The finite element method for mechanics of solids with ANSYS applications / [author], Ellis H. Dill.

Includes bibliographical references and index.

Contents Preface Author chapter 1 Finite Element Concepts 1.1. Introduction 1.2. Direct Stiffness Method 1.2.1. Merging the Element Stiffness Matrices 1.2.2. Augmenting the Element Stiffness Matrix 1.2.3. Stiffness Matrix Is Banded 1.3. The Energy Method 1.4. Truss Example 1.5. Axially Loaded Rod Example 1.5.1. Augmented Matrices for the Rod 1.5.2. Merge of Element Matrices for the Rod 1.6. Force Method 1.7. Other Structural Components 1.7.1. Space Truss 1.7.2. Beams and Frames 1.7.2.1. General Beam Equations 1.7.3. Plates and Shells 1.7.4. Two- or Three-Dimensional Solids 1.8. Problems References Bibliography chapter 2 Linear Elasticity 2.1. Basic Equations 2.1.1. Geometry of Deformation 2.1.2. Balance of Momentum 2.1.3. Virtual Work 2.1.4. Constitutive Relations 2.1.5. Boundary Conditions and Initial Conditions 2.1.6. Incompressible Materials 2.1.7. Plane Strain 2.1.8. Plane Stress 2.1.9. Tensile Test 2.1.10. Pure Shear 2.1.11. Pure Bending 2.1.12. Bending and Shearing 2.1.13. Properties of Solutions 2.1.14. A Plane Stress Example with a Singularity in Stress 2.2. Potential Energy 2.2.1. Proof of Minimum Potential Energy 2.3. Matrix Notation 2.4. Axially Symmetric Deformations 2.4.1. Cylindrical Coordinates 2.4.2. Axial Symmetry 2.4.3. Plane Stress and Plane Strain 2.5. Problems References Bibliography chapter 3 Finite Element Method for Linear Elasticity 3.1. Finite Element Approximation 3.1.1. Potential Energy 3.1.2. Finite Element Equations 3.1.3. Basic Equations in Matrix Notation 3.1.4. Basic Equations Using Virtual Work 3.1.5. Underestimate of Displacements 3.1.6. Nondimensional Equations 3.1.7. Uniaxial Stress 3.2. General Equations for an Assembly of Elements 3.2.1. Generalized Variational Principle 3.2.2. Potential Energy 3.2.3. Hybrid Displacement Functional 3.2.4. Hybrid Stress and Complementary Energy 3.2.5. Mixed Methods of Analysis 3.3. Nearly Incompressible Materials 3.3.1. Nearly Incompressible Plane Strain Bibliography chapter 4 The Triangle and the Tetrahedron 4.1. Linear Functions over a Triangular Region 4.2. Triangular Element for Plane Stress and Plane Strain 4.3. Plane Quadrilateral from Four Triangles 4.3.1. Square Element Formed from Four Triangles 4.4. Plane Stress Example: Short Beam 4.4.1. Extrapolation of the Solution 4.5. Linear Strain Triangles 4.6. Four-Node Tetrahedron 4.7. Ten-Node Tetrahedron 4.8. Problems chapter 5 The Quadrilateral and the Hexahedron 5.1. Four-Node Plane Rectangle 5.1.1. Stress Calculations 5.1.2. Plane Stress Example: Pure Bending 5.1.3. Plane Strain Example: Bending with Shear 5.1.4. Plane Stress Example: Short Beam 5.2. Improvements to Four-Node Quadrilateral 5.2.1. Wilson[–]Taylor Quadrilateral 5.2.2. Enhanced Strain Formulation 5.2.3. Approximate Volumetric Strains 5.2.4. Reduced Integration on the k Term 5.2.5. Reduced Integration on the λ Term 5.2.6. Uniform Reduced Integration 5.2.7. Example Using Improved Elements 5.3. Numerical Integration 5.4. Coordinate Transformations 5.5. Isoparametric Quadrilateral 5.5.1. Wilson-Taylor Element 5.5.2. Three-Node Triangle as a Special Case of Rectangle 5.6. Eight-Node Quadrilateral 5.6.1. Nodal Loads 5.6.2. Plane Stress Example: Pure Bending 5.6.3. Plane Stress Example: Bending with Shear 5.6.4. Plane Stress Example: Short Beam 5.6.5. General Quadrilateral Element 5.7. Eight-Node Block 5.8. Twenty-Node Solid 5.9. Singularity Element 5.10. Mixed U-P Elements 5.10.1. Plane Strain 5.10.2. Alternative Formulation for Plane Strain 5.10.3. 3D Elements 5.11. Problems References Bibliography chapter 6 Errors and Convergence of Finite Element Solution 6.1. General Remarks 6.2. Element Shape Limits 6.2.1. Aspect Ratio 6.2.2. Parallel Deviation for a Quadrilateral 6.2.3. Large Corner Angle 6.2.4. Jacobian Ratio 6.3. Patch Test 6.3.1. Wilson-Taylor Quadrilateral References chapter 7 Heat Conduction in Elastic Solids 7.1. Differential Equations and Virtual Work 7.2. Example Problem: One-Dimensional Transient Heat Flux 7.3. Example: Hollow Cylinder 7.4. Problems chapter 8 Finite Element Method for Plasticity 8.1. Theory of Plasticity 8.1.1. Tensile Test 8.1.2. Plane Stress 8.1.3. Summary of Plasticity 8.2. Finite Element Formulation for Plasticity 8.2.1. Fundamental Solution 8.2.2. Iteration to Improve the Solution 8.3. Example: Short Beam 8.4. Problems Bibliography chapter 9 Viscoelasticity 9.1. Theory of Linear Viscoelasticity 9.1.1. Recurrence Formula for History 9.1.2. Viscoelastic Example 9.2. Finite Element Formulation for Viscoelasticity 9.2.1. Basic Step-by-Step Solution Method 9.2.2. Step-by-Step Calculation with Load Correction 9.2.3. Plane Strain Example 9.3. Problems Bibliography chapter 10 Dynamic Analyses 10.1. Dynamical Equations 10.1.1. Lumped Mass 10.1.2. Consistent Mass 10.2. Natural Frequencies 10.2.1. Lumped Mass 10.2.2. Consistent Mass 10.3. Mode Superposition Solution 10.4. Example: Axially Loaded Rod 10.4.1. Exact Solution for Axially Loaded Rod 10.4.2. Finite Element Model 10.4.2.1. One-Element Model 10.4.2.2. Two-Element Model 10.4.3. Mode Superposition for Continuum Model of the Rod 10.5. Example: Short Beam 10.6. Dynamic Analysis with Damping 10.6.1. Viscoelastic Damping 10.6.2. Viscous Body Force 10.6.3. Analysis of Damped Motion by Mode Superposition 10.7. Numerical Solution of Differential Equations 10.7.1. Constant Average Acceleration 10.7.2. General Newmark Method 10.7.3. General Methods 10.7.3.1. Implicit Methods in General 10.7.3.2. Explicit Methods in General 10.7.4. Stability Analysis of Newmark's Method 10.7.5. Convergence, Stability, and Error 10.7.6. Example: Numerical Integration for Axially Loaded Rod 10.8. Example: Analysis of Short Beam 10.9. Problems Bibliography chapter 11 Linear Elastic Fracture Mechanics 11.1. Fracture Criterion 11.1.1. Analysis of Sheet 11.1.2. Fracture Modes 11.1.2.1. Mode I 11.1.2.2. Mode II 11.1.2.3. Mode III 11.2. Determination of K by Finite Element Analysis 11.2.1. Crack Opening Displacement Method 11.3. J-Integral for Plane Regions 11.4. Problems References Bibliography chapter 12 Plates and Shells 12.1. Geometry of Deformation 12.2. Equations of Equilibrium 12.3. Constitutive Relations for an Elastic Material 12.4. Virtual Work 12.5. Finite Element Relations for Bending 12.6. Classical Plate Theory 12.7. Plate Bending Example 12.8. Problems References Bibliography chapter 13 Large Deformations 13.1. Theory of Large Deformations 13.1.1. Virtual Work 13.1.2. Elastic Materials 13.1.3. Mooney-Rivlin Model of an Incompressible Material 13.1.4. Generalized Mooney-Rivlin Model 13.1.5. Polynomial Formula 13.1.6. Ogden's Function 13.1.7. Blatz-Ko Model 13.1.8. Logarithmic Strain Measure 13.1.9. Yeoh Model 13.1.10. Fitting Constitutive Relations to Experimental Data 13.1.10.1. Volumetric Data 13.1.10.2. Tensile Test 13.1.10.3. Biaxial Test 13.2. Finite Elements for Large Displacements 13.2.1. Lagrangian Formulation 13.2.2. Basic Step-by-Step Analysis 13.2.3. Iteration Procedure 13.2.4. Updated Reference Configuration 13.2.5. Example I 13.2.6. Example II 13.3. Structure of Tangent Modulus 13.4. Stability and Buckling 13.4.1. Beam-Column 13.5. Snap Through Buckling 13.5.1. Shallow Arch 13.6. Problems References Bibliography chapter 14 Constraints and Contact 14.1. Application of Constraints 14.1.1. Lagrange Multipliers 14.1.2. Perturbed Lagrangian Method 14.1.3. Penalty Functions 14.1.4. Augmented Lagrangian Method 14.2. Contact Problems 14.2.1. Example: A Truss Contacts a

Rigid Foundation 14.2.1.1. Load Fy> 0 Is Applied with Fx = 0 14.2.1.2. Loads Are Ramped Up Together: Fx = 27a, Fy = 12.8a 14.2.2. Lagrange Multiplier, No Friction Force 14.2.2.1. Stick Condition 14.2.2.2. Slip Condition 14.2.3. Lagrange Multiplier, with Friction 14.2.3.1. Stick Condition 14.2.3.2. Slip Condition 14.2.4. Penalty Method 14.2.4.1. Stick Condition 14.2.4.2. Slip Condition 14.3. Finite Element Analysis 14.3.1. Example: Contact of a Cylinder with a Rigid Plane 14.3.2. Hertz Contact Problem 14.4. Dynamic Impact 14.5. Problems References Bibliography chapter 15 ANSYS APDL Examples 15.1. ANSYS Instructions 15.1.1. ANSYS File Names 15.1.2. Graphic Window Controls 15.1.2.1. Graphics Window Logo 15.1.2.2. Display of Model 15.1.2.3. Display of Deformed and Undeformed Shape White on White 15.1.2.4. Adjusting Graph Colors 15.1.2.5. Printing from Windows Version of ANSYS 15.1.2.6. Some Useful Notes 15.2. ANSYS Elements SURF153, SURF154 15.3. Truss Example 15.4. Beam Bending 15.5. Beam with a Distributed Load 15.6. One Triangle 15.7. Plane Stress Example Using Triangles 15.8. Cantilever Beam Modeled as Plane Stress 15.9. Plane Stress: Pure Bending 15.10. Plane Strain Bending Example 15.11. Plane Stress Example: Short Beam 15.12. Sheet with a Hole 15.12.1. Solution Procedure 15.13. Plasticity Example 15.14. Viscoelasticity Creep Test 15.15. Viscoelasticity Example 15.16. Mode Shapes and Frequencies of a Rod 15.17. Mode Shapes and Frequencies of a Short Beam 15.18. Transient Analysis of Short Beam 15.19. Stress Intensity Factor by Crack Opening Displacement 15.20. Stress Intensity Factor by J-Integral 15.21. Stretching of a Nonlinear Elastic Sheet 15.22. Nonlinear Elasticity: Tensile Test 15.23. Column Buckling 15.24. Column Post-Buckling 15.25. Snap Through 15.26. Plate Bending Example 15.27. Clamped Plate 15.28. Gravity Load on a Cylindrical Shell 15.29. Plate Buckling 15.30. Heated Rectangular Rod 15.31. Heated Cylindrical Rod 15.32. Heated Disk 15.33. Truss Contacting a Rigid Foundation 15.34. Compression of a Rubber Cylinder between Rigid Plates 15.35. Hertz Contact Problem 15.36. Elastic Rod Impacting a Rigid Wall 15.37. Curve Fit for Nonlinear Elasticity Using Blatz-Ko Model 15.38. Curve Fit for Nonlinear Elasticity Using Polynomial Model Bibliography chapter 16 ANSYS Workbench 16.1. Two- and Three-Dimensional Geometry 16.2. Stress Analysis 16.3. Short Beam Example 16.3.1. Short Beam Geometry 16.3.2. Short Beam, Static Loading 16.3.3. Short Beam, Transient Analysis 16.4. Filleted Bar Example 16.5. Sheet with a Hole Bibliography Index

"The finite element method (FEM) has become the standard method used by engineers for the solution of static and dynamic problems for elastic and inelastic structures and machines. This volume explores the theory behind the method and instruction in use of ANSYS, a commonly used commercial finite element program. Totally, self contained, the book provides the necessary background on solid mechanics (elasticity, plasticity, viscoelasticity) and mathematics. It includes theory and examples and contains detailed instructions for solutions using ANSYS for small and large deformation elasticity, plasticity, viscoelasicity, vibrations, wave propagation, fracture mechanics, building, plates and shells, and contact problems"-- Provided by publisher.

"The purpose of this book is to explain the application of finite the element method to problems in the mechanics of solids. It is intended for practicing engineers who use the finite element method for stress analysis and for graduate students in engineering who want to understand the finite element method for their research. It is also designed to be a textbook for a graduate course in engineering. The application of the finite element method is illustrated by using the ANSYSʼ computer program. Step by step instructions for the use of ANSYS APDL and ANSYS Workbench in more than 40 examples are included. The required background material in the mechanics of solids is provided so that the work is self-contained for the knowledgeable reader. A more complete treatment of solid mechanics is provided in the book: Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity, by Ellis H. Dill, CRC Press, 2007. References to that book are abbreviated by 'Dill: Chapter--'"