Variational Problems In Materials Science
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| Author | : Gianni Dal Maso |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 166 |
| Release | : 2006-06-23 |
| Genre | : Technology & Engineering |
| ISBN | : 3764375655 |
Download Variational Problems in Materials Science Book in PDF, Epub and Kindle
This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.
| Author | : Gianni Dal Maso |
| Publisher | : Birkhäuser |
| Total Pages | : 162 |
| Release | : 2006-03-17 |
| Genre | : Technology & Engineering |
| ISBN | : 9783764375645 |
Download Variational Problems in Materials Science Book in PDF, Epub and Kindle
This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.
| Author | : Hans Petter Langtangen |
| Publisher | : Springer Nature |
| Total Pages | : 395 |
| Release | : 2019-09-26 |
| Genre | : Mathematics |
| ISBN | : 3030237885 |
Download Introduction to Numerical Methods for Variational Problems Book in PDF, Epub and Kindle
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
| Author | : Siegfried Carl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2007-06-07 |
| Genre | : Mathematics |
| ISBN | : 038746252X |
Download Nonsmooth Variational Problems and Their Inequalities Book in PDF, Epub and Kindle
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.
| Author | : Giuseppe Buttazzo |
| Publisher | : Oxford University Press |
| Total Pages | : 282 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780198504658 |
Download One-dimensional Variational Problems Book in PDF, Epub and Kindle
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
| Author | : Raul Serapioni |
| Publisher | : Birkhäuser |
| Total Pages | : 199 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034892446 |
Download Variational Methods for Discontinuous Structures Book in PDF, Epub and Kindle
In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.
| Author | : Andrej Cherkaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 561 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461211883 |
Download Variational Methods for Structural Optimization Book in PDF, Epub and Kindle
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
| Author | : Gianpietro Del Piero |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 89 |
| Release | : 2013-08-30 |
| Genre | : Science |
| ISBN | : 9400772262 |
Download A Variational Approach to Fracture and Other Inelastic Phenomena Book in PDF, Epub and Kindle
This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material’s strength induced by plasticity and damage. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
| Author | : William Strieder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 121 |
| Release | : 2013-03-07 |
| Genre | : Mathematics |
| ISBN | : 3642656242 |
Download Variational Methods Applied to Problems of Diffusion and Reaction Book in PDF, Epub and Kindle
This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free Path Statistics . 8 1. 5. Void Point-Surface Statistics . 11 1. 6. Variational Principles Applied to the Diffusion Equation. 12 1. 7. Notation. 16 Chapter 2. Diffusion Through a Porous Medium . 18 2. 1. Introduction 18 2. 2. Diffusion Through an Isotropic Porous Medium 18 2. 3. Variational Formulation for De . 20 2. 4. Bounds on De for an Isotropic Suspension 22 2. 5.
| Author | : N. Kikuchi |
| Publisher | : SIAM |
| Total Pages | : 508 |
| Release | : 1988-01-01 |
| Genre | : Science |
| ISBN | : 9781611970845 |
Download Contact Problems in Elasticity Book in PDF, Epub and Kindle
The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.
