The Bending Theory Of Fully Nonlinear Beams PDF Download
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Author | : Angelo Marcello Tarantino |
Publisher | : Springer |
Total Pages | : 87 |
Release | : 2019-03-13 |
Genre | : Technology & Engineering |
ISBN | : 3030146766 |
Download The Bending Theory of Fully Nonlinear Beams Book in PDF, ePub and Kindle
This book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semi-inverse approach, the book formulates a three-dimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of cross-sections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book’s closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams.
Author | : Dewey H. Hodges |
Publisher | : Progress in Astronautics and A |
Total Pages | : 344 |
Release | : 2006 |
Genre | : Technology & Engineering |
ISBN | : |
Download Nonlinear Composite Beam Theory Book in PDF, ePub and Kindle
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 | : R. Frisch-Fay |
Publisher | : |
Total Pages | : 240 |
Release | : 1962 |
Genre | : Elastic rods and wires |
ISBN | : |
Download Flexible Bars Book in PDF, ePub and Kindle
Author | : Mohammad Amin Rashidifar |
Publisher | : Anchor Academic Publishing |
Total Pages | : 149 |
Release | : 2015-08 |
Genre | : Science |
ISBN | : 3954894203 |
Download Nonlinear Vibrations of Cantilever Beams and Plates Book in PDF, ePub and Kindle
Many engineering problems can be solved using a linear approximation. In the Finite Element Analysis (FEA) the set of equations, describing the structural behaviour is then linear K d = F (1.1) In this matrix equation, K is the stiffness matrix of the structure, d is the nodal displacements vector and F is the external nodal force vector. Characteristics of linear problems is that the displacements are proportional to the loads, the stiffness of the structure is independent on the value of the load level. Though behaviour of real structures is nonlinear, e.g. displacements are not proportional to the loads; nonlinearities are usually unimportant and may be neglected in most practical problems.
Author | : Erasmo Carrera |
Publisher | : John Wiley & Sons |
Total Pages | : 171 |
Release | : 2011-07-28 |
Genre | : Science |
ISBN | : 1119951046 |
Download Beam Structures Book in PDF, ePub and Kindle
Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. The Carrera Unified Formulation (CUF) has hierarchical properties, that is, the error can be reduced by increasing the number of the unknown variables. This formulation is extremely suitable for computer implementations and can deal with most typical engineering challenges. It overcomes the problem of classical formulae that require different formulas for tension, bending, shear and torsion; it can be applied to any beam geometries and loading conditions, reaching a high level of accuracy with low computational cost, and can tackle problems that in most cases are solved by employing plate/shell and 3D formulations. Key features: compares classical and modern approaches to beam theory, including classical well-known results related to Euler-Bernoulli and Timoshenko beam theories pays particular attention to typical applications related to bridge structures, aircraft wings, helicopters and propeller blades provides a number of numerical examples including typical Aerospace and Civil Engineering problems proposes many benchmark assessments to help the reader implement the CUF if they wish to do so accompanied by a companion website hosting dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own www.mul2.com Researchers of continuum mechanics of solids and structures and structural analysts in industry will find this book extremely insightful. It will also be of great interest to graduate and postgraduate students of mechanical, civil and aerospace engineering.
Author | : Maurizio Garrione |
Publisher | : Springer Nature |
Total Pages | : 115 |
Release | : 2019-10-31 |
Genre | : Mathematics |
ISBN | : 3030302180 |
Download Nonlinear Equations for Beams and Degenerate Plates with Piers Book in PDF, ePub and Kindle
This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.
Author | : Walter Lacarbonara |
Publisher | : Springer Science & Business Media |
Total Pages | : 812 |
Release | : 2013-01-09 |
Genre | : Science |
ISBN | : 1441912762 |
Download Nonlinear Structural Mechanics Book in PDF, ePub and Kindle
This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
Author | : Levon G. Petrosian |
Publisher | : John Wiley & Sons |
Total Pages | : 528 |
Release | : 2020-05-11 |
Genre | : Technology & Engineering |
ISBN | : 1119592836 |
Download Static and Dynamic Analysis of Engineering Structures Book in PDF, ePub and Kindle
An authoritative guide to the theory and practice of static and dynamic structures analysis Static and Dynamic Analysis of Engineering Structures examines static and dynamic analysis of engineering structures for methodological and practical purposes. In one volume, the authors – noted engineering experts – provide an overview of the topic and review the applications of modern as well as classic methods of calculation of various structure mechanics problems. They clearly show the analytical and mechanical relationships between classical and modern methods of solving boundary value problems. The first chapter offers solutions to problems using traditional techniques followed by the introduction of the boundary element methods. The book discusses various discrete and continuous systems of analysis. In addition, it offers solutions for more complex systems, such as elastic waves in inhomogeneous media, frequency-dependent damping and membranes of arbitrary shape, among others. Static and Dynamic Analysis of Engineering Structures is filled with illustrative examples to aid in comprehension of the presented material. The book: Illustrates the modern methods of static and dynamic analysis of structures; Provides methods for solving boundary value problems of structural mechanics and soil mechanics; Offers a wide spectrum of applications of modern techniques and methods of calculation of static, dynamic and seismic problems of engineering design; Presents a new foundation model. Written for researchers, design engineers and specialists in the field of structural mechanics, Static and Dynamic Analysis of Engineering Structures provides a guide to analyzing static and dynamic structures, using traditional and advanced approaches with real-world, practical examples.
Author | : Ali H. Nayfeh |
Publisher | : John Wiley & Sons |
Total Pages | : 763 |
Release | : 2008-07-11 |
Genre | : Science |
ISBN | : 3527617574 |
Download Linear and Nonlinear Structural Mechanics Book in PDF, ePub and Kindle
* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Provides ready-to-use governing equations.
Author | : Liviu Librescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 627 |
Release | : 2006-01-15 |
Genre | : Technology & Engineering |
ISBN | : 1402042035 |
Download Thin-Walled Composite Beams Book in PDF, ePub and Kindle
Annotation This is the first monograph devoted to the foundation of the theory of composite anisotropic thin-walled beams and to its applications in various problems involving the aeronautical/aerospace, helicopter, naval and mechanical structures. Throughout the theoretical part, an effort was made to provide the treatment of the subject by using the equations of the 3-D elasticity theory. Non-classical effects such as transverse shear, warping constraint, anisotropy of constituent materials yielding the coupling of twist-bending (lateral), bending (transversal)-extension have been included and their implications have been thoroughly analyzed. Thermal effects have been included and in order to be able to circumvent their deleterious effects, functionally graded materials have been considered in their construction. Implications of the application of the tailoring technique and of the active feedback control on free vibration, dynamic response, instability and aeroelasticity of such structures have been amply investigated. Special care was exercised throughout this work to address and validate the adopted solution methodologies and the obtained results against those available in the literature and obtained via numerical or experimental means.