1.5.7 Patch test for beam elements

Product: ABAQUS/Standard  

Elements tested

B21    B21H    B22    B22H    B23    B23H    B31    B31H    B31OS    B31OSH   

B32    B32H    B32OS    B32OSH    B33    B33H   

PIPE21    PIPE21H    PIPE22    PIPE22H    PIPE31    PIPE31H    PIPE32    PIPE32H   

Problem description

Model:

Area, A = 0.01.

Material:

Linear elastic, Young's modulus = 30.0 × 106, Poisson's ratio = 0.3.

Loading and boundary conditions for Step 1:

0.0 at 0, 0.0 at 10; displacement boundary conditions applied at the end nodes: 0.01 + 0.01x.

Loading and boundary conditions for Step 2:

The node at 0 is fixed; 0 at 10; concentrated load at the free end: 3000.

Loading and boundary conditions for Step 3:

0.0 at 0, 0.0 at 10; displacement boundary conditions applied at the end nodes: 0.01 + 0.01x, where x is the value of the coordinates in the undeformed geometry.

Reference solution

The analytical results for each step are presented below.

Step 1: PERTURBATION

Section forces: axial force 3000; tip displacement: 1.0 × 10–2.

Step 2: NLGEOM

Section forces: axial force 3000; tip displacement: 1.005 × 10–2.

Step 3: PERTURBATION

Section forces: axial force 2970; tip displacement: 9.90 × 10–3.

Results and discussion

All elements yield exact solutions except the cubic beams, which differ from the analytical solution by about 2% for the NLGEOM step and the subsequent perturbation step. The elements are recommended only for linear analysis.

Input files

eb22rxp6.inp

B21 elements.

eb2hrxp6.inp

B21H elements.

eb23rxp6.inp

B22 elements.

eb2irxp6.inp

B22H elements.

eb2arxp6.inp

B23 elements.

eb2jrxp6.inp

B23H elements.

eb32rxp6.inp

B31 elements.

eb3hrxp6.inp

B31H elements.

ebo2ixp6.inp

B31OS elements.

ebohixp6.inp

B31OSH elements.

eb33rxp6.inp

B32 elements.

eb3irxp6.inp

B32H elements.

ebo3ixp6.inp

B32OS elements.

eboiixp6.inp

B32OSH elements.

eb3arxp6.inp

B33 elements.

eb3jrxp6.inp

B33H elements.

ep22pxp6.inp

PIPE21 elements.

ep2hpxp6.inp

PIPE21H elements.

ep23pxp6.inp

PIPE22 elements.

ep2ipxp6.inp

PIPE22H elements.

ep32pxp6.inp

PIPE31 elements.

ep3hpxp6.inp

PIPE31H elements.

ep33pxp6.inp

PIPE32 elements.

ep3ipxp6.inp

PIPE32H elements.

ebmod1p6.inp

External file used to store common portions of the input files for this problem.

ebmod2p6.inp

External file used to store common portions of the input files for this problem.