Geometric Continuum Mechanics And Induced Beam Theories

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Geometric Continuum Mechanics and Induced Beam Theories

Author : Simon R. Eugster
Publisher : Springer
ISBN 13 : 3319164953
Total Pages : 146 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Geometric Continuum Mechanics and Induced Beam Theories by : Simon R. Eugster

Download or read book Geometric Continuum Mechanics and Induced Beam Theories written by Simon R. Eugster and published by Springer. This book was released on 2015-03-19 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories

Author : Isaac E Elishakoff
Publisher : World Scientific
ISBN 13 : 9813236531
Total Pages : 798 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories by : Isaac E Elishakoff

Download or read book Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories written by Isaac E Elishakoff and published by World Scientific. This book was released on 2019-10-29 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refined theory of beams, which takes into account both rotary inertia and shear deformation, was developed jointly by Timoshenko and Ehrenfest in the years 1911-1912. In over a century since the theory was first articulated, tens of thousands of studies have been performed utilizing this theory in various contexts. Likewise, the generalization of the Timoshenko-Ehrenfest beam theory to plates was given by Uflyand and Mindlin in the years 1948-1951.The importance of these theories stems from the fact that beams and plates are indispensable, and are often occurring elements of every civil, mechanical, ocean, and aerospace structure.Despite a long history and many papers, there is not a single book that summarizes these two celebrated theories. This book is dedicated to closing the existing gap within the literature. It also deals extensively with several controversial topics, namely those of priority, the so-called 'second spectrum' shear coefficient, and other issues, and shows vividly that the above beam and plate theories are unnecessarily overcomplicated.In the spirit of Einstein's dictum, 'Everything should be made as simple as possible but not simpler,' this book works to clarify both the Timoshenko-Ehrenfest beam and Uflyand-Mindlin plate theories, and seeks to articulate everything in the simplest possible language, including their numerous applications.This book is addressed to graduate students, practicing engineers, researchers in their early career, and active scientists who may want to have a different look at the above theories, as well as readers at all levels of their academic or scientific career who want to know the history of the subject. The Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories are the key reference works in the study of stocky beams and thick plates that should be given their due and remain important for generations to come, since classical Bernoulli-Euler beam and Kirchhoff-Love theories are applicable for slender beams and thin plates, respectively.Related Link(s)

Developments and Novel Approaches in Nonlinear Solid Body Mechanics

Author : Bilen Emek Abali
Publisher : Springer Nature
ISBN 13 : 3030504603
Total Pages : 491 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Developments and Novel Approaches in Nonlinear Solid Body Mechanics by : Bilen Emek Abali

Download or read book Developments and Novel Approaches in Nonlinear Solid Body Mechanics written by Bilen Emek Abali and published by Springer Nature. This book was released on 2020-07-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing—for example, 3D printing— and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

The Geometrical Language of Continuum Mechanics

Author : Marcelo Epstein
Publisher : Cambridge University Press
ISBN 13 : 113949046X
Total Pages : 325 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Geometrical Language of Continuum Mechanics by : Marcelo Epstein

Download or read book The Geometrical Language of Continuum Mechanics written by Marcelo Epstein and published by Cambridge University Press. This book was released on 2010-07-26 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.

Higher Gradient Materials and Related Generalized Continua

Author : Holm Altenbach
Publisher : Springer Nature
ISBN 13 : 303030406X
Total Pages : 246 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Higher Gradient Materials and Related Generalized Continua by : Holm Altenbach

Download or read book Higher Gradient Materials and Related Generalized Continua written by Holm Altenbach and published by Springer Nature. This book was released on 2019-11-04 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: • The structural size is very small. • The microstructure is complex. • The effects are localized. As such, the development of generalized continuum models is helpful and results in a better description of the behavior of structures or materials. At the same time, there are more and more experimental studies supporting the new models because the number of material parameters is higher.

Evaluation of Scientific Sources in Mechanics

Author : Francesco dell'Isola
Publisher : Springer Nature
ISBN 13 : 3030805506
Total Pages : 377 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Evaluation of Scientific Sources in Mechanics by : Francesco dell'Isola

Download or read book Evaluation of Scientific Sources in Mechanics written by Francesco dell'Isola and published by Springer Nature. This book was released on 2021-08-12 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works.

Geometric Continuum Mechanics

Author : Reuven Segev
Publisher : Springer Nature
ISBN 13 : 3030426831
Total Pages : 418 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Geometric Continuum Mechanics by : Reuven Segev

Download or read book Geometric Continuum Mechanics written by Reuven Segev and published by Springer Nature. This book was released on 2020-05-13 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

Advanced Topics in Nonsmooth Dynamics

Author : Remco Leine
Publisher : Springer
ISBN 13 : 3319759728
Total Pages : 462 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Advanced Topics in Nonsmooth Dynamics by : Remco Leine

Download or read book Advanced Topics in Nonsmooth Dynamics written by Remco Leine and published by Springer. This book was released on 2018-06-07 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.

Virtual Work Approach to Mechanical Modeling

Author : Jean Salençon
Publisher : John Wiley & Sons
ISBN 13 : 1786302950
Total Pages : 362 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Virtual Work Approach to Mechanical Modeling by : Jean Salençon

Download or read book Virtual Work Approach to Mechanical Modeling written by Jean Salençon and published by John Wiley & Sons. This book was released on 2018-03-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is centred about the Principle of virtual work and the related method for mechanical modelling. It aims at showing and enhancing the polyvalence and versatility of the virtual work approach in the mechanical modelling process. The virtual work statement is set as the principle at the root of a force modelling method that can be implemented on any geometrical description. After experimentally induced hypotheses have been made on the geometrical parameters that describe the concerned system and subsystems, the method provides a unifying framework for building up consistently associated force models where external and internal forces are introduced through their virtual rates of work. Systems described as three-dimensional, curvilinear or planar continua are considered: force models are established with the corresponding equations of motion; the validation process points out that enlarging the domain of relevance of the model for practical applications calls for an enrichment of the geometrical description that takes into account the underlying microstructure.

Set-Valued Force Laws

Author : Christoph Glocker
Publisher : Springer Science & Business Media
ISBN 13 : 3540444793
Total Pages : 222 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Set-Valued Force Laws by : Christoph Glocker

Download or read book Set-Valued Force Laws written by Christoph Glocker and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality.

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Author : Yuriy I. Dimitrienko
Publisher : Springer Science & Business Media
ISBN 13 : 9400700342
Total Pages : 742 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Nonlinear Continuum Mechanics and Large Inelastic Deformations by : Yuriy I. Dimitrienko

Download or read book Nonlinear Continuum Mechanics and Large Inelastic Deformations written by Yuriy I. Dimitrienko and published by Springer Science & Business Media. This book was released on 2010-12-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Advances in Peridynamics

Author : Erdogan Madenci
Publisher : Springer Nature
ISBN 13 : 3030978583
Total Pages : 433 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Advances in Peridynamics by : Erdogan Madenci

Download or read book Advances in Peridynamics written by Erdogan Madenci and published by Springer Nature. This book was released on 2022-05-20 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent improvements in peridynamic modeling of structures. It provides sufficient theory and numerical implementation helpful to both new and existing researchers in the field. The main focus of the book is on the non-ordinary state-based (NOSB) peridynamics (PD) and its applications for performing finite deformation. It presents the framework for modeling high stretch polymers, viscoelastic materials, thermoelasticity, plasticity, and creep. It provides a systematic derivation for dimensionally reduced structures such as axisymmetric structures and beams. Also, it presents a novel approach to impose boundary conditions without suffering from displacement kinks near the boundary. Furthermore, it presents refinements to bond-based PD model by including rotation kinematics for modeling isotropic and composite materials. Moreover, it presents a PD – FEM coupling framework in ANSYS based on principle for virtual work. Lastly, it presents an application of neural networks in the peridynamic (PINN) framework. Sample codes are provided for readers to develop hands-on experience on peridynamic modeling. Describes new developments in peridynamics and their applications in the presence of material and geometric nonlinearity; Describes an approach to seamlessly couple PD with FE; Introduces the use of the neural network in the PD framework to solve engineering problems; Provides theory and numerical examples for researchers and students to self-study and apply in their research (Codes are provided as supplementary material); Provides theoretical development and numerical examples suitable for graduate courses.

Elasticity

Author : Martin H. Sadd
Publisher : Elsevier
ISBN 13 : 008047747X
Total Pages : 474 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Elasticity by : Martin H. Sadd

Download or read book Elasticity written by Martin H. Sadd and published by Elsevier. This book was released on 2010-08-04 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. - Contains exercises for student engagement as well as the integration and use of MATLAB Software - Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

Modeling Nonlinear Problems in the Mechanics of Strings and Rods

Author : Oliver M. O'Reilly
Publisher : Springer
ISBN 13 : 331950598X
Total Pages : 434 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Modeling Nonlinear Problems in the Mechanics of Strings and Rods by : Oliver M. O'Reilly

Download or read book Modeling Nonlinear Problems in the Mechanics of Strings and Rods written by Oliver M. O'Reilly and published by Springer. This book was released on 2017-03-10 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.

Mechanics and Strength of Materials

Author : Vitor Dias da Silva
Publisher : Springer Science & Business Media
ISBN 13 : 354030813X
Total Pages : 532 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Mechanics and Strength of Materials by : Vitor Dias da Silva

Download or read book Mechanics and Strength of Materials written by Vitor Dias da Silva and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a clear and thorough presentation of the fundamental principles of mechanics and strength of materials. Provides both the theory and applications of mechanics of materials on an intermediate theoretical level. Useful as a reference tool by postgraduates and researchers in the fields of solid mechanics as well as practicing engineers.

Thermal Barrier Coatings: Failure Theory and Evaluation Technology

Author : Yichun Zhou
Publisher : Springer Nature
ISBN 13 : 9811927235
Total Pages : 943 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Thermal Barrier Coatings: Failure Theory and Evaluation Technology by : Yichun Zhou

Download or read book Thermal Barrier Coatings: Failure Theory and Evaluation Technology written by Yichun Zhou and published by Springer Nature. This book was released on 2022-10-08 with total page 943 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the failure theories and evaluation techniques of thermal barrier coatings, covering the thermal-mechanical–chemical coupling theories, performance and damage characterization techniques, and related evaluations. Thermal barrier coatings are the key thermal protection materials for high-temperature components in advanced aeroengines. Coating spallation is a major technical bottleneck faced by researchers. The extremely complex microstructure, diverse service environments, and failure behaviors bring challenges to the spallation analysis in terms of the selective use of mechanical theories, experimental methods, and testing platforms. In the book, the authors provide a systematic summary of the latest research and technological advances and present their insights and findings in the past couple of decades. This book is not only suitable for researchers and engineers in thermal barrier coatings and related fields but also a good reference for upper-undergraduate and postgraduate students of materials science and mechanics majors.

New Achievements in Continuum Mechanics and Thermodynamics

Author : Bilen Emek Abali
Publisher : Springer
ISBN 13 : 3030133079
Total Pages : 586 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis New Achievements in Continuum Mechanics and Thermodynamics by : Bilen Emek Abali

Download or read book New Achievements in Continuum Mechanics and Thermodynamics written by Bilen Emek Abali and published by Springer. This book was released on 2019-03-13 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a liber amicorum dedicated to Wolfgang H. Müller, and highlights recent advances in Prof. Müller’s major fields of research: continuum mechanics, generalized mechanics, thermodynamics, mechanochemistry, and geomechanics. Over 50 of Prof. Müller’s friends and colleagues contributed to this book, which commemorates his 60th birthday and was published in recognition of his outstanding contributions.