Mathematical Modelling In Solid Mechanics

Author : Francesco dell'Isola,Mircea Sofonea,David Steigmann
Publisher : Springer
Page : 327 pages
File Size : 55,5 Mb
Release : 2017-03-10
Category : Science
ISBN : 9789811037641

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Mathematical Modelling in Solid Mechanics by Francesco dell'Isola,Mircea Sofonea,David Steigmann Pdf

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

Author : A.M. Khludnev,Jan Sokolowski
Publisher : Birkhäuser
Page : 380 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889841

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Modeling and Control in Solid Mechanics by A.M. Khludnev,Jan Sokolowski Pdf

New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way. In this monograph we focus on formal models representing contact problems for elastic and elastoplastic plates and shells. New approaches open up new fields for research. For example, in crack theory a systematic treatment of mathematical modelling and optimization of problems with cracks is required. Similarly, sensitivity analysis of solutions to problems subjected to perturbations, which forms an important part of the problem solving process, is the source of many open questions. Two aspects of sensitivity analysis, namely the behaviour of solutions under deformations of the domain of integration and perturbations of surfaces seem to be particularly demanding in this context. On writing this book we aimed at providing the reader with a self-contained study of the mathematical modelling in mechanics. Much attention is given to modelling of typical constructions applied in many different areas. Plates and shallow shells which are widely used in the aerospace industry provide good exam ples. Allied optimization problems consist in finding the constructions which are of maximal strength (endurance) and satisfy some other requirements, ego weight limitations. Mathematical modelling of plates and shells always requires a reasonable compromise between two principal needs. One of them is the accuracy of the de scription of a physical phenomenon (as required by the principles of mechanics).

Author : A.M. Khludnev,Jan Sokolowski
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 44,6 Mb
Release : 1997-01-21
Category : Computers
ISBN : 3764352388

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Modelling and Control in Solid Mechanics by A.M. Khludnev,Jan Sokolowski Pdf

This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems is the availability of the inequality type constraints imposed on solutions such as the impenetration condition for contact problems, the yield plasticity condition, etc. As a consequence, the presence of free boundaries is typical of the boundary value problems concerned. The objective of the book is to display some new methods of analyzing such problems, as well as to perform research on new models evolved from engineering practice. Readers will find a variety of new mathematical models describing some contact problems for plates and shells, an equilibrium of plates involving cracks, etc. Furthermore, some new mathematical methods are presented which were specially developed by the authors to study the problems concerned. These help to convey a comprehensive picture of the present state of mathematical problems on the free-boundary elasticity and plasticity theory. The book is intended for postgraduates, scientists and engineers.and for Students interested in problems of modelling and optimal control in the mechanics of deformable bodies.

Author : A M Khludnev,Jan Sokolowski
Publisher : Unknown
Page : 388 pages
File Size : 54,8 Mb
Release : 1997-01-21
Category : Electronic
ISBN : 3034889852

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Modeling and Control in Solid Mechanics by A M Khludnev,Jan Sokolowski Pdf

Author : Roger Temam,Alain Miranville
Publisher : Cambridge University Press
Page : 356 pages
File Size : 44,5 Mb
Release : 2005-05-19
Category : Science
ISBN : 9781139443210

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Mathematical Modeling in Continuum Mechanics by Roger Temam,Alain Miranville Pdf

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Author : A.B. Movchan,N.V. Movchan
Publisher : CRC Press
Page : 344 pages
File Size : 43,5 Mb
Release : 2020-07-26
Category : Mathematics
ISBN : 9781000142303

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Mathematical Modelling of Solids with Nonregular Boundaries by A.B. Movchan,N.V. Movchan Pdf

Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined. Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.

Author : Miguel Luiz Bucalem,Klaus-Jurgen Bathe
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 55,9 Mb
Release : 2011-03-08
Category : Technology & Engineering
ISBN : 9783540264002

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The Mechanics of Solids and Structures - Hierarchical Modeling and the Finite Element Solution by Miguel Luiz Bucalem,Klaus-Jurgen Bathe Pdf

In the recent decades, computational procedures have been applied to an increasing extent in engineering and the physical sciences. Mostly, two separate fields have been considered, namely, the analysis of solids and structures and the analysis of fluid flows. These continuous advances in analyses are of much interest to physicists, mathematicians and in particular, engineers. Also, computational fluid and solid mechanics are no longer treated as entirely separate fields of applications, but instead, coupled fluid and solid analysis is being pursued. The objective of the Book Series is to publish monographs, textbooks, and proceedings of conferences of archival value, on any subject of computational fluid dynamics, computational solid and structural mechanics, and computational multi-physics dynamics. The publications are written by and for physicists, mathematicians and engineers and are to emphasize the modeling, analysis and solution of problems in engineering.

Author : Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov
Publisher : Springer Nature
Page : 317 pages
File Size : 47,7 Mb
Release : 2023-02-21
Category : Science
ISBN : 9789811984105

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Mechanics of Solid Deformable Body by Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov Pdf

This textbook contains sections with fundamental, classical knowledge in solid mechanics, as well as original modern mathematical models to describe the state and behavior of solid deformable bodies. It has original sections with the basics of mathematical modeling in the solid mechanics, material on the basic principles, and features of mathematical formulation of model problems of solid mechanics. For successful mastering of the material, it is necessary to have basic knowledge of the relevant sections of the courses of mathematical analysis, linear algebra and tensor analysis, differential equations, and equations of mathematical physics. Each section contains a list of test questions and exercises to check the level of assimilation of the material. The textbook is intended for senior university students, postgraduates, and research fellows. It can be used in the study of general and special disciplines in various sections of solid mechanics, applied mechanics for students and undergraduates of various specializations and specialties, such as mechanics and mathematical modeling, applied mathematics, solid physics, and engineering mechanics.

Author : Ivo Babuska,Philippe G. Ciarlet,Tetsuhiko Miyoshi
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 41,9 Mb
Release : 2001-11-20
Category : Computers
ISBN : 3540423990

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Mathematical Modeling and Numerical Simulation in Continuum Mechanics by Ivo Babuska,Philippe G. Ciarlet,Tetsuhiko Miyoshi Pdf

The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the last three decades there has been great progress in the theory and practice of solving partial differential equations, and research has extended in various directions. Full-scale nonlinear problems have come within the range of nu merical simulation. The importance of mathematical modeling and analysis in science and engineering is steadily increasing. In addition, new possibili ties of analysing the reliability of computations have appeared. Many other developments have occurred: these are only the most noteworthy. This book is the record of the proceedings of the International Sympo sium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, held in Yamaguchi, Japan from 29 September to 3 October 2000. The topics covered by the symposium ranged from solids to fluids, and in cluded both mathematical and computational analysis of phenomena and algorithms. Twenty-one invited talks were delivered at the symposium. This volume includes almost all of them, and expresses aspects of the progress mentioned above. All the papers were individually refereed. We hope that this volume will be a stepping-stone for further developments in this field.

Author : Eetu N. Virtanen
Publisher : Nova Publishers
Page : 366 pages
File Size : 40,9 Mb
Release : 2008
Category : Mathematics
ISBN : 1600219756

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Applied Mathematical Modeling by Eetu N. Virtanen Pdf

This new book focuses on important research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. It includes heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimisation; finite volume, finite element, and boundary element procedures; decision sciences in an industrial and manufacturing context; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.

Author : Oxana Sadovskaya,Vladimir Sadovskii
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 53,6 Mb
Release : 2012-06-08
Category : Technology & Engineering
ISBN : 9783642290534

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Mathematical Modeling in Mechanics of Granular Materials by Oxana Sadovskaya,Vladimir Sadovskii Pdf

This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular materials and materials with different strengths. It proposes new models helping to define zones of the strain localization. The book shows how to analyze processes of the propagation of elastic and elastic-plastic waves in loosened materials, and constructs models of mixed type, describing the flow of granular materials in the presence of quasi-static deformation zones. In a last part, the book studies a numerical realization of the models on multiprocessor computer systems. The book is intended for scientific researchers, lecturers of universities, post-graduates and senior students, who specialize in the field of the deformable materials mechanics, mathematical modeling and adjacent fields of applied and calculus mathematics.

Author : Fengshan Yang
Publisher : Nova Publishers
Page : 386 pages
File Size : 48,5 Mb
Release : 2008
Category : Mathematics
ISBN : 1600219764

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Progress in Applied Mathematical Modeling by Fengshan Yang Pdf

This book presents new research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. It includes heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimisation; finite volume, finite element, and boundary element procedures; decision sciences in an industrial and manufacturing context; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.

Author : Rivka Gilat,Leslie Banks-Sills
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 45,9 Mb
Release : 2009-12-18
Category : Science
ISBN : 9789048134670

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Advances in Mathematical Modeling and Experimental Methods for Materials and Structures by Rivka Gilat,Leslie Banks-Sills Pdf

This collection of cutting-edge papers, written by leading authors in honor of Professor Jacob Aboudi, covers a wide spectrum of topics in the field, presents both theoretical and experimental approaches, and suggests directions for possible future research.

Author : Martin Kružík,Tomáš Roubíček
Publisher : Springer
Page : 617 pages
File Size : 51,8 Mb
Release : 2019-03-02
Category : Science
ISBN : 9783030020651

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Mathematical Methods in Continuum Mechanics of Solids by Martin Kružík,Tomáš Roubíček Pdf

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.

Author : Holm Altenbach,Robert V. Goldstein,Evgenii Murashkin
Publisher : Springer
Page : 447 pages
File Size : 47,5 Mb
Release : 2017-04-02
Category : Science
ISBN : 9783319560502

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Mechanics for Materials and Technologies by Holm Altenbach,Robert V. Goldstein,Evgenii Murashkin Pdf

This book shows impressively how complex mathematical modeling of materials can be applied to technological problems. Top-class researchers present the theoretical approaches in modern mechanics and apply them to real-world problems in solid mechanics, creep, plasticity, fracture, impact, and friction. They show how they can be applied to technological challenges in various fields like aerospace technology, biological sciences and modern engineering materials.