Nonlocal Euler Bernoulli Beam Theories
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| Author | : Jingkai Chen |
| Publisher | : Springer Nature |
| Total Pages | : 59 |
| Release | : 2021-02-27 |
| Genre | : Technology & Engineering |
| ISBN | : 3030697886 |
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.
| Author | : A. Cemal Eringen |
| Publisher | : Academic Press |
| Total Pages | : 676 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483276716 |
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.
| Author | : Danilo Karlicic |
| Publisher | : John Wiley & Sons |
| Total Pages | : 372 |
| Release | : 2016-01-26 |
| Genre | : Technology & Engineering |
| ISBN | : 1848215223 |
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.
| Author | : Dewey H. Hodges |
| Publisher | : Progress in Astronautics and A |
| Total Pages | : 344 |
| Release | : 2006 |
| Genre | : Technology & Engineering |
| ISBN | : |
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.
| Author | : C.M. Wang |
| Publisher | : Elsevier |
| Total Pages | : 311 |
| Release | : 2000-07-19 |
| Genre | : Science |
| ISBN | : 0080541151 |
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.
| Author | : Konstantinos I. Tserpes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2013-10-15 |
| Genre | : Science |
| ISBN | : 3319012010 |
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.
| Author | : A. Cemal Eringen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 386 |
| Release | : 2007-06-14 |
| Genre | : Science |
| ISBN | : 0387226435 |
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.
| Author | : Guang Fan Li |
| Publisher | : Trans Tech Publications Ltd |
| Total Pages | : 2871 |
| Release | : 2013-01-11 |
| Genre | : Technology & Engineering |
| ISBN | : 3038139726 |
Selected, peer reviewed papers from the 2012 International Conference on Applied Mechanics and Materials (ICAMM 2012), November 24-25, 2012, Sanya, China
| Author | : Esmaeal Ghavanloo |
| Publisher | : Springer |
| Total Pages | : 281 |
| Release | : 2019-02-19 |
| Genre | : Science |
| ISBN | : 3030116506 |
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.
| Author | : Francesco Marotti De Sciarra |
| Publisher | : William Andrew |
| Total Pages | : 344 |
| Release | : 2018-03-23 |
| Genre | : Science |
| ISBN | : 0323480624 |
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
