The finite element method for mechanics of solids with ANSYS applications. (©2012)

• Record Type: Book
• Further Information: Note: [author], Ellis H. Dill.
• Other Names: Dill, Ellis Harold, 1932-
• Contents: 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 κ 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 Augment
• Publisher Details: Boca Raton, Fla : CRC Press
• Publication Date: 2012
• Copyright Date: 2012
• Extent: 1 online resource (xv, 492 pages), illustrations
• Subjects: 620.00151825; Continuum mechanics; Finite element method; Engineering mathematics; ANSYS (Computer system); ANSYS (Computer system); Continuum mechanics; Engineering mathematics; Finite element method; Electronic books
• Languages: English
• ISBNs: 9781439845844; 1439845840
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.