Download or read book Advances in Geometric Analysis and Continuum Mechanics written by Paul Concus and published by International Press of Boston. This book was released on 1994-12-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents a conference celebrating Robert Finn's 70th birthday. The introduction discusses Finn's career, and highlights his contributions to the field of mathematics and its applications. The following papers cover advances in geometric analysis and continuum mechanics.
Download or read book Geometric Continuum Mechanics written by Reuven Segev and published by Springer Nature. This book was released on 2020-05-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundations of Geometric Continuum Mechanics written by Reuven Segev and published by Springer Nature. This book was released on 2023-10-31 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Geometric Analysis written by Stanislaw Janeczko and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers some of the most recent and important developments in geometry and theoretical physics today. Topics include Monge-Ampère equations, Kähler-Ricci flows, and other fully non-linear elliptic and parabolic equations; canonical metrics in Kähler geometry; notions of quasi-local mass in general relativity and geometric properties of gauge theories; and new algebro-geometric and symplectic methods.
Download or read book Continuum Mechanics using Mathematica written by Antonio Romano and published by Springer. This book was released on 2014-10-14 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.
Download or read book Geometric Continuum Mechanics and Induced Beam Theories written by Simon R. Eugster and published by Springer. This book was released on 2015-03-19 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Geometric Approach to Thermomechanics of Dissipating Continua written by Lalao Rakotomanana and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.
Download or read book Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers written by Hung Nguyen-Schäfer and published by Springer. This book was released on 2016-08-16 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Download or read book Contributions to Advanced Dynamics and Continuum Mechanics written by Holm Altenbach and published by Springer. This book was released on 2019-05-31 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book celebrates the 65th birthday of Prof. Alexander K. Belyaev—a well-known expert in the field of Dynamics of Mechanical Systems. In addition to reflecting Prof. Belyaev’s contributions, the papers gathered here address a range of current problems in Dynamics and Continuum Mechanics. All contributions were prepared by his friends and colleagues, and chiefly focus on theory and applications.
Download or read book Continuum Mechanics written by Antonio Romano and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.
Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov and published by Springer. This book was released on 2018-09-15 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Download or read book Tensor Analysis With Applications In Mechanics written by Leonid P Lebedev and published by World Scientific. This book was released on 2010-05-18 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems.This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells.The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems — most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book.
Download or read book Progress in Continuum Mechanics written by Holm Altenbach and published by Springer Nature. This book was released on 2023-11-05 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an insight into the current developments in the field of continuum mechanics. Twenty-five researchers present new theoretical concepts, e.g., better inclusion of the microstructure in the models describing material behavior. At the same time, there are also more applications for the theories in engineering practice. In addition to new theoretical approaches in continuum mechanics and applications, the book puts an emphasis on discussing multi-physics problems.
Download or read book Advanced Theory of Mechanisms and Machines written by M.Z. Kolovsky and published by Springer Science & Business Media. This book was released on 2012-09-03 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the theory of mechanisms and machines, based on a lecture course for mechanical engineering students at the St. Petersburg State Technical University. The material differs from traditional textbooks due to its more profound elaboration of the methods of structural, geometric, kinematic and dynamic analysis. These established and novel methods take into account the needs of modern machine design as well as the potential of computers.
Download or read book Advances in Continuum Mechanics written by Otto Brüller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recognized authors contributed to this collection of original papers from all fields of research in continuum mechanics. Special emphasis is given to time dependent and independent permanent deformations, damage and fracture. Part of the contributions is dedicated to current efforts in describing material behavior with regard to, e.g., anisotropy, thermal effects, softening, ductile and brittle fracture, porosity and granular structure. Another part deals with numerical aspects arising from the implementation of material laws in the calculations of forming processes, soil mechanics and structural mechanics. Applications of theory and numerical methods belong to the following areas: Comparison with experimental results from material testing, metal forming under thermal and dynamic conditions, failure by damage, fracture and localized deformation modes. The variety of treated topics provides a survery of the actual research in these fields; therefore, the book is addressed to those interested in special problems of continuum mechanics as well as to those interested in a general knowledge.
Download or read book Advances in Mechanics and Mathematics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards.
Download or read book Curvature of Space and Time with an Introduction to Geometric Analysis written by Iva Stavrov and published by American Mathematical Soc.. This book was released on 2020-11-12 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.
