Patch test for axisymmetric elements

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

ProductsAbaqus/StandardAbaqus/Explicit

Elements tested

  • CAX3
  • CAX3H
  • CAX3T
  • CAX4
  • CAX4H
  • CAX4I
  • CAX4IH
  • CAX4R
  • CAX4RH
  • CAX4RHT
  • CAX4RT
  • CAX6
  • CAX6H
  • CAX6M
  • CAX6MH
  • CAX8
  • CAX8H
  • CAX8R
  • CAX8RH

Problem description



Material:

Linear elastic, Young's modulus = 1.0 × 106, Poisson's ratio = 0.25.

For coupled temperature-displacement elements dummy thermal properties are prescribed to complete the material definition.

Loading for Step 1

Displacement boundary conditions applied to all exterior nodes: ur= 10−3r, uz= 10−3(r+z).

Nonuniform body force: To maintain a constant shear stress σrz= 400 and preserve equilibrium, an equilibrating body force, BZNU, is defined in user subroutine DLOAD as BZNU =-σrz/r= −400/r, where r is the radius of the integration point.

In the Abaqus/Explicit simulations this step is followed by an intermediate step in which the model is returned to its unloaded state.

Loading for Step 2

Displacement boundary conditions applied to all exterior nodes: ur= 10−2r, uz= 10−2z.

Loading for Step 3

Displacement boundary conditions applied to the deformed geometry of Step 2 at all exterior nodes: ur= 10−3r, uz= 10−3(r+z).

Nonuniform body force (as described for Step 1): BZNU =-σrz/r= −400/r.

In the Abaqus/Standard simulations this step is defined as a perturbation step; in the Abaqus/Explicit simulations a velocity boundary condition that gives rise to the perturbation is specified instead.

Reference solution

The analytical results for each step are presented below.

Step 1: PERTURBATION

  • σr=σz=σθ= 2000.

  • σrz= 400.

  • ϵr=ϵz=ϵθ= 10−3.

  • γrz= 10−3.

Step 2: NLGEOM

  • σr=σz=σθ= 19900.

  • σrz= 0

  • ϵr=ϵz=ϵθ= 9.95 × 10−3.

  • γrz= 0.

In the Abaqus/Explicit simulations this is the third step. (The second step in the Abaqus/Explicit simulations returns the model to its unloaded state.)

Step 3: PERTURBATION

  • σr=σz=σθ= 2000.

  • σrz= 400.

  • ϵr=ϵz=ϵθ= 1 × 10−3.

  • γrz= 1 × 10−3.

In the Abaqus/Explicit simulations this is the fourth step. The results from the third step in the Abaqus/Explicit simulations must be subtracted from the results of the fourth step to obtain the perturbation about the loaded state.

Results and discussion

All elements yield exact solutions.

Input files

Abaqus/Standard input files

eca3sfp5.inp

CAX3 elements.

eca3sfp5.f

User subroutine DLOAD used in eca3sfp5.inp.

eca3shp5.inp

CAX3H elements.

eca3shp5.f

User subroutine DLOAD used in eca3shp5.inp.

eca4sfp5.inp

CAX4 elements.

eca4sfp5.f

User subroutine DLOAD used in eca4sfp5.inp.

eca4shp5.inp

CAX4H elements.

eca4shp5.f

User subroutine DLOAD used in eca4shp5.inp.

eca4sip5.inp

CAX4I elements.

eca4sip5.f

User subroutine DLOAD used in eca4sip5.inp.

eca4sjp5.inp

CAX4IH elements.

eca4sjp5.f

User subroutine DLOAD used in eca4sjp5.inp.

eca4srp5.inp

CAX4R elements.

eca4srp5.f

User subroutine DLOAD used in eca4srp5.inp.

eca4syp5.inp

CAX4RH elements.

eca4syp5.f

User subroutine DLOAD used in eca4syp5.inp.

eca4typ5.inp

CAX4RHT elements.

eca4typ5.f

User subroutine DLOAD used in eca4typ5.inp.

eca4trp5.inp

CAX4RT elements.

eca4trp5.f

User subroutine DLOAD used in eca4trp5.inp.

eca6sfp5.inp

CAX6 elements.

eca6sfp5.f

User subroutine DLOAD used in eca6sfp5.inp.

eca6shp5.inp

CAX6H elements.

eca6shp5.f

User subroutine DLOAD used in eca6shp5.inp.

eca6skp5.inp

CAX6M elements.

eca6skp5.f

User subroutine DLOAD used in eca6skp5.inp.

eca6slp5.inp

CAX6MH elements.

eca6slp5.f

User subroutine DLOAD used in eca6slp5.inp.

eca8sfp5.inp

CAX8 elements.

eca8sfp5.f

User subroutine DLOAD used in eca8sfp5.inp.

eca8shp5.inp

CAX8H elements.

eca8shp5.f

User subroutine DLOAD used in eca8shp5.inp.

eca8srp5.inp

CAX8R elements.

eca8srp5.f

User subroutine DLOAD used in eca8srp5.inp.

eca8syp5.inp

CAX8RH elements.

eca8syp5.f

User subroutine DLOAD used in eca8syp5.inp.

Abaqus/Explicit input files

stresspatch_xpl_cax3t.inp

CAX3T elements.

stresspatch_xpl_cax4rt.inp

CAX4RT elements.

stresspatch_xpl_cax.f

User subroutine VDLOAD for the Abaqus/Explicit simulations.