Axisymmetric solid elements

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

This page discusses:

ProductsAbaqus/Standard

Elements tested

CAX3

CAX3H

CAX4

CAX4H

CAX4I

CAX4IH

CAX4R

CAX4RH

CAX4RHT

CAX4RT

CAX6

CAX6H

CAX6M

CAX6MH

CAX6MHT

CAX6MT

CAX8

CAX8H

CAX8R

CAX8RH

Problem description



Material:

Linear elastic, Young's modulus = 30 × 106, Poisson's ratio = 0.3.

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

Boundary conditions:

uzA=uzB=0.

Step 1

A distributed pressure loading of 1000/area is applied on each face.

Response:
Stresses

At every integration point, σrr=σθθ=σzz= −1000, σrz= 0.

Strains

εrr=εθθ=εzz= −1.3333 × 10−5, εrz= 0.

Displacements

ur= −1.33 × 10−2 along r= 1000, uz= −1.33 × 10−5z.

For lower-order elements the test description is complete. For higher-order elements, another step definition is included.

Step 2

Hydrostatic pressure loading is applied along the two vertical faces, varying from 0 at the top to 1000/area at the bottom, in addition to the loads of Step 1.

The following reference solution is obtained for Step 2 using CAXA84 axisymmetric solid elements with nonlinear, asymmetric deformation (input file eref84s3.inp) and is given at z= 0.5.

Stresses

σrr= −1500, σzz= −1000, σθθ= −1500, σrz= 0.

Strains

εrr= −2.5 × 10−5, εzz= −3.33 × 10−6, εθθ= −2.5 × 10−5, εrz= 0.

Results and discussion

Elements using reduced integration may have additional boundary conditions to those specified above. All elements yield exact solutions.

Section output requests to the results (.fil) file and to the data (.dat) file are used in some of the input files to output accumulated quantities on the face CD. The quantities are reported in a system that is local to the section.

Input files

eca3sfs3.inp

CAX3 elements.

eca3shs3.inp

CAX3H elements.

eca4sfs3.inp

CAX4 elements.

eca4shs3.inp

CAX4H elements.

eca4sis3.inp

CAX4I elements.

eca4sjs3.inp

CAX4IH elements.

eca4srs3.inp

CAX4R elements.

eca4sys3.inp

CAX4RH elements.

eca4tys3.inp

CAX4RHT elements.

eca4trs3.inp

CAX4RT elements.

eca6sfs3.inp

CAX6 elements.

eca6shs3.inp

CAX6H elements.

eca6sks3.inp

CAX6M elements.

eca6sls3.inp

CAX6MH elements.

eca6tls3.inp

CAX6MHT elements.

eca6tks3.inp

CAX6MT elements.

eca8sfs3.inp

CAX8 elements.

eca8shs3.inp

CAX8H elements.

eca8srs3.inp

CAX8R elements.

eca8sys3.inp

CAX8RH elements.