User-defined coordinate system

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

This page discusses:

ProductsAbaqus/Standard

Elements tested

S4R

The definition of local material axes by a user-defined coordinate system.

In each of the tests a user-defined coordinate system is used to define the material point orientation as shown in Figure 1.

Linear elastic, Young's modulus = 3.0 × 10⁶, Poisson's ratio = 0.3.

$u_{x}$ = $u_{y}$ = $u_{z}$ = 0 at nodes 11 and 14, $ϕ_{z}$ = 0 for all the nodes.

Concentrated forces of 1000 are applied to nodes 12 and 13 at an angle of 45° to the x-axis.

Local coordinate directions are used in the input file xorisrdc.inp.

All tests should yield the following results:


Principal Stresses	Principal Strains
$σ_{m a x}$ = 2000.0	$ε_{m a x}$ = 6.6662E−5
$σ_{m i n}$ = 0.0	$ε_{m i n}$ = −1.9998E−5

ORIENTATION, NAME=LOCAL,
SYSTEM=RECTANGULAR,
DEFINITION=COORDINATES
2., 1.7071, 0., 1.,
1.4142, 0., 1., 0.7071, 0.
3, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=CYLINDRICAL,
DEFINITION=COORDINATES
3.0, 0., 0., 3.0, 1.0, 0.0
2, -15.

ORIENTATION, NAME=LOCAL,
SYSTEM=SPHERICAL,
DEFINITION=COORDINATES
3., .7071068, 0., 3., 1., 0.
2, -15.

ORIENTATION, NAME=LOCAL,
SYSTEM=ZRECTANGULAR,
DEFINITION=COORDINATES
0., 0., 1., 1., 1., 0.
3, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=RECTANGULAR,
DEFINITION=NODES
12, 13, 11
3, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=CYLINDRICAL,
DEFINITION=NODES
11, 12
2, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=SPHERICAL,
DEFINITION=NODES
12, 13
2, -15.

ORIENTATION, NAME=LOCAL,
SYSTEM=ZRECTANGULAR,
DEFINITION=NODES
11, 12
2, 75.

ORIENTATION, NAME=LOCAL,
SYSTEM=RECTANGULAR,
DEFINITION=OFFSET
2, 3
3, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=CYLINDRICAL,
DEFINITION=OFFSET
1, 2
2, 30.

ORIENTATION, NAME=LOCAL,
SYSTEM=SPHERICAL,
DEFINITION=OFFSET
1, 2
3, 75.

ORIENTATION, NAME=LOCAL,
SYSTEM=ZRECTANGULAR,
DEFINITION=OFFSET
2, 3
3, 30.