Download or read book Classical Beam Theories of Structural Mechanics written by Andreas Öchsner and published by Springer Nature. This book was released on 2021-06-13 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson. The understanding of basic, i.e., one-dimensional structural members, is essential in applied mechanics. A systematic and thorough introduction to the theoretical concepts for one-dimensional members keeps the requirements on engineering mathematics quite low, and allows for a simpler transfer to higher-order structural members. The new approach in this textbook is that it treats single-plane bending in the x-y plane as well in the x-z plane equivalently and applies them to the case of unsymmetrical bending. The fundamental understanding of these one-dimensional members allows a simpler understanding of thin and thick plate bending members. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of all classical structural members known in engineering mechanics. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, these partial differential equations that describe the physical problem can be derived. Nevertheless, the fundamental knowledge from the first years of engineering education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills, might be required to master this topic.
Download or read book Beam Structures written by Erasmo Carrera and published by John Wiley & Sons. This book was released on 2011-07-28 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mechanics and Analysis of Beams Columns and Cables written by S. Krenk and published by Springer Science & Business Media. This book was released on 2001-05-08 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book illustrates the use of simple maths-based analytic techniques in basic structural mechanics. It focuses on the identification of the physical background of the theories and their particular mathematical properties. And on the demonstration of mathematical techniques for analysis of simple problems in structural mechanics. The author also looks at the derivation of the solutions to a number of basic problems of structural mechanics in a form suitable for later reference. The presentation concentrates on the main principles and the characteristics of the solutions. The theory also serves as a basis for the formulation of numerical models and for intelligent interpretation of their results.
Download or read book Theories and Analyses of Beams and Axisymmetric Circular Plates written by J N Reddy and published by CRC Press. This book was released on 2022-06-30 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method. Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates. Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.
Download or read book Analysis of Shells Plates and Beams written by Holm Altenbach and published by Springer Nature. This book was released on 2020-06-03 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book commemorates the 75th birthday of Prof. George Jaiani – Georgia’s leading expert on shell theory. He is also well known outside Georgia for his individual approach to shell theory research and as an organizer of meetings, conferences and schools in the field. The collection of papers presented includes articles by scientists from various countries discussing the state of the art and new trends in the theory of shells, plates, and beams. Chapter 20 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Download or read book An Isogeometric Approach to Beam Structures written by Buntara S. Gan and published by Springer. This book was released on 2017-06-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a novel, original condensation method to beam formulation based on the isogeometric approach to reducing the degrees of freedom to conventional two-node beam elements. In this volume, the author defines the Buntara Condensation Formulation: a unique formulation in condensing the dynamic equilibrium equation for beam structures, suitable for reducing the number of unlimited dynamic equations necessary to yield a classic two-node beam element. Professor Buntara’s method overcomes the problem of the isogeometric approach where the number of degrees of freedom is increased along with the complexity of the geometrical beam element and facilitates implementation of the codes into the existing beam structures programs, and CAD geometrical data into the conventional FE beam element codes. The book proposes a new reduction method where the beam element can be treated as under the conventional beam element theory that has only two nodes at both ends.
Download or read book Refined Dynamical Theories of Beams Plates and Shells and Their Applications written by Isaac Elishakoff and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is known, classical theories of vibration of the most fre quently encountered structural elements (e. g. , beams, plates and shells) disregard the effects of the shear deformation and rotary inertia. Refined theories, with these effects taken into account, have been pioneered by Bresse, Lord Rayleigh, Timoshenko, Eric Reissner, Mindlin and others. These refined theories have been fruitfully applied in recent decades in both theoretical and prac tical solid mechanics problems. The European Mechanics Committee approved holding EURO~illCH Colloquium 219 on "Refined Dynamical Theories of Beams, Plates and Shells and Their Applications" for reviewing the recent devel opments, providing guidelines for future investigations and presenting a forum for current work of younger researchers. The Colloquium was held during September 23 - 26, 1986, at the Uni versitat-Gesamthochschule Kassel, in the city of Kassel, Federal Republic of Germany. 45 Representatives of academia and industry, from nine European countries, as well as from Israel, USA and India participated in this Colloquium. IV 36 lectures were presented during the five sessions: Session A: Theory of Vibrations of Plates and Shells Session B: Various Approaches for Dynamical Problems of Beams Session C: Random Vibrations and Dynamic Stability Session D: Vibrations of Composite Structures Session E: Special Dynamical Problems of Beams, Plates and Shells The papers in this volums were divided into two parts: papers of invited keynote lectures and those of the invited contributed lectures.
Download or read book Mechanics and Analysis of Beams Columns and Cables written by Steen Krenk and published by Springer. This book was released on 2014-04-12 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book illustrates the use of simple maths-based analytic techniques in basic structural mechanics. It focuses on the identification of the physical background of the theories and their particular mathematical properties. And on the demonstration of mathematical techniques for analysis of simple problems in structural mechanics. The author also looks at the derivation of the solutions to a number of basic problems of structural mechanics in a form suitable for later reference. The presentation concentrates on the main principles and the characteristics of the solutions. The theory also serves as a basis for the formulation of numerical models and for intelligent interpretation of their results.
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.
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.
Download or read book Mechanics and Analysis of Beams Columns and Cables written by Steen Krenk and published by Springer. This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book illustrates the use of simple maths-based analytic techniques in basic structural mechanics. It focuses on the identification of the physical background of the theories and their particular mathematical properties. And on the demonstration of mathematical techniques for analysis of simple problems in structural mechanics. The author also looks at the derivation of the solutions to a number of basic problems of structural mechanics in a form suitable for later reference. The presentation concentrates on the main principles and the characteristics of the solutions. The theory also serves as a basis for the formulation of numerical models and for intelligent interpretation of their results.
Download or read book Fundamentals of Structural Mechanics written by Keith D. Hjelmstad and published by Springer Science & Business Media. This book was released on 2007-03-14 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.
Download or read book Foundations of Classical Laminate Theory written by Andreas Öchsner and published by Springer Nature. This book was released on 2021-09-28 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear–rigid) plate elements. It focus on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai–Hill and the Tsai–Wu criteria.
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.
Download or read book Structural Stability Theory and Practice written by Sukhvarsh Jerath and published by John Wiley & Sons. This book was released on 2020-12-08 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the theory of structural stability and its applications in crucial areas in engineering Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shells combines necessary information on structural stability into a single, comprehensive resource suitable for practicing engineers and students alike. Written in both US and SI units, this invaluable guide is perfect for readers within and outside of the US. Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell offers: Detailed and patiently developed mathematical derivations and thorough explanations Energy methods that are incorporated throughout the chapters Connections between theory, design specifications and solutions The latest codes and standards from the American Institute of Steel Construction (AISC), Canadian Standards Association (CSA), Australian Standards (SAA), Structural Stability Research Council (SSRC), and Eurocode 3 Solved and unsolved practice-oriented problems in every chapter, with a solutions manual for unsolved problems included for instructors Ideal for practicing professionals in civil, mechanical, and aerospace engineering, as well as upper-level undergraduates and graduate students in structural engineering courses, Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell provides readers with detailed mathematical derivations along with thorough explanations and practical examples.
Download or read book Modern Trends in Structural and Solid Mechanics 2 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
Download or read book A Simplified Approach to the Classical Laminate Theory of Composite Materials written by Andreas Öchsner and published by Springer Nature. This book was released on 2023-09-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic introduction to composite materials, which are obtained by a layer-wise stacking of one-dimensional bar/beam elements. Each layer may have different mechanical properties but each single layer is considered as isotropic. The major idea is to provide a simplified theory to easier understand the classical two-dimensional laminate theory for composites based on laminae with unidirectional fibers. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. The so-called classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements. The procedure provides the solution of a statically indeterminate system based on a generalized stress–strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. This laminate theory is typically provided for two-dimensional plane problems, where the basic structural element is a simple superposition of a classical plane elasticity element with a thin plate element under the consideration of an orthotropic constitutive law. This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.
