Normal definitions of beams and shells

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

This page discusses:

Elements tested
Problem description
Remarks
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

S4
S4R
S4R5
S8R
S8R5
S9R5
STRI3
STRI65

Problem description

Material:

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

Boundary conditions:

End A is clamped, $u_{y} = 0$ at end C.

Loading:

$F_{x} = $ 25.0 at end C.

Section properties

$A = $ 0.25, $I_{12} = $ 0, $I_{11} = I_{22} = $ 1.0 × 10⁶, $J = $ 0.01041667.

For B23, B23H, B33, B33H, and STRI3 elements, different values of $I_{22}$ are used: vertical members, $I_{22} = $ 5.208 × 10⁻³, horizontal members, $I_{22} = $ 1.0 × 10⁻⁶.

For pipe elements a circular cross-section of outer radius 0.5 and wall thickness 0.05 is used. Five pipe elements are used along segment AB. A single linear beam element is used along BC with section properties as defined above. In Abaqus/Explicit the loading is applied using a smooth step amplitude to achieve a nearly static response at steady state, similar to that in Abaqus/Standard.

Remarks

Normal definitions written to the output file by the analysis input file processor are all correct.

Reference solution

Displacements: $u_{x}^{B} = (P l^{3}) / (3 E I) + (P l) / (k G A)$ .

For shear flexible elements properties have been defined such that the first term is negligible.

For Love-Kirchhoff (cubic) elements the second term does not apply.

Results and discussion


Element Type	$u_{x}^{B}$ (Abaqus)	$u_{x}^{B}$ (Analytical)
B21(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B22(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B23(H)	6.662 × 10⁻³	6.667 × 10⁻³
B31(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B31OS(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B32(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B32OS(H)	5.098 × 10⁻⁵	5.098 × 10⁻⁵
B33(H)	6.662 × 10⁻³	6.667 × 10⁻³
PIPE21(H)	2.166 × 10−3	2.199 × 10−3
PIPE22(H)	2.167 × 10−3	2.199 ×10−3
PIPE31(H)	2.166 × 10⁻³	2.199 × 10⁻³
PIPE32(H)	2.167 × 10⁻³	2.199 × 10⁻³
S4	5.098 × 10⁻⁵	5.098 × 10⁻⁵
S4R	5.098 × 10⁻⁵	5.098 × 10⁻⁵
S4R5	5.098 × 10⁻⁵	5.098 × 10⁻⁵
S8R	5.098 × 10⁻⁵	5.098 × 10⁻⁵
S8R5	5.098 × 10⁻⁵	5.098 × 10⁻⁵
S9R5	5.098 × 10−5	5.098 × 10−5
STRI3 $†$	6.341 × 10⁻³	6.667 × 10⁻³
STRI65 $†$	3.991 × 10⁻⁵	5.098 × 10⁻⁵

$†$ Due to the lack of symmetry for triangular meshes, the displacements at the nodes that are at point B differ slightly. The maximum values are documented here. For pipe elements in Abaqus/Explicit the results are very close to those obtained with Abaqus/Standard; the small differences can be attributed to steady-state oscillations.

Input files

eb22gxs8.inp: B21 elements.
eb2hgxs8.inp: B21H elements.
eb23gxs8.inp: B22 elements.
eb2igxs8.inp: B22H elements.
eb2agxs8.inp: B23 elements.
eb2jgxs8.inp: B23H elements.
eb32gxs8.inp: B31 elements.
eb3hgxs8.inp: B31H elements.
ebo2gxs8.inp: B31OS elements.
ebohgxs8.inp: B31OSH elements.
eb33gxs8.inp: B32 elements.
eb3igxs8.inp: B32H elements.
ebo3gxs8.inp: B32OS elements.
eboigxs8.inp: B32OSH elements.
eb3agxs8.inp: B33 elements.
eb3jgxs8.inp: B33H elements.
ep22pxs8.inp: PIPE21 elements.
ep2hpxs8.inp: PIPE21H elements.
ep23pxs8.inp: PIPE22 elements.
ep2ipxs8.inp: PIPE22H elements.
ep32pxs8.inp: PIPE31 elements.
ep3hpxs8.inp: PIPE31H elements.
ep33pxs8.inp: PIPE32 elements.
ep3ipxs8.inp: PIPE32H elements.
ese4sgs8.inp: S4 elements.
esf4sgs8.inp: S4R elements.
es54sgs8.inp: S4R5 elements.
es68sgs8.inp: S8R elements.
es58sgs8.inp: S8R5 elements.
es59sgs8.inp: S9R5 elements.
es63sgs8.inp: STRI3 elements.
es56sgs8.inp: STRI65 elements.
normdef_pipe2d_xpl.inp: PIPE21 elements in Abaqus/Explicit.
normdef_pipe3d_xpl.inp: PIPE31 elements in Abaqus/Explicit.