Beam Structures
Classical and Advanced Theories
Published on 13. July 2011
208 pages
978-1-119-97857-2 (ISBN)
Description
Beam theories are exploited worldwide to analyze civil, mechanical,automotive, and aerospace structures. Many beam approaches havebeen proposed during the last centuries by eminent scientists suchas Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most ofthese models are problem dependent: they provide reliable resultsfor a given problem, for instance a given section and cannot beapplied to a different one.
Beam Structures: Classical and Advanced Theories proposesa new original unified approach to beam theory that includespractically all classical and advanced models for beams and whichhas become established and recognised globally as the mostimportant contribution to the field in the last quarter of acentury.
The Carrera Unified Formulation (CUF) has hierarchicalproperties, that is, the error can be reduced by increasing thenumber of the unknown variables. This formulation is extremelysuitable for computer implementations and can deal with mosttypical engineering challenges. It overcomes the problem ofclassical formulae that require different formulas for tension,bending, shear and torsion; it can be applied to any beamgeometries and loading conditions, reaching a high level ofaccuracy with low computational cost, and can tackle problems thatin most cases are solved by employing plate/shell and 3Dformulations.
Key features:
* compares classical and modern approaches to beam theory,including classical well-known results related to Euler-Bernoulliand Timoshenko beam theories
* pays particular attention to typical applications related tobridge structures, aircraft wings, helicopters and propellerblades
* provides a number of numerical examples including typicalAerospace and Civil Engineering problems
* proposes many benchmark assessments to help the readerimplement the CUF if they wish to do so
* accompanied by a companion website hosting dedicated softwareMUL2 that is used to obtain the numerical solutions in the book,allowing the reader to reproduce the examples given in the book aswell as to solve other problems of their own www.mul2.com
Researchers of continuum mechanics of solids and structures andstructural analysts in industry will find this book extremelyinsightful. It will also be of great interest to graduate andpostgraduate students of mechanical, civil and aerospaceengineering.
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Book
09/2011
Wiley
€127.50
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08/2011
Wiley
€89.49
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Persons
Erasmo Carrera, Politecnico di Torino, Italy
Erasmo Carrera is Professor of Aerospace Structures and Computational Aeroelasticity and Deputy Director of Department of Aerospace Engineering at the Politecnico di Torino. He has authored circa 200 journal and conference papers. His research has concentrated on composite materials, buckling and postbuckling of multilayered structures, non-linear analysis and stability, FEM; nonlinear analysis by FEM; development of efficient and reliable FE formulations for layered structures, contact mechanics, smart structures, nonlinear dynamics and flutter, and classical and mixed methods for multilayered plates and shells.
Gaetano Giunta, Centre de Recherche Public Henri Tudor, Luxembourg
Gaetano Giunta is a research scientist in the Department of Advanced Materials and Structures in the Centre de Recherche Public Henri Tudor.
Marco Petrolo, Politecnico di Torino, Italy
Marco Petrolo is a research scientist in the Department of Aeronautics and Space Engineering at the Politecnico di Torino.
Content
Preface.
Introduction.
References.
1 Fundamental Equations of Continuous Deformable Bodies.
1.1 Displacement, strain and stresses.
1.2 Equilibrium Equations in term of Stress Components and Boundary Conditions.
1.3 Strain Displacement Relations.
1.4 Constitutive Relations: Hooke's Law.
1.5 Displacement Approach via Principle of Virtual Displacements.
References.
2 The Euler-Bernoulli and Timoshenko Theories.
2.1 The Euler-BernoulliModel.
2.1.1 Displacement field.
2.1.2 Strains.
2.1.3 Stresses and stress resultants.
2.1.4 Elastica.
2.2 The Timoshenko Model.
2.2.1 Displacement Field.
2.2.2 Strains.
2.2.3 Stresses and stress resultants.
2.2.4 Elastica.
2.3 Bending of a cantilever beam: EBBT and TBT solutions.
2.3.1 EBBT solution.
2.3.2 TBT solution.
References.
3 A refined beam theory with in-plane stretching: the complete linear expansion case, CLEC.
3.1 The CLEC displacement field.
3.2 The importance of linear stretching terms.
3.3 A Finite Element based on CLEC.
Further Readings.
4 EBBT, TBT, and CLEC in Unified Form.
4.1 Unified Formulation of CLEC.
4.2 EBBT and TBT as particular cases of CLEC.
4.3 Poisson Locking and its Correction.
4.3.1 Kinematic considerations on strains.
4.3.2 Physical considerations on strains.
4.3.3 First remedy: use of higher-order kinematics.
4.3.4 Second remedy: modification of elastic coefficients.
References.
5 Carrera Unified Formulation and Refined Beam Theories.
5.1 Unified Formulation.
5.2 Governing Equations.
5.2.1 Strong Form of the Governing Equations.
5.2.2 Weak Form of the Governing Equations.
References.
Further Readings.
6 The parabolic, cubic, quartic and N-order beam theories.
6.1 The second-order beam model, N = 2.
6.2 The third-order, N = 3, and the fourth-order,N = 4, beam models
6.3 N-order beam models.
Further Readings.
7 CUF Beam Finite Element Models: Programming and Implementation Issue Guidelines.
7.1 Preprocessing and Input Descriptions.
7.1.1 General FE Inputs.
7.1.2 Specific CUF Inputs.
7.2 FEM Code.
7.2.1 Stiffness and Mass Matrix.
7.2.2 Stiffness and Mass Matrix Numerical Examples.
7.2.3 Constraints and Reduced Models.
7.2.4 Load vector.
7.3 Postprocessing.
7.3.1 Stresses and Strains.
References.
8 Shell Capabilities of Refined Beam Theories.
8.1 C-Shaped Cross-Section and Bending-Torsional Loading.
8.2 Thin-Walled Hollow Cylinder.
8.2.1 Static Analysis: Detection of Local Effects due to a Point Load.
8.2.2 Free Vibration Analysis: Detection of Shell-Like Natural Modes.
8.3 Static and Free Vibration Analyses of an Airfoil-Shaped Beam.
8.4 Free Vibrations of a Bridge-Like Beam.
References.
9 Linearized Elastic Stability.
9.1 Critical Buckling Load Classic Solution.
9.2 Higher-Order CUF Models.
9.2.1 Governing equations fundamental nucleus.
9.2.2 Closed form analytical solution.
9.3 Examples.
References.
10 Beams Made of Functionally Graded Materials.
10.1 Functionally Graded Materials.
10.2 Material Gradation Laws.
10.2.1 Exponential gradation law.
10.2.2 Power gradation law.
10.3 Beam Modeling.
10.4 Examples.
References.
11 Multi-Model Beam Theories via the Arlequin Method.
11.1 Multi-Model Approaches.
11.1.1 Mono-theory approaches.
11.1.2 Multi-theory approaches.
11.2 The Arlequin Method in the context of the Unified Formulation.
11.3 Examples.
References.
12 Guidelines and Recommendations.
12.1 Axiomatic and Asymptotic Methods
12.2 The Mixed Axiomatic/Asymptotic Method.
12.3 Load effect.
12.4 Cross-section effect.
12.5 Output location effect.
12.6 Reduced models for different error inputs.
References.
Index.
