Mathematical Analysis Of Continuum Mechanics And Industrial Applications
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Mathematical Analysis Of Continuum Mechanics And Industrial Applications
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Author : Hiromichi Itou
language : en
Publisher: Springer
Release Date : 2016-11-18
Mathematical Analysis Of Continuum Mechanics And Industrial Applications written by Hiromichi Itou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-18 with Science categories.
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.
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Ii
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Author : Patrick van Meurs
language : en
Publisher: Springer
Release Date : 2017-11-16
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Ii written by Patrick van Meurs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Science categories.
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.
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Iii
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Author : Hiromichi Itou
language : en
Publisher: Springer Nature
Release Date : 2020-08-29
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Iii written by Hiromichi Itou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-29 with Science categories.
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.
Variational Views In Mechanics
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Author : Paolo Maria Mariano
language : en
Publisher: Springer Nature
Release Date : 2022-02-08
Variational Views In Mechanics written by Paolo Maria Mariano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
Mathematical Methods And Models In Composites Second Edition
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Author : Vladislav Mantic
language : en
Publisher: World Scientific
Release Date : 2023-03-10
Mathematical Methods And Models In Composites Second Edition written by Vladislav Mantic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-10 with Mathematics categories.
Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.
The History Of Theoretical Material And Computational Mechanics Mathematics Meets Mechanics And Engineering
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Author : Erwin Stein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-04
The History Of Theoretical Material And Computational Mechanics Mathematics Meets Mechanics And Engineering written by Erwin Stein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-04 with Science categories.
This collection of 23 articles is the output of lectures in special sessions on “The History of Theoretical, Material and Computational Mechanics” within the yearly conferences of the GAMM in the years 2010 in Karlsruhe, Germany, 2011 in Graz, Austria, and in 2012 in Darmstadt, Germany; GAMM is the “Association for Applied Mathematics and Mechanics”, founded in 1922 by Ludwig Prandtl and Richard von Mises. The contributions in this volume discuss different aspects of mechanics. They are related to solid and fluid mechanics in general and to specific problems in these areas including the development of numerical solution techniques. In the first part the origins and developments of conservation principles in mechanics and related variational methods are treated together with challenging applications from the 17th to the 20th century. Part II treats general and more specific aspects of material theories of deforming solid continua and porous soils. and Part III presents important theoretical and engineering developments in fluid mechanics, beginning with remarkable inventions in old Egypt, the still dominating role of the Navier-Stokes PDEs for fluid flows and their complex solutions for a wide field of parameters as well as the invention of pumps and turbines in the 19th and 20th century. The last part gives a survey on the development of direct variational methods – the Finite Element Method – in the 20th century with many extensions and generalizations.
Analysis And Design Methods
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Author : Catherine Fairhurst
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Analysis And Design Methods written by Catherine Fairhurst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Technology & Engineering categories.
Analysis and Design Methods
Mathematics In Berlin
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Author : Heinrich Begehr
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematics In Berlin written by Heinrich Begehr and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.
Micro And Macromechanical Properties Of Materials
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Author : Yichun Zhou
language : en
Publisher: CRC Press
Release Date : 2013-09-26
Micro And Macromechanical Properties Of Materials written by Yichun Zhou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Science categories.
This is an English translation of a Chinese textbook that has been designated a national planned university textbook, the highest award given to scientific textbooks in China. The book provides a complete overview of mechanical properties and fracture mechanics in materials science, mechanics, and physics. It details the macro- and micro-mechanical properties of metal structural materials, nonmetal structural materials, and various functional materials. It also discusses the macro and micro failure mechanism under different loadings and contains research results on thin film mechanics, smart material mechanics, and more.
Continuum Mechanics Volume I
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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30
Continuum Mechanics Volume I written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.
The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.