Nonlinear Analysis Scientific Computation And Continuum Mechanics Applied To The Science Of Materials
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Nonlinear Analysis Scientific Computation And Continuum Mechanics Applied To The Science Of Materials
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Author : Morton E. Gurtin
language : en
Publisher:
Release Date : 1993
Nonlinear Analysis Scientific Computation And Continuum Mechanics Applied To The Science Of Materials written by Morton E. Gurtin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Continuum mechanics categories.
Computational Reality
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Author : Bilen Emek Abali
language : en
Publisher: Springer
Release Date : 2016-10-22
Computational Reality written by Bilen Emek Abali and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-22 with Science categories.
This book presents the theory of continuum mechanics for mechanical, thermodynamical, and electrodynamical systems. It shows how to obtain governing equations and it applies them by computing the reality. It uses only open-source codes developed under the FEniCS project and includes codes for 20 engineering applications from mechanics, fluid dynamics, applied thermodynamics, and electromagnetism. Moreover, it derives and utilizes the constitutive equations including coupling terms, which allow to compute multiphysics problems by incorporating interactions between primitive variables, namely, motion, temperature, and electromagnetic fields. An engineering system is described by the primitive variables satisfying field equations that are partial differential equations in space and time. The field equations are mostly coupled and nonlinear, in other words, difficult to solve. In order to solve the coupled, nonlinear system of partial differential equations, the book uses a novel collection of open-source packages developed under the FEniCS project. All primitive variables are solved at once in a fully coupled fashion by using finite difference method in time and finite element method in space.
Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy
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Author : Gennadii V. Demidenko
language : en
Publisher: Springer Nature
Release Date : 2020-04-03
Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy written by Gennadii V. Demidenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Science categories.
This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.
Nonlinear Partial Differential Equations And Their Applications
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Author : Doina Cioranescu
language : en
Publisher: Elsevier
Release Date : 2002-06-21
Nonlinear Partial Differential Equations And Their Applications written by Doina Cioranescu and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-21 with Mathematics categories.
This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.
Computational Continuum Mechanics
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Author : Ahmed A. Shabana
language : en
Publisher: John Wiley & Sons
Release Date : 2018-01-30
Computational Continuum Mechanics written by Ahmed A. Shabana and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Technology & Engineering categories.
An updated and expanded edition of the popular guide to basic continuum mechanics and computational techniques This updated third edition of the popular reference covers state-of-the-art computational techniques for basic continuum mechanics modeling of both small and large deformations. Approaches to developing complex models are described in detail, and numerous examples are presented demonstrating how computational algorithms can be developed using basic continuum mechanics approaches. The integration of geometry and analysis for the study of the motion and behaviors of materials under varying conditions is an increasingly popular approach in continuum mechanics, and absolute nodal coordinate formulation (ANCF) is rapidly emerging as the best way to achieve that integration. At the same time, simulation software is undergoing significant changes which will lead to the seamless fusion of CAD, finite element, and multibody system computer codes in one computational environment. Computational Continuum Mechanics, Third Edition is the only book to provide in-depth coverage of the formulations required to achieve this integration. Provides detailed coverage of the absolute nodal coordinate formulation (ANCF), a popular new approach to the integration of geometry and analysis Provides detailed coverage of the floating frame of reference (FFR) formulation, a popular well-established approach for solving small deformation problems Supplies numerous examples of how complex models have been developed to solve an array of real-world problems Covers modeling of both small and large deformations in detail Demonstrates how to develop computational algorithms using basic continuum mechanics approaches Computational Continuum Mechanics, Third Edition is designed to function equally well as a text for advanced undergraduates and first-year graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.
Nonlinear Continuum Mechanics And Large Inelastic Deformations
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Author : Yuriy I. Dimitrienko
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-25
Nonlinear Continuum Mechanics And Large Inelastic Deformations written by Yuriy I. Dimitrienko 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 2010-12-25 with Science categories.
The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.
Nonlinear Continuum Mechanics
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Author : Carlos Agelet de Saracibar
language : en
Publisher: Springer Nature
Release Date : 2023-08-22
Nonlinear Continuum Mechanics written by Carlos Agelet de Saracibar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-22 with Technology & Engineering categories.
This textbook on Continuum Mechanics presents 9 chapters. Chapters 1 and 2 are devoted to Tensor Algebra and Tensor Analysis. Part I of the book includes the next 3 chapters. All the content here is valid for both solid and fluid materials. At the end of Part I, the reader should be able to set up in local spatial/material form, the fundamental governing equations and inequalities for a Continuum Mechanics problem. Part II of the book, Chapters 6 to 10, is devoted to presenting some nonlinear constitutive models for Nonlinear Solid Mechanics, including Finite Deformation Hyperelasticity, Finite Deformation Plasticity, Finite Deformation Coupled Thermoplasticity, and Finite Deformation Contact Mechanics. The constitutive equations are derived within a thermodynamically consistent framework. Finite deformation elastoplasticity models are based on a multiplicative decomposition of the deformation gradient and the notion of an intermediate configuration. Different formulations based on the intermediate configuration, the current or spatial configuration, and the material configuration are considered. The last chapter is devoted to Variational Methods in Solid Mechanics, a fundamental topic in Computational Mechanics. The book may be used as a textbook for an advanced Master’s course on Nonlinear Continuum Mechanics for graduate students in Civil, Mechanical or Aerospace Engineering, Applied Mathematics, or Applied Physics, with an interest in Continuum Mechanics and Computational Mechanics.
Nonlinear Continua
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Author : Eduardo N. Dvorkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27
Nonlinear Continua written by Eduardo N. Dvorkin 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 2006-01-27 with Science categories.
This book develops a modern presentation of Continuum Mechanics, oriented towards numerical applications in the fields of nonlinear analysis of solids, structures and fluid mechanics. The kinematics of the continuum deformation, including pull-back / push-forward transformations between different configurations, stress and strain measures, balance principles, constitutive relations and variational principles are developed using general curvilinear coordinates. Even though the mathematical presentation of the different topics is quite rigorous, an effort is made to link formal developments with engineering physical intuition.
Nonlinear Analysis And Continuum Mechanics
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Author : Giuseppe Butazzo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Analysis And Continuum Mechanics written by Giuseppe Butazzo 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 2012-12-06 with Science categories.
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.
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.