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| Author | : Paul Mansour Naghdi |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 1962 |
| Genre | : |
| ISBN | : |
| Author | : P. M. NAGHDI |
| Publisher | : |
| Total Pages | : 1 |
| Release | : 1962 |
| Genre | : |
| ISBN | : |
The analysis is concerned with an exact, complete, and fully general nonlinear theory of elastic shells founded under the Kirchhoff hypothesis (Arch. Rat'l Mech. and Anal., 1:295323, 1958). Since the fully general equations of equilibrium in terms of stress and couple resultants and the appropriate boundary conditions are well known, the main task is the determination of suitable strain measures and the derivation of constitutive equations. (Author).
| Author | : A. Libai |
| Publisher | : Elsevier |
| Total Pages | : 429 |
| Release | : 2012-12-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0323150810 |
The Nonlinear Theory of Elastic Shells: One Spatial Dimension presents the foundation for the nonlinear theory of thermoelastic shells undergoing large strains and large rotations. This book discusses several relatively simple equations for practical application. Organized into six chapters, this book starts with an overview of the description of nonlinear elastic shell. This text then discusses the foundation of three-dimensional continuum mechanics that are relevant to the shell theory approach. Other chapters cover several topics, including birods, beamshells, and axishells that begins with a derivation of the equations of motion by a descent from the equations of balance of linear and rotational momentum of a three-dimensional material continuum. This book discusses as well the approach to deriving complete field equations for one- or two-dimensional continua from the integral equations of motion and thermodynamics of a three-dimensional continuum. The final chapter deals with the analysis of unishells. This book is a valuable resource for physicists, mathematicians, and scientists.
| Author | : W. L. Wainwright |
| Publisher | : |
| Total Pages | : 64 |
| Release | : 1963 |
| Genre | : |
| ISBN | : |
| Author | : Paul Seide |
| Publisher | : |
| Total Pages | : 99 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
A general nonlinear theory of shells is derived from three-dimensional nonlinear elasticity theory and used to obtain exact linear perturbation equations for the determination of bifurcation points. These are specialized (1) to flat plates under inplane loading which preserves their flatness prior to buckling and (2) to shells of revolution which deform axisymmetrically under axisymmetric loading. The Love-Kirchhoff hypotheses for plates and shells are used. For the flat plate the strain-energy function is otherwise arbitrary, while for the shell of revolution the material must be either transversely isotropic or with axes of orthotropy coinciding with the shell generators and parallels. The specific example of a simply supported flat plate under uniform longitudinal compression, with the strain-energy function chosen as similar to that for small deformations of isotropic flat plates, is solved. Corrections to the classical theory are found to be of the same order of magnitude as those caused by shearing strains in planes normal to the middle surface. (Author).
| Author | : Marco Amabili |
| Publisher | : Cambridge University Press |
| Total Pages | : 585 |
| Release | : 2018-11-01 |
| Genre | : Science |
| ISBN | : 1108577636 |
This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.
| Author | : Bayard Spence Wilson |
| Publisher | : |
| Total Pages | : 176 |
| Release | : 1958 |
| Genre | : Elastic plates and shells |
| ISBN | : |
| Author | : Reinhold Kienzler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 258 |
| Release | : 2013-06-01 |
| Genre | : Science |
| ISBN | : 3540399054 |
Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.
| Author | : Stuart Antman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 845 |
| Release | : 2005-11-24 |
| Genre | : Mathematics |
| ISBN | : 0387276491 |
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.
| Author | : Philippe G. Ciarlet |
| Publisher | : Elsevier |
| Total Pages | : 662 |
| Release | : 2000-05-11 |
| Genre | : Mathematics |
| ISBN | : 0080511236 |
The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.
