Geometric Continuum Mechanics PDF Download
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| Author | : Reuven Segev |
| Publisher | : Springer Nature |
| Total Pages | : 416 |
| Release | : 2020-05-13 |
| Genre | : Mathematics |
| ISBN | : 3030426831 |
Download Geometric Continuum Mechanics Book in PDF, ePub and Kindle
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
| Author | : Marcelo Epstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 325 |
| Release | : 2010-07-26 |
| Genre | : Science |
| ISBN | : 113949046X |
Download The Geometrical Language of Continuum Mechanics Book in PDF, ePub and Kindle
Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.
| Author | : Reuven Segev |
| Publisher | : Springer Nature |
| Total Pages | : 410 |
| Release | : 2023-10-31 |
| Genre | : Mathematics |
| ISBN | : 3031356551 |
Download Foundations of Geometric Continuum Mechanics Book in PDF, ePub and Kindle
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
| Author | : Gui-Qiang G. Chen |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2015-08-11 |
| Genre | : Mathematics |
| ISBN | : 331918573X |
Download Differential Geometry and Continuum Mechanics Book in PDF, ePub and Kindle
This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.
| Author | : |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 370 |
| Release | : 2019-03-04 |
| Genre | : Science |
| ISBN | : 3110563215 |
Download Geometry of Incompatible Deformations Book in PDF, ePub and Kindle
| Author | : Manuel De Leon |
| Publisher | : World Scientific |
| Total Pages | : 226 |
| Release | : 2021-04-23 |
| Genre | : Mathematics |
| ISBN | : 9811232563 |
Download Material Geometry: Groupoids In Continuum Mechanics Book in PDF, ePub and Kindle
This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
| Author | : Simon R. Eugster |
| Publisher | : Springer |
| Total Pages | : 146 |
| Release | : 2015-03-19 |
| Genre | : Science |
| ISBN | : 3319164953 |
Download Geometric Continuum Mechanics and Induced Beam Theories Book in PDF, ePub and Kindle
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
| Author | : Ciprian D. Coman |
| Publisher | : Springer Nature |
| Total Pages | : 519 |
| Release | : 2019-11-02 |
| Genre | : Technology & Engineering |
| ISBN | : 9402417710 |
Download Continuum Mechanics and Linear Elasticity Book in PDF, ePub and Kindle
This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).
| Author | : John W. Rudnicki |
| Publisher | : John Wiley & Sons |
| Total Pages | : 229 |
| Release | : 2014-09-22 |
| Genre | : Science |
| ISBN | : 1118927672 |
Download Fundamentals of Continuum Mechanics Book in PDF, ePub and Kindle
A concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering
| Author | : Daniel Aubram |
| Publisher | : |
| Total Pages | : 99 |
| Release | : 2009 |
| Genre | : |
| ISBN | : 9783832281540 |
Download Differential Geometry Applied to Continuum Mechanics Book in PDF, ePub and Kindle
