Programming the finite element method /

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"Provides an updated version of Fortran 2003 (all the Fortran programs and subroutines are listed in full in the text but will also be made available online)"--

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Smith, I. M. (Ian Moffat), 1940- (Autor), Griffiths, D. V. (Autor), Margetts, Lee (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Chichester, West Sussex, UK : Wiley, 2014.
Edición:Fifth edition.
Temas:
Finite element method > Data processing.
Engineering > Data processing.
FORTRAN 2003 (Computer program language)
Ingénierie > Informatique.
Fortran 2003 (Langage de programmation)
TECHNOLOGY & ENGINEERING > Drafting & Mechanical Drawing.
Engineering > Data processing
Finite element method > Data processing
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: 1. Preliminaries: Computer Strategies
  • 1.1. Introduction
  • 1.2. Hardware
  • 1.3. Memory Management
  • 1.4. Vector Processors
  • 1.5. Multi-core Processors
  • 1.6. Co-processors
  • 1.7. Parallel Processors
  • 1.8. Applications Software
  • 1.8.1. Compilers
  • 1.8.2. Arithmetic
  • 1.8.3. Conditions
  • 1.8.4. Loops
  • 1.9. Array Features
  • 1.9.1. Dynamic Arrays
  • 1.9.2. Broadcasting
  • 1.9.3. Constructors
  • 1.9.4. Vector Subscripts
  • 1.9.5. Array Sections
  • 1.9.6. Whole-array Manipulations
  • 1.9.7. Intrinsic Procedures for Arrays
  • 1.9.8. Modules
  • 1.9.9. Subprogram Libraries
  • 1.9.10. Structured Programming
  • 1.10. Third-party Libraries
  • 1.10.1. BIAS Libraries
  • 1.10.2. Maths Libraries
  • 1.10.3. User Subroutines
  • 1.10.4. MPI Libraries
  • 1.11. Visualisation
  • 1.11.1. Starting ParaView
  • 1.11.2. Display Restrained Nodes
  • 1.11.3. Display Applied Loads
  • 1.11.4. Display Deformed Mesh
  • 1.12. Conclusions
  • References
  • 2. Spatial Discretisation by Finite Elements
  • 2.1. Introduction
  • 2.2. Rod Element
  • 2.2.1. Rod Stiffness Matrix
  • 2.2.2. Rod Mass Element
  • 2.3. Eigenvalue Equation
  • 2.4. Beam Element
  • 2.4.1. Beam Element Stiffness Matrix
  • 2.4.2. Beam Element Mass Matrix
  • 2.5. Beam with an Axial Force
  • 2.6. Beam on an Elastic Foundation
  • 2.7. General Remarks on the Discretisation Process
  • 2.8. Alternative Derivation of Element Stiffness
  • 2.9. Two-dimensional Elements: Plane Stress
  • 2.10. Energy Approach and Plane Strain
  • 2.10.1. Thermoelasticity
  • 2.11. Plane Element Mass Matrix
  • 2.12. Axisymmetric Stress and Strain
  • 2.13. Three-dimensional Stress and Strain
  • 2.14. Plate Bending Element
  • 2.15. Summary of Element Equations for Solids
  • 2.16. Flow of Fluids: Navier
  • Stokes Equations
  • 2.17. Simplified Flow Equations
  • 2.17.1. Steady State
  • 2.17.2. Transient State
  • 2.17.3. Convection
  • 2.18. Further Coupled Equations: Biot Consolidation
  • 2.19. Conclusions
  • References
  • 3. Programming Finite Element Computations
  • 3.1. Introduction
  • 3.2. Local Coordinates for Quadrilateral Elements
  • 3.2.1. Numerical Integration for Quadrilaterals
  • 3.2.2. Analytical Integration for Quadrilaterals
  • 3.3. Local Coordinates for Triangular Elements
  • 3.3.1. Numerical Integration for Triangles
  • 3.3.2. Analytical Integration for Triangles
  • 3.4. Multi-Element Assemblies
  • 3.5. Èlement-by-Element' Techniques
  • 3.5.1. Conjugate Gradient Method for Linear Equation Systems
  • 3.5.2. Preconditioning
  • 3.5.3. Unsymmetric Systems
  • 3.5.4. Symmetric Non-Positive Definite Equations
  • 3.5.5. Eigenvalue Systems
  • 3.6. Incorporation of Boundary Conditions
  • 3.6.1. Convection Boundary Conditions
  • 3.7. Programming using Building Blocks
  • 3.7.1. Black Box Routines
  • 3.7.2. Special Purpose Routines
  • 3.7.3. Plane Elastic Analysis using Quadrilateral Elements
  • 3.7.4. Plane Elastic Analysis using Triangular Elements
  • 3.7.5. Axisymmetric Strain of Elastic Solids
  • 3.7.6. Plane Steady Laminar Fluid Flow
  • 3.7.7. Mass Matrix Formation
  • 3.7.8. Higher-Order 2D Elements
  • 3.7.9. Three-Dimensional Elements
  • 3.7.10. Assembly of Elements
  • 3.8. Solution of Equilibrium Equations
  • 3.9. Evaluation of Eigenvalues and Eigenvectors
  • 3.9.1. Jacobi Algorithm
  • 3.9.2. Lanczos and Arnoldi Algorithms
  • 3.10. Solution of First-Order Time-Dependent Problems
  • 3.11. Solution of Coupled Navier
  • Stokes Problems
  • 3.12. Solution of Coupled Transient Problems
  • 3.12.1. Absolute Load Version
  • 3.12.2. Incremental Load Version
  • 3.13. Solution of Second-Order Time-Dependent Problems
  • 3.13.1. Modal Superposition
  • 3.13.2. Newmark or Crank
  • Nicolson Method
  • 3.13.3. Wilson's Method
  • 3.13.4. Complex Response
  • 3.13.5. Explicit Methods and Other Storage-Saving Strategies
  • References
  • 4. Static Equilibrium of Structures
  • 4.1. Introduction
  • Program 4.1 One-dimensional analysis of axially loaded elastic rods using 2-node rod elements
  • Program 4.2 Analysis of elastic pin-jointed frames using 2-node rod elements in two or three dimensions
  • Program 4.3 Analysis of elastic beams using 2-node beam elements (elastic foundation optional)
  • Program 4.4 Analysis of elastic rigid-jointed frames using 2-node beam/rod elements in two or three dimensions
  • Program 4.5 Analysis of elastic
  • plastic beams or frames using 2-node beam or beam/rod elements in one, two or three dimensions
  • Program 4.6 Stability (buckling) analysis of elastic beams using 2-node beam elements (elastic foundation optional)
  • Program 4.7 Analysis of plates using 4-node rectangular plate elements. Homogeneous material with identical elements. Mesh numbered in x- or y-direction
  • 4.2. Conclusions
  • 4.3. Glossary of Variable Names
  • 4.4. Exercises
  • References
  • 5. Static Equilibrium of Linear Elastic Solids
  • 5.1. Introduction
  • Program 5.1 Plane or axisymmetric strain analysis of a rectangular elastic solid using 3-, 6-, 10- or 15-node right-angled triangles or 4-, 8- or 9-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z)-direction
  • Program 5.2 Non-axisymmetric analysis of a rectangular axisymmetric elastic solid using 8-node rectangular quadrilaterals. Mesh numbered in r- or z -direction
  • Program 5.3 Three-dimensional analysis of a cuboidal elastic solid using 8-, 14- or 20-node brick hexahedra. Mesh numbered in xz-planes then in the y-direction
  • Program 5.4 General 2D (plane strain) or 3D analysis of elastic solids. Gravity loading option
  • Program 5.5 Plane or axisymmetric thermoelastic analysis of an elastic solid using 3-, 6-, 10- or 15-node right-angled triangles or 4-, 8- or 9-node rectangular quadrilaterals. Mesh numbered in x(r)- or y (z)-direction
  • Program 5.6 Three-dimensional strain of a cuboidal elastic solid using 8-, 14- or 20-node brick hexahedra. Mesh numbered in xz-planes then in the y-direction. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver
  • Program 5.7 Three-dimensional strain of a cuboidal elastic solid using 8-, 14- or 20-node brick hexahedra. Mesh numbered in xz-planes then in the y-direction. No global stiffness matrix. Diagonally preconditioned conjugate gradient solver. Optimised maths library, ABAQUS UMAT version
  • 5.2. Glossary of Variable Names
  • 5.3. Exercises
  • References
  • 6. Material Non-linearity
  • 6.1. Introduction
  • 6.2. Stress
  • strain Behaviour
  • 6.3. Stress Invariants
  • 6.4. Failure Criteria
  • 6.4.1. Von Mises
  • 6.4.2. Mohr
  • Coulomb and Tresca
  • 6.5. Generation of Body Loads
  • 6.6. Viscoplasticity
  • 6.7. Initial Stress
  • 6.8. Corners on the Failure and Potential Surfaces
  • Program 6.1 Plane-strain-bearing capacity analysis of an elastic
  • plastic (von Mises) material using 8-node rectangular quadrilaterals. Flexible smooth footing. Load control. Viscoplastic strain method
  • Program 6.2 Plane-strain-bearing capacity analysis of an elastic
  • plastic (von Mises) material using 8-node rectangular quadrilaterals. Flexible smooth footing. Load control. Viscoplastic strain method. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver
  • Program 6.3 Plane-strain-bearing capacity analysis of an elastic
  • plastic (Mohr
  • Coulomb) material using 8-node rectangular quadrilaterals. Rigid smooth footing. Displacement control. Viscoplastic strain method
  • Program 6.4 Plane-strain slope stability analysis of an elastic
  • plastic (Mohr
  • Coulomb) material using 8-node rectangular quadrilaterals. Gravity loading. Viscoplastic strain method
  • Program 6.5 Plane-strain earth pressure analysis of an elastic
  • plastic (Mohr
  • Coulomb) material using 8-node rectangular quadrilaterals. Rigid smooth wall.
  • Initial stress method
  • 6.9. Elastoplastic Rate Integration
  • 6.9.1. Forward Euler Method
  • 6.9.2. Backward Euler Method
  • 6.10. Tangent Stiffness Approaches
  • 6.10.1. Inconsistent Tangent Matrix
  • 6.10.2. Consistent Tangent Matrix
  • 6.10.3. Convergence Criterion
  • Program 6.6 Plane-strain-bearing capacity analysis of an elastic
  • plastic (von Mises) material using 8-node rectangular quadrilaterals, Flexible smooth footing, Load control. Consistent tangent stiffness. Closest point projection method (CPPM)
  • Program 6.7 Plane-strain-bearing capacity analysis of an elastic
  • plastic (von Mises) material using 8-node rectangular quadrilaterals. Flexible smooth footing. Load control. Consistent tangent stiffness. CPPM. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver
  • Program 6.8 Plane-strain-bearing capacity analysis of an elastic
  • plastic (von Mises) material using 8-node rectangular quadrilaterals. Flexible smooth footing. Load control. Consistent tangent stiffness. Radial return method (RR) with ̀line search'
  • 6.11. Geotechnical Processes of Embanking and Excavation
  • 6.11.1. Embanking
  • Program 6.9 Plane-strain construction of an elastic
  • plastic (Mohr
  • Coulomb) embankment in layers on a foundation using 8-node quadrilaterals. Viscoplastic strain method
  • 6.11.2. Excavation
  • Program 6.10 Plane-strain construction of an elastic
  • plastic (Mohr
  • Coulomb) excavation in layers using 8-node quadrilaterals. Viscoplastic strain method
  • 6.12. Undrained Analysis
  • Program 6.11 Axisymmetric ùndrained' strain of an elastic
  • plastic (Mohr
  • Coulomb) solid using 8-node rectangular quadrilaterals. Viscoplastic strain method.
  • Note continued: Program 6.12 Three-dimensional strain analysis of an elastic
  • plastic (Mohr
  • Coulomb) slope using 20-node hexahedra. Gravity loading. Viscoplastic strain method
  • Program 6.13 Three-dimensional strain analysis of an elastic
  • plastic (Mohr
  • Coulomb) slope using 20-node hexahedra. Gravity loading. Viscoplastic strain method. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver
  • 6.13. Glossary of Variable Names
  • 6.14. Exercises
  • References
  • 7. Steady State Flow
  • 7.1. Introduction
  • Program 7.1 One-dimensional analysis of steady seepage using 2-node line elements
  • Program 7.2 Plane or axisymmetric analysis of steady seepage using 4-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z) -direction
  • Program 7.3 Analysis of plane free surface flow using 4-node quadrilaterals. Ànalytical' form of element conductivity matrix
  • Program 7.4 General two- (plane) or three-dimensional analysis of steady seepage
  • Program 7.5 General two- (plane) or three-dimensional analysis of steady seepage. No global conductivity matrix assembly. Diagonally preconditioned conjugate gradient solver
  • 7.2. Glossary of Variable Names
  • 7.3. Exercises
  • References
  • 8. Transient Problems: First Order (Uncoupled)
  • 8.1. Introduction
  • Program 8.1 One-dimensional transient (consolidation) analysis using 2-node ̀line' elements. Implicit time integration using the ̀theta' method
  • Program 8.2 One-dimensional transient (consolidation) analysis (settlement and excess pore pressure) using 2-node ̀line' elements. Implicit time integration using the ̀theta' method
  • Program 8.3 One-dimensional consolidation analysis using 2-node ̀line' elements. Explicit time integration. Element by element. Lumped mass
  • Program 8.4 Plane or axisymmetric transient (consolidation) analysis using 4-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z)-direction. Implicit time integration using the ̀theta' method
  • Program 8.5 Plane or axisymmetric transient (consolidation) analysis using 4-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z)-direction. Implicit time integration using the ̀theta' method. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver
  • Program 8.6 Plane or axisymmetric transient (consolidation) analysis using 4-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z)-direction. Explicit time integration using the ̀theta = 0' method
  • Program 8.7 Plane or axisymmetric transient (consolidation) analysis using 4-node rectangular quadrilaterals. Mesh numbered in x(r)- or y(z)-direction. ̀theta' method using an element-by-element product algorithm
  • 8.2. Comparison of Programs 8.4, 8.5, 8.6 and 8.7
  • Program 8.8 General two- (plane) or three-dimensional transient (consolidation) analysis. Implicit time integration using the ̀theta' method
  • Program 8.9 Plane analysis of the diffusion
  • convection equation using 4-node rectangular quadrilaterals. Implicit time integration using the ̀theta' method. Self-adjoint transformation
  • Program 8.10 Plane analysis of the diffusion
  • convection equation using 4-node rectangular quadrilaterals. Implicit time integration using the ̀theta' method. Untransformed solution
  • Program 8.11 Plane or axisymmetric transient thermal conduction analysis using 4-node rectangular quadrilaterals. Implicit time integration using the ̀theta' method. Option of convection and flux boundary conditions
  • 8.3. Glossary of Variable Names
  • 8.4. Exercises
  • References
  • 9. Coupled Problems
  • 9.1. Introduction
  • Program 9.1 Analysis of the plane steady-state Navier
  • Stokes equation using 8-node rectangular quadrilaterals for velocities coupled to 4-node rectangular quadrilaterals for pressures. Mesh numbered in x-direction. Freedoms numbered in the order u
  • p
  • v
  • Program 9.2 Analysis of the plane steady-state Navier
  • Stokes equation using 8-node rectangular quadrilaterals for velocities coupled to 4-node rectangular quadrilaterals for pressures. Mesh numbered in x-direction. Freedoms numbered in the order u
  • p
  • v. Element-by-element solution using BiCGStab(l) with no preconditioning. No global matrix [ect.]
  • Program 9.3 One-dimensional coupled consolidation analysis of a Biot poroelastic solid using 2-node ̀line' elements. Freedoms numbered in the order v
  • uw
  • Program 9.4 Plane strain consolidation analysis of a Biot elastic solid using 8-node rectangular quadrilaterals for displacements coupled to 4-node rectangular quadrilaterals for pressures. Freedoms numbered in order u
  • v
  • uw. Incremental load version
  • Program 9.5 Plane strain consolidation analysis of a Biot elastic solid using 8-node rectangular quadrilaterals for displacements coupled to 4-node rectangular quadrilaterals for pressures. Freedoms numbered in order u
  • v
  • uw. Incremental load version. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient [ect.]
  • Program 9.6 Plane strain consolidation analysis of a Biot poroelastic
  • plastic (Mohr
  • Coulomb) material using 8-node rectangular quadrilaterals for displacements coupled to 4-node rectangular quadrilaterals for pressures. Freedoms numbered in the order u
  • v
  • uw. Viscoplastic strain method
  • 9.2. Glossary of Variable Names
  • 9.3. Exercises
  • References
  • 10. Eigenvalue Problems
  • 10.1. Introduction
  • Program 10.1 Eigenvalue analysis of elastic beams using 2-node beam elements, Lumped mass
  • Program 10.2 Eigenvalue analysis of an elastic solid in plane strain using 4- or 8-node rectangular quadrilaterals. Lumped mass. Mesh numbered in y-direction
  • Program 10.3 Eigenvalue analysis of an elastic solid in plane strain using 4-node rectangular quadrilaterals. Lanczos method. Consistent mass. Mesh numbered in y-direction
  • Program 10.4 Eigenvalue analysis of an elastic solid in plane strain using 4-node rectangular quadrilaterals with ARPACK. Lumped mass. Element-by-element formulation. Mesh numbered in y-direction
  • 10.2. Glossary of Variable Names
  • 10.3. Exercises
  • References
  • 11. Forced Vibrations
  • 11.1. Introduction
  • Program 11.1 Forced vibration analysis of elastic beams using 2-node beam elements. Consistent mass. Newmark time stepping
  • Program 11.2 Forced vibration analysis of an elastic solid in plane strain using 4- or 8-node rectangular quadrilaterals. Lumped mass. Mesh numbered in the y-direction. Modal superposition
  • Program 11.3 Forced vibration analysis of an elastic solid in plane strain using rectangular 8-node quadrilaterals. Lumped or consistent mass. Mesh numbered in the y-direction. Implicit time integration using the ̀theta' method
  • Program 11.4 Forced vibration analysis of an elastic solid in plane strain using rectangular 8-node quadrilaterals. Lumped or consistent mass. Mesh numbered in the y-direction. Implicit time integration using Wilson's method
  • Program 11.5 Forced vibration of a rectangular elastic solid in plane strain using 8-node quadrilateral elements numbered in the y-direction. Lumped mass, complex response
  • Program 11.6 Forced vibration analysis of an elastic solid in plane strain using uniform size rectangular 4-node quadrilaterals. Mesh numbered in the y-direction. Lumped or consistent mass. Mixed explicit/implicit time integration
  • Program 11.7 Forced vibration analysis of an elastic solid in plane strain using rectangular 8-node quadrilaterals. Lumped or consistent mass. Mesh numbered in the y-direction. Implicit time integration using the ̀theta' method. No global matrix assembly. Diagonally preconditioned conjugate gradient solver
  • Program 11.8 Forced vibration analysis of an elastic
  • plastic (von Mises) solid in plane strain using rectangular 8-node quadrilateral elements. Lumped mass. Mesh numbered in the y-direction.
  • Explicit time integration
  • 11.2. Glossary of Variable Names
  • 11.3. Exercises
  • References
  • 12. Parallel Processing of Finite Element Analyses
  • 12.1. Introduction
  • 12.2. Differences between Parallel and Serial Programs
  • 12.2.1. Parallel Libraries
  • 12.2.2. Global Variables
  • 12.2.3. MPI Library Routines
  • 12.2.4. _pp Appendage
  • 12.2.5. Simple Test Problems
  • 12.2.6. Reading and Writing
  • 12.2.7. Rest Instead of nf
  • 12.2.8. Gathering and Scattering
  • 12.2.9. Reindexing
  • 12.2.10. Domain Composition
  • 12.2.11. Third-party Mesh-partitioning Tools
  • 12.2.12. Load Balancing
  • Program 12.1 Three-dimensional analysis of an elastic solid. Compare Program 5.6
  • Program 12.2 Three-dimensional analysis of an elastoplastic (Mohr
  • Coulomb) solid. Compare Program 6.13
  • Program 12.3 Three-dimensional Laplacian flow. Compare Program 7.5
  • Program 12.4 Three-dimensional transient heat conduction
  • implicit analysis in time. Compare Program 8.5
  • Program 12.5 Three-dimensional transient flow
  • explicit analysis in time. Compare Program 8.6
  • Program 12.6 Three-dimensional steady-state Navier
  • Stokes analysis. Compare Program 9.2
  • Program 12.7 Three-dimensional analysis of Biot poro elastic solid. Incremental version. Compare Program 9.5
  • Program 12.8 Eigenvalue analysis of three-dimensional elastic solid. Compare Program 103
  • Program 12.9 Forced vibration analysis of a three-dimensional elastic solid. Implicit integration in time. Compare Program 11.7
  • Program 12.10 Forced vibration analysis of three-dimensional elasto plastic solid. Explicit integration in time. Compare Program 11.8
  • 12.3. Graphics Processing Units.
  • Note continued: Program 12.11 Three-dimensional strain of an elastic solid using 8-, 14- or 20-node brick hexahedra. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. GPU version. Compare Program 5.7
  • 12.4. Cloud Computing
  • 12.5. Conclusions
  • 12.6. Glossary of Variable Names
  • References.

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