Download or read book Mathematical Analysis of Continuum Mechanics and Industrial Applications written by Hiromichi Itou and published by Springer. This book was released on 2016-11-18 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.
Download or read book Mathematical Analysis of Continuum Mechanics and Industrial Applications II written by Patrick van Meurs and published by Springer. This book was released on 2017-11-16 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.
Download or read book Mathematical Analysis of Continuum Mechanics and Industrial Applications III written by Hiromichi Itou and published by Springer Nature. This book was released on 2020-08-29 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.
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 Analysis and Continuum Mechanics written by Stuart S. Antman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 39 papers in this collection are devoted mostly to the exact mathematical analysis of problems in continuum mechanics, but also to problems of a purely mathematical nature mainly connected to partial differential equations from continuum physics. All the papers are dedicated to J. Serrin and were originally published in the "Archive of Rational Mechanics and Analysis".
Download or read book Applications Of Tensor Analysis In Continuum Mechanics written by Michael J Cloud and published by World Scientific. This book was released on 2018-07-10 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA 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. 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.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.
Download or read book Continuum Mechanics using Mathematica written by Antonio Romano and published by Birkhäuser. This book was released on 2008-11-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines mathematical tools, principles, and fundamental applications of continuum mechanics, providing a solid basis for a deeper study of more challenging problems in elasticity, fluid mechanics, plasticity, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes. The work is suitable for advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering.
Download or read book Nonlinear Analysis and Continuum Mechanics written by Giuseppe Butazzo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations.
Download or read book Continuum Mechanics and Linear Elasticity written by Ciprian D. Coman and published by Springer Nature. This book was released on 2019-11-02 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Mathematical Applications in Continuum and Structural Mechanics written by Francesco Marmo and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a range of research projects focusing on innovative numerical and modeling strategies for the nonlinear analysis of structures and metamaterials. The topics covered concern various analysis approaches based on classical finite element solutions, structural optimization, and analytical solutions in order to present a comprehensive overview of the latest scientific advances. Although based on pioneering research, the contributions are focused on immediate and direct application in practice, providing valuable tools for researchers and practicing professionals alike. .
Download or read book Recent Developments and Innovative Applications in Computational Mechanics written by Dana Mueller-Hoeppe and published by Springer Science & Business Media. This book was released on 2011-01-11 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 60th birthday. It contains contributions from friends and collaborators as well as current and former PhD students from almost all continents. As a very diverse group of people, the authors cover a wide range of topics from fundamental research to industrial applications: contact mechanics, finite element technology, micromechanics, multiscale approaches, particle methods, isogeometric analysis, stochastic methods and further research interests. In summary, the volume presents an overview of the international state of the art in computational mechanics, both in academia and industry.
Download or read book Introduction to Continuum Mechanics written by Vladimir M. Entov and published by Birkhäuser. This book was released on 2016-01-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications. Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
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 Continuum Mechanics written by Myron B. Allen, III and published by John Wiley & Sons. This book was released on 2015-06-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.
Download or read book Mathematics Applied to Continuum Mechanics written by Lee A. Segel and published by SIAM. This book was released on 2007-07-12 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.
Download or read book Mathematical Methods in Continuum Mechanics of Solids written by Martin Kružík and published by Springer. This book was released on 2019-03-02 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.
Download or read book Continuum Mechanics Volume 1 written by C. S. Jog and published by Cambridge University Press. This book was released on 2015-06-25 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.
