Description
Taylor & Francis Ltd The Finite Element Method For Mechanics Of Solids With Ansys Applications 2011 Edition by Ellis H. Dill
While the finite element method (FEM) has become the standard technique used to solve static and dynamic problems associated with structures and machines, ANSYS software has developed into the engineer's software of choice to model and numerically solve those problems. An invaluable tool to help engineers master and optimize analysis, The Finite Element Method for Mechanics of Solids with ANSYS Applications explains the foundations of FEM in detail, enabling engineers to use it properly to analyze stress and interpret the output of a finite element computer program such as ANSYS.Illustrating presented theory with a wealth of practical examples, this book covers topics including:Essential background on solid mechanics (including small- and large-deformation elasticity, plasticity, and viscoelasticity) and mathematicsAdvanced finite element theory and associated fundamentals, with examplesUse of ANSYS to derive solutions for problems that deal with vibration, wave propagation, fracture mechanics, plates and shells, and contactTotally self-contained, this text presents step-by-step instructions on how to use ANSYS Parametric Design Language (APDL) and the ANSYS Workbench to solve problems involving static/dynamic structural analysis (both linear and non-linear) and heat transfer, among other areas. It will quickly become a welcome addition to any engineering library, equally useful to students and experienced engineers alike. Chapter 1: Finite Element Concepts1.1 Introduction1.2 Direct Stiffness Method1.2.1 Merging the Element Stiffness Matrices1.2.2 Augmenting the Element Stiffness Matrix1.2.3 Stiffness Matrix Is Banded1.3 The Energy Method1.4 Truss Example1.5 Axially Loaded Rod Example1.5.1 Augmented Matrices for the Rod1.5.2 Merge of Element Matrices for the Rod1.6 Force Method1.7 Other Structural Components1.7.1 Space Truss1.7.2 Beams and Frames1.7.2.1 General Beam Equations1.7.3 Plates and Shells1.7.4 Two- or Three-Dimensional Solids1.8 ProblemsReferencesBibliographyChapter 2: Linear Elasticity2.1 Basic Equations2.1.1 Geometry of Deformation2.1.2 Balance of Momentum2.1.3 Virtual Work2.1.4 Constitutive Relations2.1.5 Boundary Conditions and Initial Conditions 2.1.6 Incompressible Materials2.1.7 Plane Strain2.1.8 Plane Stress2.1.9 Tensile Test2.1.10 Pure Shear2.1.11 Pure Bending2.1.12 Bending and Shearing2.1.13 Properties of Solutions2.1.14 A Plane Stress Example with a Singularity in Stress2.2 Potential Energy2.2.1 Proof of Minimum Potential Energy2.3 Matrix Notation2.4 Axially Symmetric Deformations2.4.1 Cylindrical Coordinates2.4.2 Axial Symmetry2.4.3 Plane Stress and Plane Strain2.5 ProblemsReferencesBibliographyChapter 3: Finite Element Method for Linear Elasticity3.1 Finite Element Approximation3.1.1 Potential Energy3.1.2 Finite Element Equations3.1.3 Basic Equations in Matrix Notation3.1.4 Basic Equations Using Virtual Work3.1.5 Underestimate of Displacements3.1.6 Nondimensional Equations3.1.7 Uniaxial Stress3.2 General Equations for an Assembly of Elements3.2.1 Generalized Variational Principle3.2.2 Potential Energy3.2.3 Hybrid Displacement Functional3.2.4 Hybrid Stress and Complementary Energy3.2.5 Mixed Methods of Analysis3.3 Nearly Incompressible Materials3.3.1 Nearly Incompressible Plane StrainBibliographyChapter 4: The Triangle and the Tetrahedron4.1 Linear Functions over a Triangular Region4.2 Triangular Element for Plane Stress and Plane Strain4.3 Plane Quadrilateral from Four Triangles4.3.1 Square Element Formed from Four Triangles 4.4 Plane Stress Example: Short Beam4.4.1 Extrapolation of the Solution4.5 Linear Strain Triangles4.6 Four-Node Tetrahedron4.7 Ten-Node Tetrahedron4.8 ProblemsChapter 5: The Quadrilateral and the Hexahedron5.1 Four-Node Plane Rectangle5.1.1 Stress Calculations5.1.2 Plane Stress Example: Pure Bending5.1.3 Plane Strain Example: Bending with Shear5.1.4 Plane Stress Example: Short Beam5.2 Improvements to Four-Node Quadrilateral5.2.1 Wilson-Taylor Quadrilateral5.2.2 Enhanced Strain Formulation5.2.3 Approximate Volumetric Strains5.2.4 Reduced Integration on the Term5.2.5 Reduced Integration on the Term5.2.6 Uniform Reduced Integration5.2.7 Example Using Improved Elements5.3 Numerical Integration5.4 Coordinate Transformations5.5 Isoparametric Quadrilateral5.5.1 Wilson-Taylor Element5.5.2 Three-Node Triangle as a Special Case of Rectangle5.6 Eight-Node Quadrilateral5.6.1 Nodal Loads5.6.2 Plane Stress Example: Pure Bending5.6.3 Plane Stress Example: Bending with Shear5.6.4 Plane Stress Example: Short Beam5.6.5 General Quadrilateral Element5.7 Eight-Node Block5.8 Twenty-Node Solid5.9 Singularity Element5.10 Mixed U-P Elements5.10.1 Plane Strain5.10.2 Alternative Formulation for Plane Strain5.10.3 3D Elements5.11 ProblemsReferencesBibliographyChapter 6: Errors and Convergence of Finite Element Solution6.1 General Remarks6.2 Element Shape Limits6.2.1 Aspect Ratio6.2.2 Parallel Deviation for a Quadrilateral6.2.3 Large Corner Angle6.2.4 Jacobian Ratio6.3 Patch Test6.3.1 Wilson-Taylor QuadrilateralReferencesChapter 7: Heat Conduction in Elastic Solids7.1 Differential Equations and Virtual Work7.2 Example Problem: One-Dimensional Transient Heat Flux7.3 Example: Hollow Cylinder7.4 ProblemsChapter 8: Finite Element Method for Plasticity8.1 Theory of Plasticity8.1.1 Tensile Test8.1.2 Plane Stress8.1.3 Summary of Plasticity8.2 Finite Element Formulation for Plasticity8.2.1 Fundamental Solution8.2.2 Iteration to Improve the Solution8.3 Example: Short Beam8.4 ProblemsBibliographyChapter 9: Viscoelasticity9.1 Theory of Linear Viscoelasticity9.1.1 Recurrence Formula for History9.1.2 Viscoelastic Example9.2 Finite Element Formulation for Viscoelasticity9.2.1 Basic Step-by-Step Solution Method9.2.2 Step-by-Step Calculation with Load Correction9.2.3 Plane Strain Example9.3 ProblemsBibliographyChapter 10: Dynamic Analyses10.1 Dynamical Equations10.1.1 Lumped Mass10.1.2 Consistent Mass 10.2 Natural Frequencies 10.2.1 Lumped Mass10.2.2 Consistent Mass 10.3 Mode Superposition Solution10.4 Example: Axially Loaded Rod10.4.1 Exact Solution for Axially Loaded Rod10.4.2 Finite Element Model10.4.2.1 One-Element Model10.4.2.2 Two-Element Model10.4.3 Mode Superposition for Continuum Model of the Rod10.5 Example: Short Beam10.6 Dynamic Analysis with Damping 10.6.1 Viscoelastic Damping10.6.2 Viscous Body Force 10.6.3 Analysis of Damped Motion by Mode Superposition10.7 Numerical Solution of Differential Equations10.7.1 Constant Average Acceleration10.7.2 General Newmark Method10.7.3 General Methods10.7.3.1 Implicit Methods in General 10.7.3.2 Explicit Methods in General 10.7.4 Stability Analysis of Newmark's Method10.7.5 Convergence, Stability, and Error10.7.6 Example: Numerical Integration for Axially Loaded Rod10.8 Example: Analysis of Short Beam10.9 ProblemsBibliographyChapter 11: Linear Elastic Fracture Mechanics11.1 Fracture Criterion11.1.1 Analysis of Sheet11.1.2 Fracture Modes11.1.2.1 Mode I11.1.2.2 Mode II11.1.2.3 Mode III 11.2 Determination of K by Finite Element Analysis11.2.1 Crack Opening Displacement Method11.3 J-Integral for Plane Regions11.4 ProblemsReferencesBibliographyChapter 12: Plates and Shells12.1 Geometry of Deformation12.2 Equations of Equilibrium12.3 Constitutive Relations for an Elastic Material12.4 Virtual Work12.5 Finite Element Relations for Bending12.6 Classical Plate Theory12.7 Plate Bending Example12.8 ProblemsReferencesBibliographyChapter 13: Large Deformations13.1 Theory of Large Deformations13.1.1 Virtual Work13.1.2 Elastic Materials13.1.3 Mooney-Rivlin Model of an Incompressible Material13.1.4 Generalized Mooney-Rivlin Model13.1.5 Polynomial Formula13.1.6 Ogden's Function13.1.7 Blatz-Ko Model13.1.8 Logarithmic Strain Measure13.1.9 Yeoh Model13.1.10 Fitting Constitutive Relations to Experimental Data13.1.10.1. Volumetric Data13.1.10.2. Tensile Test13.1.10.3. Biaxial Test13.2 Finite Elements for Large Displacements13.2.1 Lagrangian Formulation13.2.2 Basic Step-by-Step Analysis13.2.3 Iteration Procedure13.2.4 Updated Reference Configuration13.2.5 Example I13.2.6 Example II13.3 Structure of Tangent Modulus13.4 Stability and Buckling13.4.1 Beam-Column13.5 Snap-Through Buckling13.5.1 Shallow Arch13.6 ProblemsReferencesBibliographyChapter 14: Constraints and Contact14.1 Application of Constraints14.1.1 Lagrange Multipliers14.1.2 Perturbed Lagrangian Method14.1.3 Penalty Functions14.1.4 Augmented Lagrangian Method14.2 Contact Problems14.2.1 Example: A Truss Contacts a Rigid Foundation14.2.1.1 Load Fy > 0 Is Applied with Fx = 014.2.1.2 Loads Are Ramped Up Together: Fx = 27 , Fy = 12.8 14.2.2 Lagrange Multiplier, No Friction Force14.2.2.1 Stick Condition14.2.2.2 Slip Condition14.2.3 Lagrange Multiplier, with Friction14.2.3.1 Stick Condition14.2.3.2 Slip Condition14.2.4 Penalty Method 14.2.4.1 Stick Condition14.2.4.2 Slip Condition14.3 Finite Element Analysis14.3.1 Example: Contact of a Cylinder with a Rigid Plane14.3.2 Hertz Contact Problem14.4 Dynamic Impact14.5 ProblemsReferencesBibliographyChapter 15: ANSYS APDL Examples15.1 ANSYS Instructions15.1.1 ANSYS File Names15.1.2 Graphic Window Controls15.1.2.1 Graphics Window Logo15.1.2.2 Display of Model15.1.2.3 Display of Deformed and Undeformed Shape White on White15.1.2.4 Adjusting Graph Colors15.1.2.5 Printing from Windows Version of ANSYS15.1.2.6 Some Useful Notes15.2 ANSYS Elements SURF153, SURF15415.3 Truss Example15.4 Beam Bending15.5 Beam with a Distributed Load15.6 One Triangle15.7 Plane Stress Example Using Triangles15.8 Cantilever Beam Modeled as Plane Stress15.9 Plane Stress: Pure Bending15.10 Plane Strain Bending Example15.11 Plane Stress Example: Short Beam15.12 Sheet with a Hole15.12.1 Solution Procedure15.13 Plasticity Example15.14 Viscoelasticity Creep Test15.15 Viscoelasticity Example15.16 Mode Shapes and Frequencies of a Rod15.17 Mode Shapes and Frequencies of a Short Beam15.18 Transient Analysis of Short Beam15.19 Stress Intensity Factor by Crack Opening Displacement15.20 Stress Intensity Factor by J-Integral15.21 Stretching of a Nonlinear Elastic Sheet15.22 Nonlinear Elasticity: Tensile Test15.23 Column Buckling15.24 Column Post-Buckling 15.25 Snap-Through15.26 Plate Bending Example15.27 Clamped Plate15.28 Gravity Load on a Cylindrical Shell15.29 Plate Buckling15.30 Heated Rectangular Rod15.31 Heated Cylindrical Rod15.32 Heated Disk15.33 Truss Contacting a Rigid Foundation15.34 Compression of a Rubber Cylinder between Rigid Plates15.35 Hertz Contact Problem15.36 Elastic Rod Impacting a Rigid Wall15.37 Curve Fit for Nonlinear Elasticity Using Blatz-Ko Model15.38 Curve Fit for Nonlinear Elasticity Using Polynomial ModelBibliographyChapter 16: ANSYS Workbench16.1 Two- and Three-Dimensional Geometry16.2 Stress Analysis16.3 Short Beam Example16.3.1 Short Beam Geometry16.3.2 Short Beam, Static Loading16.3.3 Short Beam, Transient Analysis16.4 Filleted Bar Example16.5 Sheet with a HoleBibliographyIndexshow more