Nonlocal Euler Bernoulli Beam Theories

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Nonlocal Euler–Bernoulli Beam Theories

Author : Jingkai Chen
Publisher : Springer Nature
ISBN 13 : 3030697886
Total Pages : 59 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Nonlocal Euler–Bernoulli Beam Theories by : Jingkai Chen

Download or read book Nonlocal Euler–Bernoulli Beam Theories written by Jingkai Chen and published by Springer Nature. This book was released on 2021-02-27 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringen’s stress-gradient beam theory, the Mindlin’s strain-gradient beam theory, the higher-order beam theory and the peridynamic beam theory. Benchmark examples are solved analytically and numerically using these nonlocal beam equations, including the simply-supported beam, the clamped-clamped beam and the cantilever beam. Results show that beam deformations governed by different nonlocal theories at different boundary conditions show complex behaviors. Specifically, the Eringen’s stress-gradient beam equation and the peridynamic beam equation yield a much softer beam deformation for simply-supported beam and clamped-clamped beam, while the beam governed by the Mindlin’s strain-gradient beam equation is much stiffer. The cantilever beam exhibits a completely different behavior. The higher-order beam equation can be stiffer or softer depending on the values of the two nonlocal parameters. Moreover, the deformation fluctuation of the truncated order peridynamic beam equation is observed and explained from the singularity aspect of the solution expression. This research casts light on the fundamental explanation of nonlocal beam theories in nano-electromechanical systems.

Linear Theory

Author : A. Cemal Eringen
Publisher : Academic Press
ISBN 13 : 1483276716
Total Pages : 676 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Linear Theory by : A. Cemal Eringen

Download or read book Linear Theory written by A. Cemal Eringen and published by Academic Press. This book was released on 2013-10-22 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastodynamics, Volume II: Linear Theory is a continuation of Volume I and discusses the dynamical theory of linear isotropic elasticity. The volume deals with the fundamental theorems regarding elastodynamics and the different mathematical methods of solution and their employment in one, two, and three dimensions. The text outlines the fundamentals of linear elastodynamics and explains basic equations, displacement formulation, stress formulation, and the uniqueness theorem of elastodynamics. The book also investigates elastodynamic problems involving one-space dimension in governing boundaries, equations, and initial conditions. The book then compares two-dimensional problems as being subject to more precise mathematical analysis compared to three-dimensional situations by using scalar wave equations. The text then analyzes elastodynamic problems in three space dimensions when the solution depends on the condition of separability of the vector wave equation and the satisfaction of the boundary conditions. The diffraction of elastic waves is also described using two approaches: the integral equation method or the Eigen function technique. The book can prove valuable to researchers and practitioners whose work involves advanced statistics, general physics, and thermodynamics.

Nonlocal Continuum Field Theories

Author : A. Cemal Eringen
Publisher : Springer Science & Business Media
ISBN 13 : 0387226435
Total Pages : 386 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Nonlocal Continuum Field Theories by : A. Cemal Eringen

Download or read book Nonlocal Continuum Field Theories written by A. Cemal Eringen and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

Non-local Structural Mechanics

Author : Danilo Karlicic
Publisher : John Wiley & Sons
ISBN 13 : 1848215223
Total Pages : 372 pages
Book Rating : 4.8/5 (482 download)

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Book Synopsis Non-local Structural Mechanics by : Danilo Karlicic

Download or read book Non-local Structural Mechanics written by Danilo Karlicic and published by John Wiley & Sons. This book was released on 2016-01-26 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serving as a review on non-local mechanics, this book provides an introduction to non-local elasticity theory for static, dynamic and stability analysis in a wide range of nanostructures. The authors draw on their own research experience to present fundamental and complex theories that are relevant across a wide range of nanomechanical systems, from the fundamentals of non-local mechanics to the latest research applications.

Shear Deformable Beams and Plates

Author : C.M. Wang
Publisher : Elsevier
ISBN 13 : 0080541151
Total Pages : 311 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Shear Deformable Beams and Plates by : C.M. Wang

Download or read book Shear Deformable Beams and Plates written by C.M. Wang and published by Elsevier. This book was released on 2000-07-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on the theory and analysis of beams and plates deal with the classical (Euler-Bernoulli/Kirchoff) theories but few include shear deformation theories in detail. The classical beam/plate theory is not adequate in providing accurate bending, buckling, and vibration results when the thickness-to-length ratio of the beam/plate is relatively large. This is because the effect of transverse shear strains, neglected in the classical theory, becomes significant in deep beams and thick plates. This book illustrates how shear deformation theories provide accurate solutions compared to the classical theory. Equations governing shear deformation theories are typically more complicated than those of the classical theory. Hence it is desirable to have exact relationships between solutions of the classical theory and shear deformation theories so that whenever classical theory solutions are available, the corresponding solutions of shear deformation theories can be readily obtained. Such relationships not only furnish benchmark solutions of shear deformation theories but also provide insight into the significance of shear deformation on the response. The relationships for beams and plates have been developed by many authors over the last several years. The goal of this monograph is to bring together these relationships for beams and plates in a single volume. The book is divided into two parts. Following the introduction, Part 1 consists of Chapters 2 to 5 dealing with beams, and Part 2 consists of Chapters 6 to 13 covering plates. Problems are included at the end of each chapter to use, extend, and develop new relationships.

Modeling of Carbon Nanotubes, Graphene and their Composites

Author : Konstantinos I. Tserpes
Publisher : Springer Science & Business Media
ISBN 13 : 3319012010
Total Pages : 341 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Modeling of Carbon Nanotubes, Graphene and their Composites by : Konstantinos I. Tserpes

Download or read book Modeling of Carbon Nanotubes, Graphene and their Composites written by Konstantinos I. Tserpes and published by Springer Science & Business Media. This book was released on 2013-10-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large part of the research currently being conducted in the fields of materials science and engineering mechanics is devoted to carbon nanotubes and their applications. In this process, modeling is a very attractive investigation tool due to the difficulties in manufacturing and testing of nanomaterials. Continuum modeling offers significant advantages over atomistic modeling. Furthermore, the lack of accuracy in continuum methods can be overtaken by incorporating input data either from experiments or atomistic methods. This book reviews the recent progress in continuum modeling of carbon nanotubes and their composites. The advantages and disadvantages of continuum methods over atomistic methods are comprehensively discussed. Numerical models, mainly based on the finite element method, as well as analytical models are presented in a comparative way starting from the simulation of isolated pristine and defected nanotubes and proceeding to nanotube-based composites. The ability of continuum methods to bridge different scales is emphasized. Recommendations for future research are given by focusing on what still continuum methods have to learn from the nano-scale. The scope of the book is to provide current knowledge aiming to support researchers entering the scientific area of carbon nanotubes to choose the appropriate modeling tool for accomplishing their study and place their efforts to further improve continuum methods.

Nonlinear Composite Beam Theory

Author : Dewey H. Hodges
Publisher : Progress in Astronautics and A
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Nonlinear Composite Beam Theory by : Dewey H. Hodges

Download or read book Nonlinear Composite Beam Theory written by Dewey H. Hodges and published by Progress in Astronautics and A. This book was released on 2006 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From an authoritative expert whose work on modern helicopter rotor blade analysis has spanned over three decades, comes the first consistent and rigorous presentation of beam theory. Beginning with an overview of the theory developed over the last 60 years, Dr. Hodges addresses the kinematics of beam deformation, provides a simple way to characterize strain in an initially curved and twisted beam, and offers cross-sectional analysis for beams with arbitrary cross sections and composed of arbitrary materials. He goes on to present a way to accurately recover all components of cross-sectional strain and stress before providing a natural one-dimensional (1-D) theory of beams. Sample results for both cross-sectional and 1-D analysis are presented as is a parallel treatment for thin-walled beams.

Applied Mechanics and Materials I

Author : Guang Fan Li
Publisher : Trans Tech Publications Ltd
ISBN 13 : 3038139726
Total Pages : 2871 pages
Book Rating : 4.0/5 (381 download)

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Book Synopsis Applied Mechanics and Materials I by : Guang Fan Li

Download or read book Applied Mechanics and Materials I written by Guang Fan Li and published by Trans Tech Publications Ltd. This book was released on 2013-01-11 with total page 2871 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected, peer reviewed papers from the 2012 International Conference on Applied Mechanics and Materials (ICAMM 2012), November 24-25, 2012, Sanya, China

Computational Continuum Mechanics of Nanoscopic Structures

Author : Esmaeal Ghavanloo
Publisher : Springer
ISBN 13 : 3030116506
Total Pages : 281 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Computational Continuum Mechanics of Nanoscopic Structures by : Esmaeal Ghavanloo

Download or read book Computational Continuum Mechanics of Nanoscopic Structures written by Esmaeal Ghavanloo and published by Springer. This book was released on 2019-02-19 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of nonlocal elasticity theory as applied to the prediction of the mechanical characteristics of various types of biological and non-biological nanoscopic structures with different morphologies and functional behaviour. It combines fundamental notions and advanced concepts, covering both the theory of nonlocal elasticity and the mechanics of nanoscopic structures and systems. By reporting on recent findings and discussing future challenges, the book seeks to foster the application of nonlocal elasticity based approaches to the emerging fields of nanoscience and nanotechnology. It is a self-contained guide, and covers all relevant background information, the requisite mathematical and computational techniques, theoretical assumptions, physical methods and possible limitations of the nonlocal approach, including some practical applications. Mainly written for researchers in the fields of physics, biophysics, mechanics, and nanoscience, as well as computational engineers, the book can also be used as a reference guide for senior undergraduate and graduate students, as well as practicing engineers working in a range of areas, such as computational condensed matter physics, computational materials science, computational nanoscience and nanotechnology, and nanomechanics.

Experimental Characterization, Predictive Mechanical and Thermal Modeling of Nanostructures and Their Polymer Composites

Author : Francesco Marotti De Sciarra
Publisher : William Andrew
ISBN 13 : 0323480624
Total Pages : 344 pages
Book Rating : 4.3/5 (234 download)

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Book Synopsis Experimental Characterization, Predictive Mechanical and Thermal Modeling of Nanostructures and Their Polymer Composites by : Francesco Marotti De Sciarra

Download or read book Experimental Characterization, Predictive Mechanical and Thermal Modeling of Nanostructures and Their Polymer Composites written by Francesco Marotti De Sciarra and published by William Andrew. This book was released on 2018-03-23 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental Characterization, Predictive Mechanical and Thermal Modeling of Nanostructures and Their Polymer Composite focuses on the recent observations and predictions regarding the size-dependent mechanical properties, material properties and processing issues of carbon nanotubes (CNTs) and other nanostructured materials. The book takes various approaches, including dedicated characterization methods, theoretical approaches and computer simulations, providing a detailed examination of the fundamental mechanisms governing the deviations of the properties of CNTs and other nanostructured materials. The book explores their applications in materials science, mechanics, engineering, chemistry and physics due to their unique and appealing properties. The use of such materials is, however, still largely limited due to the difficulty in tuning their properties and morphological and structural features. - Presents a thorough discussion on how to effectively model the properties of carbon nanotubes and their polymer nanocomposites - Includes a size-dependent analysis of properties and multiscale modeling - Outlines the fundamentals and procedures of computational modeling as it is applied to carbon nanotubes and other nanomaterials

Static And Dynamic Problems Of Nanobeams And Nanoplates

Author : Snehashish Chakraverty
Publisher : World Scientific
ISBN 13 : 9813143932
Total Pages : 212 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Static And Dynamic Problems Of Nanobeams And Nanoplates by : Snehashish Chakraverty

Download or read book Static And Dynamic Problems Of Nanobeams And Nanoplates written by Snehashish Chakraverty and published by World Scientific. This book was released on 2016-10-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will deal with different sections associated with bending, buckling and vibration of nanobeams and nanoplates along with systematic description of handling the complexities when nanoscales are considered. The introduction includes basic ideas concerned with nanostructures, the algorithms and iterations followed in numerical methods and introduction to beam and plate theories in conjunction with nonlocal elasticity theory applied in nanostructures.Next, the investigation of nanobeams and nanoplates subjected to different sets of boundary conditions based on various nonlocal theories will be included. The varieties of physical and geometrical parameters that influence the bending, buckling and vibration mechanisms will be summarized.Finally, effect of environments such as thermal environment, Winkler-Pasternak elastic foundations and non-uniformity etc. on the buckling and vibration mechanisms will be illustrated.

Carbon Nanotubes and Nanosensors

Author : Isaac Elishakoff
Publisher : John Wiley & Sons
ISBN 13 : 1118565886
Total Pages : 308 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Carbon Nanotubes and Nanosensors by : Isaac Elishakoff

Download or read book Carbon Nanotubes and Nanosensors written by Isaac Elishakoff and published by John Wiley & Sons. This book was released on 2013-03-04 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main properties that make carbon nanotubes (CNTs) a promising technology for many future applications are: extremely high strength, low mass density, linear elastic behavior, almost perfect geometrical structure, and nanometer scale structure. Also, CNTs can conduct electricity better than copper and transmit heat better than diamonds. Therefore, they are bound to find a wide, and possibly revolutionary use in all fields of engineering. The interest in CNTs and their potential use in a wide range of commercial applications; such as nanoelectronics, quantum wire interconnects, field emission devices, composites, chemical sensors, biosensors, detectors, etc.; have rapidly increased in the last two decades. However, the performance of any CNT-based nanostructure is dependent on the mechanical properties of constituent CNTs. Therefore, it is crucial to know the mechanical behavior of individual CNTs such as their vibration frequencies, buckling loads, and deformations under different loadings. This title is dedicated to the vibration, buckling and impact behavior of CNTs, along with theory for carbon nanosensors, like the Bubnov-Galerkin and the Petrov-Galerkin methods, the Bresse-Timoshenko and the Donnell shell theory.

Structural Dynamics in Uncertain Environments

Author : Subrat Kumar Jena
Publisher : CRC Press
ISBN 13 : 1040154727
Total Pages : 162 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Structural Dynamics in Uncertain Environments by : Subrat Kumar Jena

Download or read book Structural Dynamics in Uncertain Environments written by Subrat Kumar Jena and published by CRC Press. This book was released on 2024-12-09 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The uncertainties or randomness of the material properties of structural components are of serious concern to engineers. Structural analysis is usually done by taking into account only deterministic or crisp parameters; however, building materials can have the aspects of uncertainty. The causes of this uncertainty or randomness are defects in atomic configurations, measurement errors, environmental conditions, and other factors. The influence of uncertainties is more profound for nanoscale and microstructures due to their small-scale effects. Several nanoscale experiments and molecular dynamics studies also support the claim of possible attachment of randomness for various parameters. With regard to these concerns, it is necessary to propose new models that specifically integrate and effectively overcome imprecisely defined parameters of the system. Structural Dynamics in Uncertain Environments presents the uncertainty modeling of nanobeams, microbeams, and Funtionally Graded (FG) beams using non-probabilistic approaches which include interval and fuzzy concepts. Vibration and stability analyses of the beams are conducted using different analytical, semi-analytical, and numerical methods for finding exact and/or approximate solutions of governing equations arising in uncertain environments. In this context, this book addresses structural uncertainties and investigates the dynamic behavior of micro-, nano-, and FG beams. Examines the concepts of fuzzy uncertain environments in structural dynamics Presents comprehensive analysis of propagation of uncertainty in vibration and buckling analyses Explains efficient mathematical methods to handle uncertainties in the governing equations

Analytical Methods in Nonlinear Oscillations

Author : Ebrahim Esmailzadeh
Publisher : Springer
ISBN 13 : 9402415424
Total Pages : 296 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Analytical Methods in Nonlinear Oscillations by : Ebrahim Esmailzadeh

Download or read book Analytical Methods in Nonlinear Oscillations written by Ebrahim Esmailzadeh and published by Springer. This book was released on 2018-06-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.

Wave Propagation in Materials and Structures

Author : Srinivasan Gopalakrishnan
Publisher : CRC Press
ISBN 13 : 1482262800
Total Pages : 972 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Wave Propagation in Materials and Structures by : Srinivasan Gopalakrishnan

Download or read book Wave Propagation in Materials and Structures written by Srinivasan Gopalakrishnan and published by CRC Press. This book was released on 2016-11-03 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on basic and advanced concepts of wave propagation in diverse material systems and structures. Topics are organized in increasing order of complexity for better appreciation of the subject. Additionally, the book provides basic guidelines to design many of the futuristic materials and devices for varied applications. The material in the book also can be used for designing safer and more lightweight structures such as aircraft, bridges, and mechanical and structural components. The main objective of this book is to bring both the introductory and the advanced topics of wave propagation into one text. Such a text is necessary considering the multi-disciplinary nature of the subject. This book is written in a step-by step modular approach wherein the chapters are organized so that the complexity in the subject is slowly introduced with increasing chapter numbers. Text starts by introducing all the fundamental aspects of wave propagations and then moves on to advanced topics on the subject. Every chapter is provided with a number of numerical examples of increasing complexity to bring out the concepts clearly The solution of wave propagation is computationally very intensive and hence two different approaches, namely, the Finite Element method and the Spectral Finite method are introduced and have a strong focus on wave propagation. The book is supplemented by an exhaustive list of references at the end of the book for the benefit of readers.

Energy Principles and Variational Methods in Applied Mechanics

Author : J. N. Reddy
Publisher : John Wiley & Sons
ISBN 13 : 1119087392
Total Pages : 1069 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Energy Principles and Variational Methods in Applied Mechanics by : J. N. Reddy

Download or read book Energy Principles and Variational Methods in Applied Mechanics written by J. N. Reddy and published by John Wiley & Sons. This book was released on 2017-07-21 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates. It begins with a review of the basic equations of mechanics, the concepts of work and energy, and key topics from variational calculus. It presents virtual work and energy principles, energy methods of solid and structural mechanics, Hamilton’s principle for dynamical systems, and classical variational methods of approximation. And it takes a more unified approach than that found in most solid mechanics books, to introduce the finite element method. Featuring more than 200 illustrations and tables, this Third Edition has been extensively reorganized and contains much new material, including a new chapter devoted to the latest developments in functionally graded beams and plates. Offers clear and easy-to-follow descriptions of the concepts of work, energy, energy principles and variational methods Covers energy principles of solid and structural mechanics, traditional variational methods, the least-squares variational method, and the finite element, along with applications for each Provides an abundance of examples, in a problem-solving format, with descriptions of applications for equations derived in obtaining solutions to engineering structures Features end-of-the-chapter problems for course assignments, a Companion Website with a Solutions Manual, Instructor's Manual, figures, and more Energy Principles and Variational Methods in Applied Mechanics, Third Edition is both a superb text/reference for engineering students in aerospace, civil, mechanical, and applied mechanics, and a valuable working resource for engineers in design and analysis in the aircraft, automobile, civil engineering, and shipbuilding industries.

Wave Propagation in Nanostructures

Author : Srinivasan Gopalakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 3319010328
Total Pages : 365 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Wave Propagation in Nanostructures by : Srinivasan Gopalakrishnan

Download or read book Wave Propagation in Nanostructures written by Srinivasan Gopalakrishnan and published by Springer Science & Business Media. This book was released on 2013-09-10 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and Graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures. The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behavior in these low dimensional structures.