Contents

# Contents

Introduction

Overview

Analysis capabilities

Mesh generation

Introduction

Structured mesh generation

The Quadrilateral Region

Mapping technique

Automatic meshing

Region connectivity

Unstructured mesh generation

Mesh editing

Mesh refinement

Deletion meshes

Nodes renumbering

Transforming meshes (p-refinement)

Formulation of the element matrices and vectors for elasticity problem

Equilibrium equations

Boundary conditions

Strain-displacement relations

A general formula for the stiffness matrix

Plane strain case

Plan stress case

Axisymmetric elements

Finite elements types

Constant strain triangle (CST-T3)

Linear strain triangle (LST-T6)

Linear quadrilateral element (Q4)

Quadratic quadrilateral element (Q8)

Numerical integration in finite elements

Stress calculation

Consistent element nodal loads

Body forces

Distributed forces

Initial stress/strain loads

Pore pressure loads

Excavation loads

Gravity loading

Assembly and storage strategy

Incorporation of boundary conditions

Explicit specification of BC's

Imposing prescribed displacements (Penalty method)

Elastic supports

Solution of equilibrium equations

Formulation of beam-column elements

Bar or truss elements

Two-noded beam-column element

Joining beam-column elements to plane elements. Dissimilar elements.

Beam-column element connected to a plane element

Truss element connected to a plane element

Bolts elements

End anchored bolts

Fully bonded bolts

Liner elements

Geogrid elements

Nonlinear analysis formulation

Inelastic stress-strain behavior

Yield criterion

Flow rule

Hardening rule

Incremental stress-strain relations

Failure criteria

The Von-Mises yielding criteria

Mohr-Coulomb and Tresca yielding criteria

Elastic-plastic procedures

Constant-stiffness method

Generation of self-equilibrationg body loads

Initial strain method

Initial stress method

Solution procedure

Tangent (variable) stiffness method

Integration of the constitutive relations. Consistent tangent matrix

Solution procedure

Steady state analysis

Initial conditions

Initial ground

conditions

Initial geostatic stresses

Dynamic and seismic analysis

Staged constructions

Analysis types

Slope stability analysis

Bearing capacity analysis

Staged construction analysis.

Bibliography

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