Geometric Continuum Mechanics And Induced Beam Theories

Author : Simon R. Eugster
Publisher : Springer
Page : 146 pages
File Size : 50,7 Mb
Release : 2015-03-19
Category : Science
ISBN : 9783319164953

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Geometric Continuum Mechanics and Induced Beam Theories by Simon R. Eugster Pdf

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.

Author : Bilen Emek Abali,Ivan Giorgio
Publisher : Springer Nature
Page : 491 pages
File Size : 53,5 Mb
Release : 2020-07-18
Category : Science
ISBN : 9783030504601

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Developments and Novel Approaches in Nonlinear Solid Body Mechanics by Bilen Emek Abali,Ivan Giorgio Pdf

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.

Author : Francesco dell'Isola,Simon R. Eugster,Mario Spagnuolo,Emilio Barchiesi
Publisher : Springer Nature
Page : 377 pages
File Size : 49,8 Mb
Release : 2021-08-12
Category : Science
ISBN : 9783030805500

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Evaluation of Scientific Sources in Mechanics by Francesco dell'Isola,Simon R. Eugster,Mario Spagnuolo,Emilio Barchiesi Pdf

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.

Author : Holm Altenbach,Wolfgang H. Müller,Bilen Emek Abali
Publisher : Springer Nature
Page : 231 pages
File Size : 47,5 Mb
Release : 2019-11-04
Category : Technology & Engineering
ISBN : 9783030304065

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Higher Gradient Materials and Related Generalized Continua by Holm Altenbach,Wolfgang H. Müller,Bilen Emek Abali Pdf

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.

Author : Jean Salençon
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 42,8 Mb
Release : 2018-03-27
Category : Mathematics
ISBN : 9781786302953

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Virtual Work Approach to Mechanical Modeling by Jean Salençon Pdf

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.

Author : Erdogan Madenci,Pranesh Roy,Deepak Behera
Publisher : Springer Nature
Page : 433 pages
File Size : 54,8 Mb
Release : 2022-05-20
Category : Science
ISBN : 9783030978587

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Advances in Peridynamics by Erdogan Madenci,Pranesh Roy,Deepak Behera Pdf

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.

Author : Isaac E Elishakoff
Publisher : World Scientific
Page : 798 pages
File Size : 51,7 Mb
Release : 2019-10-29
Category : Technology & Engineering
ISBN : 9789813236530

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Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories by Isaac E Elishakoff Pdf

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)

Author : Remco Leine,Vincent Acary,Olivier Brüls
Publisher : Springer
Page : 457 pages
File Size : 49,5 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319759722

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Advanced Topics in Nonsmooth Dynamics by Remco Leine,Vincent Acary,Olivier Brüls Pdf

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.

Author : A. Cemal Eringen
Publisher : Elsevier
Page : 288 pages
File Size : 55,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323140607

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Continuum Physics by A. Cemal Eringen Pdf

Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. This book provides precise presentations of exact continuum theories on materially non-uniform or non-simple bodies that can respond to short- and long-range inter-particle loads and fields. This volume consists of three parts. Part I is devoted to the study of continuum field theories for bodies having inner structure. All materials, to some extent, are composed of particles that behave like small rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. The developments of nonlocal theories of nonpolar and polar continua are covered in Parts II and III. This publication is valuable to students and researchers interested in polar and nonlocal field theories.

Author : Holm Altenbach,Victor Eremeyev
Publisher : Springer Nature
Page : 593 pages
File Size : 47,7 Mb
Release : 2023-12-03
Category : Science
ISBN : 9783031432101

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Advances in Linear and Nonlinear Continuum and Structural Mechanics by Holm Altenbach,Victor Eremeyev Pdf

This book offers a current image of modern mechanics. The book reflects current state of the art in the field of continuum mechanics and mechanics of structures including recent achievements in classic and non-classic approaches. The chapters are written by leading specialist in the field, so the book collects cutting edge investigations in the field. As a target we consider the society starting from beginners, i.e. master and PhD students, and also leaders in the field, that is professors of universities and civil, mechanical and aerospace engineers.

Author : Marcelo Epstein
Publisher : Cambridge University Press
Page : 325 pages
File Size : 51,8 Mb
Release : 2010-07-26
Category : Science
ISBN : 9781139490467

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The Geometrical Language of Continuum Mechanics by Marcelo Epstein Pdf

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.

Author : Francesco dell'Isola,Mircea Sofonea,David Steigmann
Publisher : Springer
Page : 327 pages
File Size : 54,7 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 : Dusan Krajcinovic,Jean Lemaitre
Publisher : Springer
Page : 304 pages
File Size : 48,8 Mb
Release : 1987-12-22
Category : Science
ISBN : UCSD:31822003211711

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Continuum Damage Mechanics Theory and Application by Dusan Krajcinovic,Jean Lemaitre Pdf

Author : Esmaeal Ghavanloo,S. Ahmad Fazelzadeh,Francesco Marotti de Sciarra
Publisher : Springer Nature
Page : 463 pages
File Size : 47,5 Mb
Release : 2021-04-02
Category : Science
ISBN : 9783030630508

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Size-Dependent Continuum Mechanics Approaches by Esmaeal Ghavanloo,S. Ahmad Fazelzadeh,Francesco Marotti de Sciarra Pdf

This book offers a comprehensive and timely report of size-dependent continuum mechanics approaches. Written by scientists with worldwide reputation and established expertise, it covers the most recent findings, advanced theoretical developments and computational techniques, as well as a range of applications, in the field of nonlocal continuum mechanics. Chapters are concerned with lattice-based nonlocal models, Eringen’s nonlocal models, gradient theories of elasticity, strain- and stress-driven nonlocal models, and peridynamic theory, among other topics. This book provides researchers and practitioners with extensive and specialized information on cutting-edge theories and methods, innovative solutions to current problems and a timely insight into the behavior of some advanced materials and structures. It also offers a useful reference guide to senior undergraduate and graduate students in mechanical engineering, materials science, and applied physics.

Author : Reuven Segev,Marcelo Epstein
Publisher : Springer Nature
Page : 416 pages
File Size : 45,6 Mb
Release : 2020-05-13
Category : Mathematics
ISBN : 9783030426835

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Geometric Continuum Mechanics by Reuven Segev,Marcelo Epstein Pdf

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.