finite element analysis of composite materials using ansys

363 Pages·2013·2.62 MB·English

Materials Science/Mechanical Engineering/Civil Engineering
FINITE ELEMENT ANALYSIS Barbero SECOND EDITION
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OF COMPOSITE MATERIALS I
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USING ANSYS® E

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SECOND EDITION M
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Ever J. Barbero T

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Designing structures using composite materials poses unique challenges, L
especially due to the need for concurrent design of both material Y
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and structure. Professors are faced with two options: textbooks that
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teach the theory of advanced mechanics of composites, but lack S FINITE ELEMENT ANALYSIS
computational examples of advanced analysis, and books on finite O
element analysis that may or may not demonstrate very limited F
applications to composites. But there is a third option that makes the
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other two obsolete: Ever J. Barbero’s Finite Element Analysis O OF COMPOSITE MATERIALS
of Composite Materials Using ANSYS®, Second Edition. M

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The Only Finite Element Analysis Book on the Market Using O
ANSYS® to Analyze Composite Materials S USING ANSYS®
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By layering detailed theoretical and conceptual discussions with fully
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developed examples, this text supplies the missing link between theory
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and implementation. In-depth discussions cover all of the major aspects of
advanced analysis, including three-dimensional effects, viscoelasticity, edge A
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effects, elastic instability, damage, and delamination. This second edition of
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the bestseller has been completely revised to incorporate advances in the R
state of the art in such areas as modeling of damage in composites. In I
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addition, all 50+ worked examples have been updated to reflect the newest
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version of ANSYS®. Including some use of MATLAB®, these examples S
demonstrate how to use the concepts to formulate and execute finite element
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analyses and how to interpret the results in engineering terms. In addition,
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the source code for each example is available to students for download I
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online via a companion website featuring a special area reserved for
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instructors. A solutions manual is available upon qualifying course adoption.

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Cementing applied computational and analytical experience to a firm N Ever J. Barbero
foundation of basic concepts and theory, Finite Element Analysis of S
Composite Materials Using ANSYS®, Second Edition offers a Y
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modern, practical, and versatile classroom tool for today’s engineering
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classroom.
SECOND
EDITION
K15077
ISBN: 978-1-4665-1689-2
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9 781466 516892
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FINITE ELEMENT ANALYSIS
OF COMPOSITE MATERIALS
USING ANSYS®
SECOND EDITION
K15077_FM.indd 1 11/8/13 1:10 PM
Composite Materials: Analysis and Design
Series Editor
Ever J. Barbero
PUBLISHED
Finite Element Analysis of Composite Materials Using ANSYS,® Second Edition,
Ever J. Barbero
Smart Composites: Mechanics and Design, Rani El-Hajjar, Valeria La Saponara,
and Anastasia Muliana
Finite Element Analysis of Composite Materials with Abaqus, Ever J. Barbero
FRP Deck and Steel Girder Bridge Systems: Analysis and Design,
Julio F. Davalos, An Chen, Bin Zou, and Pizhong Qiao
Introduction to Composite Materials Design, Second Edition, Ever J. Barbero
Finite Element Analysis of Composite Materials, Ever J. Barbero
K15077_FM.indd 2 11/8/13 1:10 PM
FINITE ELEMENT ANALYSIS
OF COMPOSITE MATERIALS
USING ANSYS®
SECOND EDITION
Ever J. Barbero
K15077_FM.indd 3 11/8/13 1:10 PM
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB® software.
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Dedicado a la memoria de mi padre, Ever Francisco Barbero
(1928–2007).
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Contents
Series Preface xiii
Preface xv
Acknowledgments xix
List of Symbols xxi
List of Examples xxix
Errata xxxi
1 Mechanics of Orthotropic Materials 1
1.1 Lamina Coordinate System . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Contracted Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5.1 Alternate Contracted Notation . . . . . . . . . . . . . . . . . 5
1.6 Equilibrium and Virtual Work . . . . . . . . . . . . . . . . . . . . . 6
1.7 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.7.1 Traction Boundary Conditions . . . . . . . . . . . . . . . . . 8
1.7.2 Free Surface Boundary Conditions . . . . . . . . . . . . . . . 8
1.8 Continuity Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8.1 Traction Continuity . . . . . . . . . . . . . . . . . . . . . . . 9
1.8.2 Displacement Continuity . . . . . . . . . . . . . . . . . . . . . 9
1.9 Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.10 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . 10
1.10.1 Stress Transformation . . . . . . . . . . . . . . . . . . . . . . 13
1.10.2 Strain Transformation . . . . . . . . . . . . . . . . . . . . . . 15
1.11 Transformation of Constitutive Equations . . . . . . . . . . . . . . . 16
1.12 3D Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . 17
1.12.1 Anisotropic Material . . . . . . . . . . . . . . . . . . . . . . . 18
1.12.2 Monoclinic Material . . . . . . . . . . . . . . . . . . . . . . . 19
vii
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viii Finite Element Analysis of Composite Materials
1.12.3 Orthotropic Material . . . . . . . . . . . . . . . . . . . . . . . 20
1.12.4 Transversely Isotropic Material . . . . . . . . . . . . . . . . . 22
1.12.5 Isotropic Material . . . . . . . . . . . . . . . . . . . . . . . . 23
1.13 Engineering Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.13.1 Restrictions on Engineering Constants . . . . . . . . . . . . . 28
1.14 From 3D to Plane Stress Equations . . . . . . . . . . . . . . . . . . . 29
1.15 Apparent Laminate Properties . . . . . . . . . . . . . . . . . . . . . 31
Suggested Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Introduction to Finite Element Analysis 37
2.1 Basic FEM Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.1.1 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.2 Element Equations . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.3 Approximation over an Element . . . . . . . . . . . . . . . . 39
2.1.4 Interpolation Functions . . . . . . . . . . . . . . . . . . . . . 40
2.1.5 Element Equations for a Specific Problem . . . . . . . . . . . 42
2.1.6 Assembly of Element Equations . . . . . . . . . . . . . . . . . 43
2.1.7 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 44
2.1.8 Solution of the Equations . . . . . . . . . . . . . . . . . . . . 44
2.1.9 Solution Inside the Elements . . . . . . . . . . . . . . . . . . 44
2.1.10 Derived Results . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2 General Finite Element Procedure . . . . . . . . . . . . . . . . . . . 45
2.3 Solid Modeling, Analysis, and Visualization . . . . . . . . . . . . . . 49
2.3.1 Model Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.2 Material and Section Properties . . . . . . . . . . . . . . . . . 52
2.3.3 Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.4 Solution Steps . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.5 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.6 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 54
2.3.7 Meshing and Element Type . . . . . . . . . . . . . . . . . . . 56
2.3.8 Solution Phase . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.3.9 Post-Processing and Visualization . . . . . . . . . . . . . . . 56
Suggested Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3 Elasticity and Strength of Laminates 63
3.1 Kinematics of Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.1 First-Order Shear Deformation Theory . . . . . . . . . . . . . 65
3.1.2 Kirchhoff Theory . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Finite Element Analysis of Laminates . . . . . . . . . . . . . . . . . 71
3.2.1 Element Types . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.2 Sandwich Shells. . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.3 Nodes and Curvature . . . . . . . . . . . . . . . . . . . . . . 74
3.2.4 Drilling Rotation . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.5 A-B-D-H Input Data for Laminate FEA . . . . . . . . . . . . 74
3.2.6 Equivalent Orthotropic Input for Laminate FEA . . . . . . . 77
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