abquas基准手册.pdf

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Abaqus 6.10 PDF Documentation

Abaqus Benchmarks Manual

Legal Notices

Locations

Preface

Contents

1.0.1 Introduction

1. Analysis Tests

1.1 Static stress/displacement analysis

1.1.1 Beam/gap example

Problem description

Results and discussion

Input file

1.1.2 Analysis of an anisotropic layered plate

Problem description

Failure measures

Results and discussion

Input files

Reference

1.1.3 Composite shells in cylindrical bending

Problem description

Failure measures

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Input files

Reference

1.1.4 Thick composite cylinder subjected to internal pressure

Problem description

Geometry and model

Results and discussion

Input files

References

1.1.5 Uniform collapse of straight and curved pipe segments

Problem description

Models

Elbow element

Shell element

Constraints and boundary conditions for the shell element model

Results and discussion

Initially straight pipe

Initially curved pipe

Input files

References

1.1.6 Snap-through of a shallow, cylindrical roof under a point load

Problem description

Modeling and solution control

Results and discussion

Input files

References

1.1.7 Pressurized rubber disc

Problem description

Loading and solution method

Results and discussion

Input files

References

1.1.8 Uniaxial stretching of an elastic sheet with a circular hole

Problem description

Loading and controls

Results and discussion

Input files

References

1.1.9 Necking of a round tensile bar

Problem description

Material

Boundary conditions and loading

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Input files

References

1.1.10 Concrete slump test

Problem description

Material parameters

Solution controls in Abaqus/Standard

Results and discussion

Input files

References

1.1.11 The Hertz contact problem

Problem description

Contact modeling

Substructure Abaqus/Standard model

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Dynamic analysis in Abaqus/Standard

Input files

References

1.1.12 Crushing of a pipe

Problem description

Results and discussion

Input files

References

1.2 Buckling analysis

1.2.1 Buckling analysis of beams

Problem description

Results and discussion

Input files

Reference

1.2.2 Buckling of a ring in a plane under external pressure

Problem description

Element choice

Eigenvalue buckling load estimates

Results and discussion

Input files

Reference

1.2.3 Buckling of a cylindrical shell under uniform axial pressure

Problem description

Analysis procedure

Eigenvalue buckling prediction

Load-displacement analysis on imperfect geometries

Results and discussion

Eigenvalue buckling prediction

Load-displacement analysis on imperfect geometries

Input files

Reference

1.2.4 Buckling of a simply supported square plate

Problem description

Eigenvalue buckling prediction

Load-displacement studies on imperfect geometries

Results and discussion

Input files

Reference

1.2.5 Lateral buckling of an L-bracket

Problem description

Results and discussion

Input files

References

1.2.6 Buckling of a column with general contact

Problem description

Results and discussion

Input files

1.3 Dynamic stress/displacement analysis

1.3.1 Subspace dynamic analysis of a cantilever beam

Problem description

Analysis

Results and discussion

Input files

Reference

1.3.2 Double cantilever elastic beam under point load

Problem description

Results and discussion

Input files

1.3.3 Explosively loaded cylindrical panel

Problem description

Controls and tolerances

Results and discussion

Input files

References

1.3.4 Free ring under initial velocity: comparison of rate-independent and rate-dependent plasticity

Problem description

Initial nodal velocities

Solution controls in Abaqus/Standard

Results and discussion

Input files

References

1.3.5 Large rotation of a one degree of freedom system

Problem description

Exact solution: truss model

Exact solution: spring model

Results and discussion

Input files

1.3.6 Motion of a rigid body in Abaqus/Standard

I. Force-free motion of a rigid body

Problem description

Results and discussion

Input file

II. Forced motion of a rigid body

Problem description

Analytical solution

Results and discussion

Case 1

Case 2

Input files

References

1.3.7 Rigid body dynamics with Abaqus/Explicit

Problem description

Co-simulation with MADYMO

Results and discussion

Input files

1.3.8 Revolute MPC verification: rotation of a crank

Problem description

Results and discussion

Input files

1.3.9 Pipe whip simulation

Problem description

Results and discussion

Input files

Reference

1.3.10 Impact of a copper rod

Problem description

Results and discussion

Input files

References

1.3.11 Frictional braking of a rotating rigid body

Problem description

Results and discussion

Input files

1.3.12 Compression of cylindrical shells with general contact

Problem description

Results and discussion

Input files

1.3.13 Steady-state slip of a belt drive

Problem description

Results and discussion

Input files

1.3.14 Crash simulation of a motor vehicle

Problem description

Controls and tolerances

Material

Results and discussion

Input file

Reference

1.3.15 Truss impact on a rigid wall

Problem description

Results and discussion

Input files

1.3.16 Plate penetration by a projectile

Problem description

Results and discussion

Input files

Reference

1.3.17 Oblique shock reflections

Problem description

Adaptive meshing

Results and discussion

Input file

References

1.4 Mode-based dynamic analysis

1.4.1 Free vibrations of a spherical shell

Problem description

Analytical solution

Results and discussion

Input files

References

1.4.2 Eigenvalue analysis of a beam under various end constraints and loadings

Problem description

Boundary conditions and loadings

Results and discussion

Input files

Reference

1.4.3 Vibration of a cable under tension

Problem description

Results and discussion

Input files

Reference

1.4.4 Free and forced vibrations with damping

Problem description

Results and discussion

Input files

Reference

1.4.5 Verification of Rayleigh damping options with direct integration and modal superposition

Problem description

Results and discussion

Input files

1.4.6 Eigenvalue analysis of a cantilever plate

Problem description

Results and discussion

Input files

References

1.4.7 Vibration of a rotating cantilever plate

Problem description

Analysis

Substructure analysis

Results and discussion

Input files

References

1.4.8 Response spectrum analysis of a simply supported beam

Problem description

Response spectra definition

Results and discussion

Input files

Reference

1.4.9 Linear analysis of a rod under dynamic loading

Problem description

Eigenvalue calculations

Alternate normalization

Modal dynamic analysis

Tip load—damped system

Base acceleration—damped system

Static preload—undamped system (one mode only)

Response spectrum analysis

Steady-state analysis

Random response analysis

Results and discussion

Modal dynamic analysis: tip load–damped system

Modal dynamic analysis: tip load–undamped system

Modal dynamic analysis: base acceleration–damped system

Modal dynamic analysis: static preload–undamped system (one mode only)

Response spectrum analysis

Steady-state analysis

Random response analysis

Input files

1.4.10 Random response to jet noise excitation

Problem description

Loading via user subroutines

Results and discussion

Input files

Reference

1.4.11 Random response of a cantilever subjected to base motion

Problem description

Results and discussion

Input file

Reference

1.4.12 Double cantilever subjected to multiple base motions

Problem description

Results and discussion

Input files

1.4.13 Analysis of a cantilever subject to earthquake motion

Problem description

Time domain analysis

Response spectrum analysis

Results and discussion

* MODAL DYNAMIC

* DYNAMIC

* RESPONSE SPECTRUM

* BASELINE CORRECTION

Input files

References

1.4.14 Residual modes for modal response analysis

Problem description

Results and discussion

Input file

Reference

1.5 Steady-state transport analysis

1.5.1 Steady-state transport analysis

I. Frictional effects

Problem description

Results and discussion

Additional frictional tests

Input files

Reference

II. Inertia effects

Problem description

Results and discussion

Input files

III. Material convection effects

Problem description

Results and discussion

Additional material convection tests

Input files

1.5.2 Steady-state spinning of a disk in contact with a foundation

Problem description

Results and discussion

Input files

Reference

1.6 Heat transfer and thermal-stress analysis

1.6.1 Convection and diffusion of a temperature pulse

Problem description

One-dimensional case

Two-dimensional case

Results and discussion

One-dimensional case

Two-dimensional case

Axisymmetric and three-dimensional element tests

Input files

References

1.6.2 Freezing of a square solid: the two-dimensional Stefan problem

Problem description

Material

Boundary conditions

Time increment controls

Results and discussion

Input files

Reference

1.6.3 Coupled temperature-displacement analysis: one-dimensional gap conductance and radiation

Problem description

Solution

Case 1

Case 2

Results and discussion

Input files

1.6.4 Quenching of an infinite plate

Problem description

Analysis sequence

Controls

Results and discussion

Input files

Reference

1.6.5 Two-dimensional elemental cavity radiation viewfactor calculations

I. Two infinitely long, directly opposed parallel plates of the same finite width

Problem description

Analytical solution

Results and discussion

Input file

Reference

II. Two infinitely long parallel plates of different widths; the centerlines of each plate are connected by the perpendicular between the pl

Problem description

Analytical solution

Results and discussion

Input file

Reference

III. Two infinitely long plates of unequal widths h and w, having one common edge and at an angle of 90° to each other

Problem description

Analytical solution

Results and discussion

Input file

Reference

IV. Two infinitely long plates of equal finite width w, having one common edge and having an included angle of α to each other

Problem description

Analytical solution

Results and discussion

Input files

Reference

1.6.6 Axisymmetric elemental cavity radiation viewfactor calculations

I. Parallel circular disks with centers along the same normal

Problem description

Analytical solution

Results and discussion

Input file

Reference

II. Two concentric cylinders of same finite length

Problem description

Analytical solution

Results and discussion

Input file

Reference

III. Concentric cylinders of infinite length

Problem description

Analytical solution

Results and discussion

Input file

Reference

IV. Coaxial right circular cylinders of different radii, one on top of the other

Problem description

Analytical solution

Results and discussion

Input file

Reference

1.6.7 Three-dimensional elemental cavity radiation viewfactor calculations

I. Identical, directly opposed parallel rectangles

Problem description

Analytical solution

Results and discussion

Input files

Reference

II. Two infinitely long, directly opposed parallel plates of the same finite width

Problem description

Analytical solution

Results and discussion

Input file

Reference

III. Coaxial parallel squares of different sizes

Problem description

Analytical solution

Results and discussion

Input files

Reference

IV. Two infinitely long parallel plates of different widths; the centerlines of each plate are connected by the perpendicular between the pl

Problem description

Analytical solution

Results and discussion

Input file

Reference

V. Two finite rectangles of the same length, having one common edge and at an angle of 90° to each other

Problem description

Analytical solution

Results and discussion

Input files

Reference

VI. Two infinitely long plates of unequal widths h and w, having one common edge and at an angle of 90° to each other

Problem description

Analytical solution

Results and discussion

Input file

Reference

VII. Two rectangles with one common edge and an included angle of Φ

Problem description

Analytical solution

Results and discussion

Input files

Reference

VIII. Rectangles having a common edge and forming an arbitrary angle; one rectangle is infinitely long

Problem description

Analytical solution

Results and discussion

Input file

Reference

IX. Two infinitely long plates of equal finite width w, having one common edge and having an included angle of α to each other

Problem description

Analytical solution

Results and discussion

Input file

Reference

1.6.8 Radiation analysis of a plane finned surface

Problem description

Material and boundary conditions

Results and discussion

Input files

References

1.7 Eulerian analysis

1.7.1 Eulerian analysis of a collapsing water column

Problem description

Results and discussion

Python script

Input file

Reference

1.7.2 Deflection of an elastic dam under water pressure

Problem description

Results and discussion

Python script

Input file

Reference

1.8 Electrical analysis

1.8.1 Eigenvalue analysis of a piezoelectric cube with various electrode configurations

Problem description

Models

Results and discussion

Input files

References

1.8.2 Modal dynamic analysis for piezoelectric materials

Problem description

Results and discussion

Input files

Reference

1.8.3 Steady-state dynamic analysis for piezoelectric materials

Problem description

Results and discussion

Input files

Reference

1.9 Coupled pore fluid flow and stress analysis

1.9.1 Partially saturated flow in a porous medium

Problem description

Material

Loading and controls

Results and discussion

Input files

1.9.2 Demand wettability of a porous medium: coupled analysis

Problem description

Material

Loading and controls

Results and discussion

Input files

1.9.3 Wicking in a partially saturated porous medium

Problem description

Material

Loading and controls

Results and discussion

Input files

1.9.4 Desaturation in a column of porous material

Problem description

Material

Loading and controls

Results and discussion

Input files

References

1.10 Mass diffusion analysis

1.10.1 Thermo-mechanical diffusion of hydrogen in a bending beam

Problem description

Results and discussion

Input files

Reference

1.11 Acoustic analysis

1.11.1 A simple coupled acoustic-structural analysis

Problem description

Steady-state vibration

Results and discussion

Input files

1.11.2 Analysis of a point-loaded, fluid-filled, spherical shell

Problem description

Results and discussion

Input file

Reference

1.11.3 Acoustic radiation impedance of a sphere in breathing mode

Problem description

Results and discussion

Input files

References

1.11.4 Acoustic-structural interaction in an infinite acoustic medium

Problem description

Results and discussion

Input files

1.11.5 Acoustic-acoustic tie constraint in two dimensions

Problem description

Results and discussion

Input files

1.11.6 Acoustic-acoustic tie constraint in three dimensions

Problem description

Results and discussion

Input files

1.11.7 A simple steady-state dynamic acoustic analysis

Problem description

Results and discussion

Input files

Reference

1.11.8 Acoustic analysis of a duct with mean flow

Problem description

Results and discussion

Input files

1.11.9 Real exterior acoustic eigenanalysis

Problem description

Results and discussion

Input files

1.11.10 Coupled exterior acoustic eigenanalysis

Problem description

Results and discussion

Input file

Reference

1.11.11 Acoustic scattering from a rigid sphere

Problem description

Results and discussion

Input file

References

1.11.12 Acoustic scattering from an elastic spherical shell

Problem description

Results and discussion

Input files

References

1.12 Adaptivity analysis

1.12.1 Indentation with different materials

Problem description

Adaptive meshing

Results and discussion

Input files

1.12.2 Wave propagation with different materials

Problem description

Results and discussion

Input files

1.12.3 Adaptivity patch test with different materials

Problem description

Results and discussion

Input files

1.12.4 Wave propagation in a shock tube

Problem description

Results and discussion

Input files

Reference

1.12.5 Propagation of a compaction wave in a shock tube

Problem description

Results and discussion

Input files

Reference

1.12.6 Advection in a rotating frame

Problem description

Results and discussion

Input files

1.12.7 Water sloshing in a pitching tank

Problem description

Adaptive meshing

Results and discussion

Input file

Reference

1.13 Abaqus/Aqua analysis

1.13.1 Pull-in of a pipeline lying directly on the seafloor

Problem description

Seafloor modeling

Material

Boundary conditions

Incrementation

Results and discussion

Input file

1.13.2 Near bottom pipeline pull-in and tow

Problem description

Material

Boundary conditions

Results and discussion

Pull-in analysis

Towing analysis

Input files

1.13.3 Slender pipe subject to drag: the “reed in the wind”

Problem description

Results and discussion

Input file

Reference

1.14 Underwater shock analysis

1.14.1 One-dimensional underwater shock analysis

I. Underwater shock impinging on a one-dimensional continuum

Problem description

Model description

Results and discussion

Input files

II. Underwater shock impinging on a one-dimensional plate

Problem description

Model description

Results and discussion

Input files

1.14.2 The submerged sphere problem

Problem description

Results and discussion

Input files

Reference

1.14.3 The submerged infinite cylinder problem

I. Infinite cylindrical shell in an infinite fluid

Problem description

Results and discussion

Input files

References

II. Infinite cylindrical shell with bottom reflection

Problem description

Results and discussion

Input files

1.14.4 The one-dimensional cavitation problem

Problem description

Single-mass case

Multiple-mass case

Submodeling

Modeling cavitation using displacement-based elements

Results and discussion

Single-mass case

Multiple-mass case

Submodeling

Modeling cavitation using displacement-based elements

Input files

References

1.14.5 Plate response to a planar exponentially decaying shock wave

Problem description

Results and discussion

Input file

References

1.14.6 Cylindrical shell response to a planar step shock wave

Problem description

Results and discussion

Input file

References

1.14.7 Cylindrical shell response to a planar exponentially decaying shock wave

Problem description

Results and discussion

Input file

References

1.14.8 Spherical shell response to a planar step wave

Problem description

Results and discussion

Input file

References

1.14.9 Spherical shell response to a planar exponentially decaying wave

Problem description

Results and discussion

Input file

References

1.14.10 Spherical shell response to a spherical exponentially decaying wave

Problem description

Results and discussion

Input file

References

1.14.11 Air-backed coupled plate response to a planar exponentially decaying wave

Problem description

Results and discussion

Input file

References

1.14.12 Water-backed coupled plate response to a planar exponentially decaying wave

Problem description

Results and discussion

Input file

References

1.14.13 Coupled cylindrical shell response to a planar step wave

Problem description

Results and discussion

Input file

References

1.14.14 Coupled spherical shell response to a planar step wave

Problem description

Results and discussion

Input file

References

1.14.15 Fluid-filled spherical shell response to a planar step wave

Problem description

Results and discussion

Input file

References

1.14.16 Response of beam elements to a planar wave

Problem description

Results and discussion

Input files

Reference

1.15 Soils analysis

1.15.1 The Terzaghi consolidation problem

Problem description

Geometry and models

Time stepping

Results and discussion

Input files

References

1.15.2 Consolidation of a triaxial test specimen

Problem description

Initial conditions

Results and discussion

Input files

References

1.15.3 Finite-strain consolidation of a two-dimensional solid

Problem description

Loading and time stepping

Results and discussion

Input files

References

1.15.4 Limit load calculations with granular materials

Problem description

Material

Loading and controls

Results and discussion

Input files

References

1.15.5 Finite deformation of an elastic-plastic granular material

Problem description

Results and discussion

Input files

Reference

1.15.6 The one-dimensional thermal consolidation problem

Problem description

Results and discussion

Input files

References

1.15.7 Consolidation around a cylindrical heat source

Problem description

Geometry and models

Boundary conditions

Analytical solution

Time stepping

Results and discussion

Input files

References

1.16 Fracture mechanics

1.16.1 Contour integral evaluation: two-dimensional case

Problem description

Geometry and model

Results and discussion

Submodeling around the crack tip

Python scripts

Input files

References

1.16.2 Contour integral evaluation: three-dimensional case

Problem description

Semi-elliptic crack in a half-space

Semi-elliptic crack in a rectangular plate

Results and discussion

Semi-elliptic crack in a half-space

Semi-elliptic crack in a rectangular plate

Python scripts

Input files

References

1.16.3 Center slant cracked plate under tension

Problem description

Results and discussion

Python scripts

Input files

1.16.4 A penny-shaped crack under concentrated forces

Problem description

Results and discussion

Input files

1.16.5 Fully plastic J -integral evaluation

Problem description

Material

Solution development

Results and discussion

Submodeling of the crack tip

Python scripts

Input files

References

1.16.6 C t -integral evaluation

Problem description

Material

Results and discussion

Input files

References

1.16.7 Nonuniform crack-face loading and J -integrals

Problem description

Results and discussion

Two-dimensional results

Three-dimensional results

Python scripts

Input files

1.16.8 Single-edged notched specimen under a thermal load

Problem description

Results and discussion

Python scripts

Input files

Reference

1.17 Substructures

1.17.1 Analysis of a frame using substructures

Problem description

One-level substructure analysis

Multilevel substructure analysis

Substructure library files

Substructure rotation and mirroring

Results and discussion

Input files

1.18 Design sensitivity analysis

1.18.1 Design sensitivity analysis for cantilever beam

Problem description

Results and discussion

Input files

References

1.18.2 Sensitivity of the stress concentration factor around a circular hole in a plate under uniaxial tension

Problem description

Results and discussion

Input file

1.18.3 Sensitivity analysis of modified NAFEMS problem 3DNLG-1: Large deflection of Z-shaped cantilever under an end load

Problem description

Results and discussion

Input files

1.19 Modeling discontinuities using XFEM

1.19.1 Crack propagation of a single-edge notch simulated using XFEM

Problem description

Geometry and model

Material

Results and discussion

Input files

Python scripts

Reference

1.19.2 Crack propagation in a plate with a hole simulated using XFEM

Problem description

Geometry and model

Material

Results and discussion

Input file

Python scripts

Reference

1.19.3 Crack propagation in a beam under impact loading simulated using XFEM

Problem description

Geometry and model

Material

Results and discussion

Input files

Python script

Reference

1.19.4 Dynamic shear failure of a single-edge notch simulated using XFEM

Problem description

Geometry and model

Material

Results and discussion

Input file

Python script

Reference

2. Element Tests

2.1 Continuum elements

2.1.1 Torsion of a hollow cylinder

Problem description

Results and discussion

Input files

Reference

2.1.2 Geometrically nonlinear analysis of a cantilever beam

Problem description

Results and discussion

Input files

References

2.1.3 Cantilever beam analyzed with CAXA and SAXA elements

Problem description

Loading and boundary conditions

Results and discussion

Input files

2.1.4 Two-point bending of a pipe due to self weight: CAXA and SAXA elements

Problem description

CAXA mesh

SAXA mesh

Reference solution

Results and discussion

Input files

2.1.5 Cook's membrane problem

Problem description

Results and discussion

Input files

References

2.2 Infinite elements

2.2.1 Wave propagation in an infinite medium

Problem description

Results and discussion

Input files

Reference

2.2.2 Infinite elements: the Boussinesq and Flamant problems

Problem description

Results and discussion

Input files

Reference

2.2.3 Infinite elements: circular load on half-space

Problem description

Results and discussion

Input files

References

2.2.4 Spherical cavity in an infinite medium

Problem description

Results and discussion

Input files

References

2.3 Structural elements

2.3.1 The barrel vault roof problem

Problem description

Results and discussion

Regular mesh

Irregular mesh

Summary

Input files

References

2.3.2 The pinched cylinder problem

Problem description

Results and discussion

Regular mesh

Irregular mesh

Submodeled analyses

Shell-to-solid coupling analyses

Parametric study using the Abaqus parametric study capability

Input files

References

2.3.3 The pinched sphere problem

Problem description

Results and discussion

Input files

References

2.3.4 Skew sensitivity of shell elements

Problem description

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

General remarks

Parametric study using a parametric study script

Input files

References

2.3.5 Performance of continuum and shell elements for linear analysis of bending problems

Problem description

Continuum elements with good bending behavior

Shell elements with good in-plane bending behavior

Objectives of the example

Incompatible mode elements

Continuum element integration schemes

Hourglass control for reduced-integration elements

Geometry and models

Cantilever beam with end shear load

Skew sensitivity analysis of cantilever beam

Buckling analysis of ring under external pressure

Results and discussion

Cantilever beam with end shear load

Skew sensitivity analysis of cantilever beam

Buckling analysis of ring under external pressure

Additional modeling considerations

Further examples

Input files

References

2.3.6 Tip in-plane shear load on a cantilevered hook

Problem description

Results and discussion

Input files

Reference

2.3.7 Analysis of a twisted beam

Problem description

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Input files

References

2.3.8 Twisted ribbon test for shells

Problem description

Results and discussion

Input files

Reference

2.3.9 Ribbon test for shells with applied moments

Problem description

Results and discussion

Input files

Reference

2.3.10 Triangular plate-bending on three point supports

Problem description

Results and discussion

Input files

Reference

2.3.11 Shell elements subjected to uniform thermal loading

Problem description

Material properties

Analytical solution

Results and discussion

Input files

2.3.12 Shell bending under a tip load

Problem description

Results and discussion

Input files

Reference

2.3.13 Variable thickness shells and membranes

Problem description

Results and discussion

Input files

2.3.14 Transient response of a shallow spherical cap

Problem description

Results and discussion

Input files

References

2.3.15 Simulation of propeller rotation

Problem description

Meshing of the blades and the hub

Order of accuracy in element formulation

Results and discussion

Summary

Input files

2.4 Acoustic elements

2.4.1 Acoustic modes of an enclosed cavity

Problem description

Results and discussion

Input files

Reference

2.5 Fluid elements

2.5.1 Fluid filled rubber bladders

Problem description

Results and discussion

Input files

2.6 Connector elements

2.6.1 Dynamic response of a two degree of freedom system

Problem description

Results and discussion

Input files

Reference

2.6.2 Linear behavior of spring and dashpot elements

Problem description

Grounded tests

Node-to-node tests

Analytical solutions

Grounded tests

Node-to-node tests

Results and discussion

Grounded tests

Node-to-node tests

Input files

2.7 Special-purpose elements

2.7.1 Delamination analysis of laminated composites

Problem description

Geometry and model

Material

Results and discussion

Input files

Python script

References

3. Material Tests

3.1 Elasticity

3.1.1 Viscoelastic rod subjected to constant axial load

Problem description

Material

Results and discussion

Input files

References

3.1.2 Transient thermal loading of a viscoelastic slab

Problem description

Material

Analysis

Results and discussion

Input files

References

3.1.3 Uniform strain, viscoplastic truss

Problem description

Results and discussion

Input files

Reference

3.1.4 Fitting of rubber test data

Problem description

Specification of material data

Experimental data of Treloar

Fitting procedures

Fitting case 1—using all three types of test data

Fitting case 2—using uniaxial tension data only

Results and discussion

Input files

References

3.1.5 Fitting of elastomeric foam test data

Problem description

Fitting procedure

Fitting case 1—results using uniaxial compression and simple shear data

Fitting case 2—results using uniaxial compression data only

Results and discussion

Input files

Reference

3.1.6 Rubber under uniaxial tension

Problem description

Results and discussion

Input files

Reference

3.1.7 Anisotropic hyperelastic modeling of arterial layers

Problem description

Material

Loading and controls

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Input files

References

3.2 Plasticity and creep

3.2.1 Uniformly loaded, elastic-plastic plate

Problem description

Case 1—Uniaxial loading

Case 2—Biaxial loading

Model and loading

Case 1—Uniaxial loading

Case 2—Biaxial loading

Results and discussion

Case 1—Uniaxial loading

Case 2—Biaxial loading

Input files

References

3.2.2 Test of ORNL plasticity theory under biaxial loading

Problem description

Biaxial loading

“Exact” solution

Results and discussion

Input files

Reference

3.2.3 One-way reinforced concrete slab

Problem description

Material

Solution control parameters and loading

Results and discussion

Abaqus/Standard results

Abaqus/Explicit results

Input files

References

3.2.4 Triaxial tests on a saturated clay

Problem description

Results and discussion

Compression of a drained triaxial specimen

Extension of a drained triaxial specimen

Input files

References

3.2.5 Uniaxial tests on jointed material

Problem description

Results and discussion

Input files

Reference

3.2.6 Verification of creep integration

Problem description

Model for simple creep and relaxation tests

Models for coupled creep and plasticity tests

Material

Solution control

Exact solutions

Results and discussion

Input files

3.2.7 Simple tests on a crushable foam specimen

Problem description

Calibration of material parameters

Results and discussion

Input files

Reference

3.2.8 Simple proportional and nonproportional cyclic tests

Problem description

Calibration of the model

Results and discussion

Acknowledgment

Input files

Reference

3.2.9 Biaxial tests on gray cast iron

Problem description

Material parameters

Results and discussion

Conclusions

Input files

Reference

3.2.10 Indentation of a crushable foam plate

Problem description

Material

Contact interaction

Loading and controls

Abaqus/Standard

Abaqus/Explicit

Results and discussion

Input files

Reference

3.2.11 Notched unreinforced concrete beam under 3-point bending

Problem description

Solution control

Results and discussion

Mesh refinement study

Influence of tension softening

Influence of speed of application of the load and curve smoothing in Abaqus/Explicit

Input files

References

3.2.12 Mixed-mode failure of a notched unreinforced concrete beam

Problem description

Loading and solution control

Results and discussion

Mesh refinement study

Influence of tension softening

Influence of shear retention

Effect of element removal

Input files

References

3.2.13 Slider mechanism with slip-rate-dependent friction

Problem description

Material

Results and discussion

Input files

3.2.14 Cylinder under internal pressure

Problem description

Results and discussion

Input files

Reference

3.2.15 Creep of a thick cylinder under internal pressure

Problem description

Loading and control

Results and discussion

Input files

References

3.2.16 Pressurization of a thick-walled cylinder

Problem description

Results and discussion

Input file

Reference

3.2.17 Stretching of a plate with a hole

Problem description

Results and discussion

Input files

3.2.18 Pressure on infinite geostatic medium

Problem description

Results and discussion

Input files

4. NAFEMS Benchmarks

4.1 Overview

4.1.1 NAFEMS benchmarks: overview

4.2 Standard benchmarks: linear elastic tests

4.2.1 LE1: Plane stress elements—elliptic membrane

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.2 LE2: Cylindrical shell bending patch test

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.3 LE3: Hemispherical shell with point loads

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.4 LE4: Axisymmetric hyperbolic shell under uniform internal pressure

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.5 LE5: Z-section cantilever

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.6 LE6: Skew plate under normal pressure

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.2.7 LE7: Axisymmetric cylinder/sphere under pressure

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.8 LE8: Axisymmetric shell under pressure

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.9 LE9: Axisymmetric branched shell under pressure

Element tested

Problem description

Reference solution

Results and discussion

Input files

4.2.10 LE10: Thick plate under pressure

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.2.11 LE11: Solid cylinder/taper/sphere—temperature loading

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.3 Standard benchmarks: linear thermo-elastic tests

4.3.1 T1: Plane stress elements—membrane with hot-spot

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.3.2 T2: One-dimensional heat transfer with radiation

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.3.3 T3: One-dimensional transient heat transfer

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.3.4 T4: Two-dimensional heat transfer with convection

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.4 Standard benchmarks: free vibration tests

4.4.1 FV2: Pin-ended double cross: in-plane vibration

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input files

4.4.2 FV4: Cantilever with off-center point masses

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input files

4.4.3 FV12: Free thin square plate

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus (for element type S4R5 )

Results and discussion

Input files

4.4.4 FV15: Clamped thin rhombic plate

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input files

4.4.5 FV16: Cantilevered thin square plate

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.4.6 FV22: Clamped thick rhombic plate

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input files

4.4.7 FV32: Cantilevered tapered membrane

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus (for element type CPS4 )

Results and discussion

Input files

4.4.8 FV41: Free cylinder: axisymmetric vibration

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Remarks

Input files

4.4.9 FV42: Thick hollow sphere: uniform radial vibration

Elements tested

Problem description

Reference solution

Radial displacement; Mode shapes predicted by Abaqus (for element type CAX8 )

Results and discussion

Input files

4.4.10 FV52: Simply supported “solid” square plate

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus (for element type C3D8I )

Results and discussion

Remarks

Input files

4.5 Proposed forced vibration benchmarks

4.5.1 Test 5: Deep simply supported beam: frequency extraction

Element tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input file

4.5.2 Test 5H: Deep simply supported beam: harmonic forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus

Results and discussion

Input files

4.5.3 Test 5T: Deep simply supported beam: transient forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus/Standard

Response predicted by Abaqus/Explicit

Results and discussion

Input files

4.5.4 Test 5R: Deep simply supported beam: random forced vibration

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.5.5 Test 13: Simply supported thin square plate: frequency extraction

Element tested

Problem description

Reference solution

Mode shapes predicted by Abaqus

Results and discussion

Input file

4.5.6 Test 13H: Simply supported thin square plate: harmonic forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus

Results and discussion

Input files

4.5.7 Test 13T: Simply supported thin square plate: transient forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus/Standard

Response predicted by Abaqus/Explicit

Results and discussion

Input files

4.5.8 Test 13R: Simply supported thin square plate: random forced vibration

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.5.9 Test 21: Simply supported thick square plate: frequency extraction

Elements tested

Problem description

Reference solution

Mode shapes predicted by Abaqus (for element type S4R5 )

Results and discussion

Input files

4.5.10 Test 21H: Simply supported thick square plate: harmonic forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus

Results and discussion

Input files

4.5.11 Test 21T: Simply supported thick square plate: transient forced vibration

Elements tested

Problem description

Reference solution

Response predicted by Abaqus/Standard

Response predicted by Abaqus/Explicit

Results and discussion

Input files

4.5.12 Test 21R: Simply supported thick square plate: random forced vibration

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.6 Proposed nonlinear benchmarks

4.6.1 NL1: Prescribed biaxial strain history, plane strain

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.6.2 NL2: Axisymmetric thick cylinder

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.6.3 NL3: Hardening with two variables under load control

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.6.4 NL4: Snap-back under displacement control

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.6.5 NL5: Straight cantilever with end moment

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.6.6 NL6: Straight cantilever with axial end point load

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.6.7 NL7: Lee's frame buckling problem

Element tested

Problem description

Reference solution

Results and discussion

Input file

4.7 Two-dimensional test cases in linear elastic fracture mechanics

4.7.1 Test 1.1: Center cracked plate in tension

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.2 Test 1.2: Center cracked plate with thermal load

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.3 Test 2.1: Single edge cracked plate in tension

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.4 Test 3: Angle crack embedded in a plate

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.5 Test 4: Cracks at a hole in a plate

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.6 Test 5: Axisymmetric crack in a bar

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.7 Test 6: Compact tension specimen

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.8 Test 7.1: T-joint weld attachment

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.7.9 Test 8.1: V-notch specimen in tension

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8 Fundamental tests of creep behavior

4.8.1 Test 1A: 2-D plane stress – uniaxial load, secondary creep

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.2 Test 1B: 2-D plane stress – uniaxial displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.3 Test 2A: 2-D plane stress – biaxial load, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.4 Test 2B: 2-D plane stress – biaxial displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.5 Test 3A: 2-D plane stress – biaxial (negative) load, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.6 Test 3B: 2-D plane stress – biaxial (negative) displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.7 Test 4A: 2-D plane stress – biaxial (double) load, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.8 Test 4B: 2-D plane stress – biaxial (double) displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.9 Test 4C: 2-D plane stress – shear loading, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.10 Test 5A: 2-D plane strain – biaxial load, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.11 Test 5B: 2-D plane strain – biaxial displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.12 Test 6A: 3-D – triaxial load, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.13 Test 6B: 3-D – triaxial displacement, secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.14 Test 7: Axisymmetric – pressurized cylinder, secondary creep

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.15 Test 8A: 2-D plane stress – uniaxial load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.16 Test 8B: 2-D plane stress – uniaxial displacement, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.17 Test 8C: 2-D plane stress – stepped load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.18 Test 9A: 2-D plane stress – biaxial load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.19 Test 9B: 2-D plane stress – biaxial displacement, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.20 Test 9C: 2-D plane stress – biaxial stepped load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.21 Test 10A: 2-D plane stress – biaxial (negative) load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.22 Test 10B: 2-D plane stress – biaxial (negative) displacement, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.23 Test 10C: 2-D plane stress – biaxial (negative) stepped load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.24 Test 11: 3-D – triaxial load, primary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input file

4.8.25 Test 12A: 2-D plane stress – uniaxial load, primary-secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.26 Test 12B: 2-D plane stress – uniaxial displacement, primary-secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.8.27 Test 12C: 2-D plane stress – stepped load, primary-secondary creep

Element tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.9 Composite tests

4.9.1 R0031(1): Laminated strip under three-point bending

Elements tested

Problem description

Reference solution

Results and discussion

Remarks

Input files

4.9.2 R0031(2): Wrapped thick cylinder under pressure and thermal loading

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.9.3 R0031(3): Three-layer sandwich shell under normal pressure loading

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.10 Geometric nonlinear tests

4.10.1 3DNLG-1: Elastic large deflection response of a Z-shaped cantilever under an end load

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus (element B32 )

Input files

4.10.2 3DNLG-2: Elastic large deflection response of a pear-shaped cylinder under end shortening

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus (element S8R5 )

Input files

4.10.3 3DNLG-3: Elastic lateral buckling of a right angle frame under in-plane end moments

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus (element B32 )

Input files

4.10.4 3DNLG-4: Lateral torsional buckling of an elastic cantilever subjected to a transverse end load

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus

Input files

4.10.5 3DNLG-5: Large deflection of a curved elastic cantilever under transverse end load

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus (element B31 )

Input files

4.10.6 3DNLG-6: Buckling of a flat plate when subjected to in-plane shear

Elements tested

Problem description

Reference solution

Results and discussion

Input files

4.10.7 3DNLG-7: Elastic large deflection response of a hinged spherical shell under pressure loading

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus

Input files

4.10.8 3DNLG-8: Collapse of a straight pipe segment under pure bending

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus

Input files

4.10.9 3DNLG-9: Large elastic deflection of a pinched hemispherical shell

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus

Input files

4.10.10 3DNLG-10: Elastic-plastic behavior of a stiffened cylindrical panel under compressive end load

Elements tested

Problem description

Reference solution

Results and discussion

Response predicted by Abaqus

Input files

Abaqus Benchmarks Manual Abaqus Version 6.5 ID: Printed on:

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Preface This section lists various resources that are available for help with using Abaqus Uniﬁed FEA software. Support Both technical engineering support (for problems with creating a model or performing an analysis) and systems support (for installation, licensing, and hardware-related problems) for Abaqus are offered through a network of local support ofﬁces. Regional contact information is listed in the front of each Abaqus manual and is accessible from the Locations page at www.simulia.com. SIMULIA Online Support System The SIMULIA Online Support System (SOSS) provides a knowledge database of SIMULIA Answers. The SIMULIA Answers are solutions to questions that we have had to answer or guidelines on how to use Abaqus, SIMULIA SLM, Isight, and other SIMULIA products. You can also submit new requests for support in the SOSS. All support incidents are tracked in the SOSS. If you are contacting us by means outside the SOSS to discuss an existing support problem and you know the incident number, please mention it so that we can consult the database to see what the latest action has been. To use the SOSS, you need to register with the system. Visit the My Support page at www.simulia.com to register. Many questions about Abaqus can also be answered by visiting the Products page and the Support page at www.simulia.com. Anonymous ftp site To facilitate data transfer with SIMULIA, an anonymous ftp account is available on the computer ftp.simulia.com. Login as user anonymous, and type your e-mail address as your password. Contact support before placing ﬁles on the site. Training All ofﬁces and representatives offer regularly scheduled public training classes. We also provide training seminars at customer sites. All training classes and seminars include workshops to provide as much practical experience with Abaqus as possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local ofﬁce or representative. Feedback We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. We will ensure that any enhancement requests you make are considered for future releases. If you wish to make a suggestion about the service or products, refer to www.simulia.com. Complaints should be addressed by contacting your local ofﬁce or through www.simulia.com by visiting the Quality Assurance section of the Support page. Abaqus Version 6.5 ID: Printed on:

Abaqus Version 6.6 ID: Printed on:

Contents 1. Analysis Tests Static stress/displacement analysis Beam/gap example Analysis of an anisotropic layered plate Composite shells in cylindrical bending Thick composite cylinder subjected to internal pressure Uniform collapse of straight and curved pipe segments Snap-through of a shallow, cylindrical roof under a point load Pressurized rubber disc Uniaxial stretching of an elastic sheet with a circular hole Necking of a round tensile bar Concrete slump test The Hertz contact problem Crushing of a pipe Buckling analysis Buckling analysis of beams Buckling of a ring in a plane under external pressure Buckling of a cylindrical shell under uniform axial pressure Buckling of a simply supported square plate Lateral buckling of an L-bracket Buckling of a column with general contact Dynamic stress/displacement analysis Subspace dynamic analysis of a cantilever beam Double cantilever elastic beam under point load Explosively loaded cylindrical panel Free ring under initial velocity: comparison of rate-independent and rate-dependent plasticity Large rotation of a one degree of freedom system Motion of a rigid body in Abaqus/Standard Rigid body dynamics with Abaqus/Explicit Revolute MPC veriﬁcation: rotation of a crank Pipe whip simulation Impact of a copper rod Frictional braking of a rotating rigid body Compression of cylindrical shells with general contact Steady-state slip of a belt drive v CONTENTS 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6 1.1.7 1.1.8 1.1.9 1.1.10 1.1.11 1.1.12 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.3.7 1.3.8 1.3.9 1.3.10 1.3.11 1.3.12 1.3.13 Abaqus ID:bmk-toc Printed on: Tue March 16 -- 12:01:38 2010

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