Geometric Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Continuum Mechanics write by Reuven Segev. This book was released on 2020-05-13. Geometric Continuum Mechanics available 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.
Foundations of Geometric Continuum Mechanics
Foundations of Geometric Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Geometric Continuum Mechanics write by Reuven Segev. This book was released on 2023-10-31. Foundations of Geometric Continuum Mechanics available 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.
The Geometrical Language of Continuum Mechanics
The Geometrical Language of Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometrical Language of Continuum Mechanics write by Marcelo Epstein. This book was released on 2010-07-26. The Geometrical Language of Continuum Mechanics available 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.
Differential Geometry and Continuum Mechanics
Differential Geometry and Continuum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry and Continuum Mechanics write by Gui-Qiang G. Chen. This book was released on 2015-08-11. Differential Geometry and Continuum Mechanics available 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.
Geometric Continuum Mechanics and Induced Beam Theories
Geometric Continuum Mechanics and Induced Beam Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Continuum Mechanics and Induced Beam Theories write by Simon R. Eugster. This book was released on 2015-03-19. Geometric Continuum Mechanics and Induced Beam Theories available 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.
