Mathematical Models In Applied Mechanics
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| Author | : Alan B. Tayler |
| Publisher | : Oxford University Press |
| Total Pages | : 292 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780198515593 |
This textbook demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modelling techniques. It has been designed specifically for final year undergraduate and graduate students, and springs from the author's extensive teachingexperience. The text is combined with twenty-one carefully ordered problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations.
| Author | : A. C. Fowler |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 1997-11-28 |
| Genre | : Mathematics |
| ISBN | : 9780521467032 |
Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines.
| Author | : J. Tinsley Oden |
| Publisher | : John Wiley & Sons |
| Total Pages | : 348 |
| Release | : 2012-02-23 |
| Genre | : Mathematics |
| ISBN | : 1118105745 |
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 | : Roger Temam |
| Publisher | : Cambridge University Press |
| Total Pages | : 356 |
| Release | : 2005-05-19 |
| Genre | : Science |
| ISBN | : 1139443216 |
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 | : Francesco dell'Isola |
| Publisher | : Springer |
| Total Pages | : 327 |
| Release | : 2017-03-10 |
| Genre | : Science |
| ISBN | : 9811037647 |
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 | : Y. Ben-Haim |
| Publisher | : Elsevier |
| Total Pages | : 240 |
| Release | : 2013-10-22 |
| Genre | : Mathematics |
| ISBN | : 1483290972 |
Recognition of the need to introduce the ideas of uncertainty in a wide variety of scientific fields today reflects in part some of the profound changes in science and engineering over the last decades. Nobody questions the ever-present need for a solid foundation in applied mechanics. Neither does anyone question nowadays the fundamental necessity to recognize that uncertainty exists, to learn to evaluate it rationally, and to incorporate it into design.This volume provides a timely and stimulating overview of the analysis of uncertainty in applied mechanics. It is not just one more rendition of the traditional treatment of the subject, nor is it intended to supplement existing structural engineering books. Its aim is to fill a gap in the existing professional literature by concentrating on the non-probabilistic model of uncertainty. It provides an alternative avenue for the analysis of uncertainty when only a limited amount of information is available. The first chapter briefly reviews probabilistic methods and discusses the sensitivity of the probability of failure to uncertain knowledge of the system. Chapter two discusses the mathematical background of convex modelling. In the remainder of the book, convex modelling is applied to various linear and nonlinear problems. Uncertain phenomena are represented throughout the book by convex sets, and this approach is referred to as convex modelling.This book is intended to inspire researchers in their goal towards further growth and development in this field.
| Author | : Oxana Sadovskaya |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 396 |
| Release | : 2012-06-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3642290531 |
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 | : A. Klarbring |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 214 |
| Release | : 2006-09-05 |
| Genre | : Technology & Engineering |
| ISBN | : 1402048351 |
This textbook on models and modeling in mechanics introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation.
| Author | : Emmanuele DiBenedetto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 364 |
| Release | : 2010-10-17 |
| Genre | : Mathematics |
| ISBN | : 0817646485 |
* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries
| Author | : Lee A. Segel |
| Publisher | : SIAM |
| Total Pages | : 598 |
| Release | : 2007-07-12 |
| Genre | : Science |
| ISBN | : 0898716209 |
This classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.
