thick plate and shell analyses, finite rotations of shell structures, anisotropic thick plates, dynamic analysis, and laminated composite panels. The book is divided into two parts. In Part I, emphasis is placed on the theoretical aspects of the analysis of plates and shells, while Part II deals with modern applications. Numerous eminent researchers in the various areas of plate and shell analyses have contributed to this work which pays special attention to aspects of research such as theory, dynamic analysis, and composite plates and shells.