TY  - BOOK
AU  - Dill,Ellis Harold
TI  - The finite element method for mechanics of solids with ANSYS applications
T2  - Advances in engineering series
SN  - 9781439845837
AV  - QA808.2 .D536 2012
PY  - 2012///]
CY  - Boca Raton, Fla.
PB  - CRC Press
KW  - Continuum mechanics
KW  - Finite element method
KW  - Engineering mathematics
KW  - ANSYS (Computer system)
N1  - 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
N2  - "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"--; "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--'"
ER  -