Mathematical Modeling in Continuum Mechanics PDF Download
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Author: Roger Temam
Publisher: Cambridge University Press
ISBN: 9780521643627
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Provides a rigorous presentation of the underlying mathematics and physics of continuum mechanics.
Author: Roger Temam
Publisher: Cambridge University Press
ISBN: 9780521643627
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Provides a rigorous presentation of the underlying mathematics and physics of continuum mechanics.
Author: Roger Temam
Publisher: Cambridge University Press
ISBN: 1139443216
Category : Science
Languages : en
Pages : 356
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Book Description
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: Martin H. Sadd
Publisher: Academic Press
ISBN: 0128116498
Category : Technology & Engineering
Languages : en
Pages : 432
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Book Description
Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. - Offers a thorough, concise and organized presentation of continuum mechanics formulation - Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems - Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study - Features extensive use of exercises, providing more material for student engagement and instructor presentation
Author: J. Tinsley Oden
Publisher: John Wiley & Sons
ISBN: 1118105745
Category : Mathematics
Languages : en
Pages : 348
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Book Description
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
Author: Ivo Babuska
Publisher: Springer Science & Business Media
ISBN: 3642562884
Category : Computers
Languages : en
Pages : 300
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Book Description
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: Martin Kružík
Publisher: Springer
ISBN: 3030020657
Category : Science
Languages : en
Pages : 624
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Book Description
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: Ismael Herrera
Publisher: John Wiley & Sons
ISBN: 1118207203
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.
Author: Fridtjov Irgens
Publisher: Springer Science & Business Media
ISBN: 3540742980
Category : Science
Languages : en
Pages : 667
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Book Description
This book presents an introduction into the entire science of Continuum Mechanics in three parts. The presentation is modern and comprehensive. Its introduction into tensors is very gentle. The book contains many examples and exercises, and is intended for scientists, practitioners and students of mechanics.
Author: Francesco dell'Isola
Publisher: Springer
ISBN: 9811037647
Category : Science
Languages : en
Pages : 327
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Book Description
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: Peter Haupt
Publisher: Springer Science & Business Media
ISBN: 3662047756
Category : Technology & Engineering
Languages : en
Pages : 666
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Book Description
The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.
