Mathematical Modelling In Solid Mechanics

Author: Francesco dell'Isola
Editor: Springer
ISBN: 9811037647
File Size: 80,23 MB
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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.

Mathematical Modelling Of Solids With Nonregular Boundaries

Author: A.B. Movchan
Editor: CRC Press
ISBN: 9780849383380
File Size: 69,64 MB
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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.

Mathematical Modeling In Continuum Mechanics

Author: Roger Temam
Editor: Cambridge University Press
ISBN: 9780521643627
File Size: 69,86 MB
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Provides a rigorous presentation of the underlying mathematics and physics of continuum mechanics.

Continuum Mechanics

Author: Myron B. Allen, III
Editor: John Wiley & Sons
ISBN: 1118909372
File Size: 13,42 MB
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Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.

Progress In Applied Mathematical Modeling

Author: Fengshan Yang
Editor: Nova Publishers
ISBN: 9781600219764
File Size: 45,95 MB
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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.

An Introduction To Mathematical Modeling

Author: J. Tinsley Oden
Editor: John Wiley & Sons
ISBN: 1118105745
File Size: 69,91 MB
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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.

Mathematical Models In The Applied Sciences

Author: A. C. Fowler
Editor: Cambridge University Press
ISBN: 9780521467032
File Size: 17,25 MB
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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.

Applied Mathematical Modeling

Author: Eetu N. Virtanen
Editor: Nova Publishers
ISBN: 9781600219757
File Size: 79,45 MB
Format: PDF
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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.

Publications Of The National Institute Of Standards And Technology Catalog

Author: National Institute of Standards and Technology (U.S.)
Editor:
ISBN:
File Size: 61,87 MB
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Research In Structural And Solid Mechanics 1982

Author:
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ISBN:
File Size: 22,97 MB
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A Symposium on Advances and Trends in Structural and Solid Mechanics was held in Washington, D.C., on October 4-7, 1982. NASA Langley Research Center and George Washington University sponsored the symposium in cooperation with the National Science Foundation, the Office of Naval Research, the Air Force Office of Scientific Research, the American Society of Civil Engineers, and the American Society of Mechanical Engineers. The objectives of the symposium were to communicate recent advances and new insights into physical behavior and to identify the trends in the solution procedures for structural and solid mechanics problems. This conference publication includes 26 papers; 19 were presented at research in progress sessions and 7 at other sessions. The papers deal with (1) computational strategies for nonlinear problems, (2) material characterization, (3) advances in boundary elements and finite element technology, (4) advanced structural applications, (5) structural stability and analytical techniques, and (6) structural dynamics and vehicle crashworthiness.

Tractable Models Of Solid Mechanics

Author: Oleg V. Gendelman
Editor: Springer Science & Business Media
ISBN: 9783642153723
File Size: 42,56 MB
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This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects – from systems with two degrees of freedom to three-dimensional continuous objects.

Publications

Author: United States. National Bureau of Standards
Editor:
ISBN:
File Size: 17,15 MB
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Proceedings Of The Army Symposium On Solid Mechanics 1968 Held At The Johns Hopkins University Baltimore Maryland September 10 11 1968

Author:
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ISBN:
File Size: 33,29 MB
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Computational Fluid And Solid Mechanics 2003

Author: K.J Bathe
Editor: Elsevier
ISBN: 9780080529479
File Size: 50,80 MB
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Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis

Surface Effects In Solid Mechanics

Author: Holm Altenbach
Editor: Springer Science & Business Media
ISBN: 3642357830
File Size: 45,48 MB
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This book summarizes the actual state of the art and future trends of surface effects in solid mechanics. Surface effects are more and more important in the precise description of the behavior of advanced materials. One of the reasons for this is the well-known from the experiments fact that the mechanical properties are significantly influenced if the structural size is very small like, for example, nanostructures. In this book, various authors study the influence of surface effects in the elasticity, plasticity, viscoelasticity. In addition, the authors discuss all important different approaches to model such effects. These are based on various theoretical frameworks such as continuum theories or molecular modeling. The book also presents applications of the modeling approaches.

Advances In Mathematical Modeling And Experimental Methods For Materials And Structures

Author: Rivka Gilat
Editor: Springer Science & Business Media
ISBN: 9048134676
File Size: 67,84 MB
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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.

The Mechanics Of Solids And Structures Hierarchical Modeling And The Finite Element Solution

Author: Miguel Luiz Bucalem
Editor: Springer Science & Business Media
ISBN: 9783540264002
File Size: 38,29 MB
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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.

Leading Edge Applied Mathematical Modeling Research

Author: Matías P. Álvarez
Editor: Nova Publishers
ISBN: 9781600219771
File Size: 65,90 MB
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This book covers new and significant 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.

Mathematical Reviews

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ISBN:
File Size: 47,75 MB
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The Mechanics Of Constitutive Modeling

Author: Niels Saabye Ottosen
Editor: Elsevier
ISBN: 9780080525693
File Size: 66,51 MB
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Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling – Thermoplasticity - Uniqueness and discontinuous bifurcations • More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. • Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. • Demonstrates each topic in a complete and self-contained framework, with extensive referencing.