Machine generated contents note: Preliminaries: Computer Strategies. Hardware Memory Management Vector Processors Multi-core Processors Co-processors Parallel Processors Applications Software Compilers Arithmetic Conditions Loops Array Features Dynamic Arrays --Broadcasting Constructors Vector Subscripts Array Sections Whole-array Manipulations Intrinsic Procedures for Arrays Modules Subprogram Libraries Structured Programming Third-party Libraries --BIAS Libraries Maths Libraries User Subroutines MPI Libraries Visualisation Starting ParaView Display Restrained Nodes Display Applied Loads Display Deformed Mesh 2.Spatial Discretisation by Finite Elements Rod Element Rod Stiffness Matrix Rod Mass Element Eigenvalue Equation Beam Element Beam Element Stiffness Matrix Beam Element Mass Matrix Beam with an Axial Force Beam on an Elastic Foundation General Remarks on the Discretisation Process Alternative Derivation of Element Stiffness Two-dimensional Elements: Plane Stress Energy Approach and Plane Strain Thermoelasticity Plane Element Mass Matrix Axisymmetric Stress and Strain Three-dimensional Stress and Strain Plate Bending Element Summary of Element Equations for Solids Flow of Fluids: Navier -- Stokes Equations Simplified Flow Equations Steady State Transient State Further Coupled Equations: Biot Consolidation. Programming Finite Element Computations Local Coordinates for Quadrilateral Elements Numerical Integration for Quadrilaterals Analytical Integration for Quadrilaterals Local Coordinates for Triangular Elements Numerical Integration for Triangles Analytical Integration for Triangles Multi-Element Assemblies Èlement-by-Element' Techniques Conjugate Gradient Method for Linear Equation Systems Preconditioning Unsymmetric Systems Symmetric Non-Positive Definite Equations Eigenvalue Systems Incorporation of Boundary Conditions Convection Boundary Conditions Programming using Building Blocks Black Box Routines Special Purpose Routines Plane Elastic Analysis using Quadrilateral Elements Plane Elastic Analysis using Triangular Elements --Axisymmetric Strain of Elastic Solids Plane Steady Laminar Fluid Flow Mass Matrix Formation --Higher-Order 2D Elements Three-Dimensional Elements Assembly of Elements Solution of Equilibrium Equations Evaluation of Eigenvalues and Eigenvectors Jacobi Algorithm Lanczos and Arnoldi Algorithms Solution of First-Order Time-Dependent Problems Solution of Coupled Navier -- Stokes Problems Solution of Coupled Transient Problems Absolute Load Version Incremental Load Version Solution of Second-Order Time-Dependent Problems Modal Superposition Newmark or Crank -- Nicolson Method Wilson's Method Complex Response Explicit Methods and Other Storage-Saving Strategies Static Equilibrium of Structures Program One-dimensional analysis of axially loaded elastic rods using 2-node rod elements Analysis of elastic pin-jointed frames using 2-node rod elements in two or three dimensions Analysis of elastic beams using 2-node beam elements (elastic foundation optional) Analysis of elastic rigid-jointed frames using 2-node beam/rod elements in two or three dimensions Analysis of elastic -- plastic beams or frames using 2-node beam or beam/rod elements in one, two or three dimensions Stability (buckling) analysis of elastic beams using 2-node beam elements (elastic foundation optional) Analysis of plates using 4-node rectangular plate elements. Homogeneous material with identical elements. Mesh numbered in x- or y-direction.Glossary of Variable Names 5.Static Equilibrium of Linear Elastic Solids 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 --Non-axisymmetric analysis of a rectangular axisymmetric elastic solid using 8-node rectangular quadrilaterals. Mesh numbered in r- or z -direction 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 --General 2D (plane strain) or 3D analysis of elastic solids. Gravity loading option 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 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 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 Glossary of Variable Names. Material Non-linearity Stress -- strain Behaviour Stress Invariants Failure Criteria -Von Mises Mohr -- Coulomb and Tresca Generation of Body Loads Viscoplasticity Initial Stress --Corners on the Failure and Potential Surfaces 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 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 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 --Plane-strain slope stability analysis of an elastic -- plastic (Mohr -- Coulomb) material using 8-node rectangular quadrilaterals. Gravity loading. Viscoplastic strain method Plane-strain earth pressure analysis of an elastic -- plastic (Mohr -- Coulomb) material using 8-node rectangular quadrilaterals. Rigid smooth wall. Initial stress method Elastoplastic Rate Integration Forward Euler Method --Backward Euler Method Tangent Stiffness Approaches Inconsistent Tangent Matrix Consistent Tangent Matrix Convergence Criterion 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) 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 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' Geotechnical Processes of Embanking and Excavation Embanking Plane-strain construction of an elastic -- plastic (Mohr -- Coulomb) embankment in layers on a foundation using 8-node quadrilaterals. Viscoplastic strain method Excavation Plane-strain construction of an elastic -- plastic (Mohr -- Coulomb) excavation in layers using 8-node quadrilaterals. Viscoplastic strain method Undrained Analysis Axisymmetric ùndrained' strain of an elastic -- plastic (Mohr -- Coulomb) solid using 8-node rectangular quadrilaterals. Viscoplastic strain method.

Rigid smooth wall Elastoplasic Rate Integration Forward Backward Euler Method Tangent Stiffnes Approaches Inconsistent Consistent Tangent Matrix Convergence Criterion Closet point projection method (CPPM) No global stiffness matrix assembly Diagonally preconditioned conjugate gradient solver Radial return method (RR) with line search The geotechnical proces of embanking and excavation embanking Plane-strain construction in layers on a foundation using 8-node quadrilaterals Excavation Unrained analysis Steady state flow One-dimensional analysis of steady seepage using 2-node line elements Plane or axisymmetric analysis of steady seepage using 4-node recantangular quadrilaterals Analysis of plane free Surface flow using 4-node quadrilaters Analytical form of element conductivity matrix General two- (plane) or three-dimensional analysis od steady seepage No global conductivity matrix assembly Diagonaly preconditioned conjugate gradient solver Transient problems One-dimensional consolidation analysis using 2-node line elements Plane or axisymmetric transit (consolidation) analysing using 4-node rectangular quadrilaterals mesch numbered Couled problems Analysis of the plane steady-state Navier Stokes equation using 8-node rectangular quadrilaterals for velocities coupled to 4-node rectangular quadrilaterals for pressures. One-dimensional coupled consolidation analysis of a Biot poroelastic solid using 2-node line elements Plane strain consolidation analysis of a Biot elastic solid poroelastic-plastic (Mohr-Coulomb) material Eigenvalue problems analysis of elastic beams solid forced vibrations Three dimensional transident heat conduction-implicit flow-exlipcit analysis in time steady state Navier-Stokes analysis of Biot poro elastic solid Eigenvalue Forced vibration analysis of three dimensional elastic solid Three dimensional strain of an elastic solid using brick hexahedra No global stiffness matrix assembly Diagonally preconditioned conjugate gradient solver GPU version Cloud computing Equivalent Nodal Loads Shape functions and element node numbering Plastic Stress-strain matrices and plastic potential derivatives main geom paralel library subprograms external subprograms