Patch test for beam elements

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

The following topics are discussed:

Elements tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/StandardAbaqus/Explicit

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

$u_{z} = θ_{x} = θ_{y} = $ 0.0 at $x = $ 0, $u_{z} = $ 0.0 at $x = $ 10; displacement boundary conditions applied at the end nodes: $u_{x} = $ 0.01 + 0.01x.

Loading and boundary conditions for Step 2

The node at $x = $ 0 is fixed; $u_{y} = $ 0 at $x = $ 10; concentrated load at the free end: $P_{x} = $ 3000.

Loading and boundary conditions for Step 3

$u_{z} = θ_{x} = θ_{y} = $ 0.0 at $x = $ 0, $u_{z} = $ 0.0 at $x = $ 10; displacement boundary conditions applied at the end nodes: $u_{x} = $ 0.01 + 0.01x, where x is the value of the coordinates in the undeformed geometry.

Loading and boundary conditions for Abaqus/Explicit

The node at $x = $ 0 is fixed; $u_{y} = $ 0 at $x = $ 10; concentrated load at the free end: $P_{x} = $ 3000 using a smooth step amplitude definition. Solution is computed at time 1.0, including geometric nonlinearity.

Reference solution

The analytical results for each step are presented below.

Step 1: PERTURBATION

Section forces: axial force $N_{x} = $ 3000; tip displacement: $u_{t i p} = $ 1.0 × 10⁻¹.

Step 2: NLGEOM

Section forces: axial force $N_{x} = $ 3000; tip displacement: $u_{t i p} = $ 1.005 × 10⁻¹.

Step 3: PERTURBATION

Section forces: axial force $N_{x} = $ 2970; tip displacement: $u_{t i p} = $ 9.90 × 10⁻².

Dynamic Step in Abaqus/Explicit:

Section forces: axial force $N_{x} = $ 3000; tip displacement: $u_{t i p} = $ 1.005 × 10⁻¹.

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. The results for pipe elements in Abaqus/Explicit are the same as those in Abaqus/Standard.

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.
patch_pipe2d_xpl.inp: PIPE21 elements in Abaqus/Explicit.
patch_pipe3d_xpl.inp: PIPE31 elements in Abaqus/Explicit.