Shell, membrane, and truss stress/displacement elements

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

This page discusses:

Axisymmetric shells
Axisymmetric membranes
CYLINDRICAL membranes
General shells and membranes: general element loading
General shells and membranes: unconstrained thermal expansion
Axisymmetric shells with nonlinear asymmetric deformation
Truss elements
Field expansion tests

ProductsAbaqus/Standard

Axisymmetric shells

Problem description

Model:


Length	10.0
Radius	5.0
Thickness	0.5
Centrifugal axis of rotation	(0, 1, 0) through origin
Gravity load vector	(0, 1, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	1.0

Initial conditions


Hydrostatic pressure datum	12.0
Hydrostatic pressure elevation	0.0

General:

Gauss integration is used for the shell cross-section in input file esa2sxd1.inp.

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

SAX1 element load tests:

esa2sxd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
esa2sxd8.inp: F.
esa2sxdi.inp: P, HP.

SAX2 element load tests:

esa3sxd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
esa3sxd8.inp: F.
esa3sxdi.inp: P, HP.

Axisymmetric membranes

Problem description

Model:


Length	10.0
Radius	5.0
Thickness	0.5
Centrifugal axis of rotation	(0, 1, 0) through origin
Gravity load vector	(0, 1, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	1.0

Initial conditions


Hydrostatic pressure datum	12.0
Hydrostatic pressure elevation	0.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

MAX1 element load tests:

ema2srd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
ema2srd8.inp: F.
ema2srdi.inp: P, HP.

MAX2 element load tests:

ema3srd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
ema3srd8.inp: F.
ema3srdi.inp: P, HP.

MGAX1 element load tests:

emg2srd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
emg2srd8.inp: F.
emg2srdi.inp: P, HP.

MGAX2 element load tests:

emg3srd1.inp: BR, BZ, GRAV, CENT, CENTRIF, P, HP.
emg3srd8.inp: F.
emg3srdi.inp: P, HP.

CYLINDRICAL membranes

Problem description

Model:


Length	10.0
Radius	5.0
Thickness	0.5
Centrifugal axis of rotation	(0, 0, 1) through origin
Coriolis axis of rotation	(0, 0, 1) through origin
Gravity load vector	(0, 0, 1)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	1.0

Initial conditions


Hydrostatic pressure datum	12.0
Hydrostatic pressure elevation	0.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

MCL6 element load tests:

emc6srd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP.
emc6srd8.inp: F.
emc6srda.inp: CORIO.
emc6srdr.inp: ROTA.

MCL9 element load tests:

emc9srd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP.
emc9srd8.inp: F.
emc9srda.inp: CORIO.
emc9srdr.inp: ROTA.

General shells and membranes: general element loading

Problem description

Model:


Square dimensions	7 × 7
Thickness	2.0
Centrifugal axis of rotation	(0, 1, 0) through origin
Coriolis axis of rotation	(0, 0, 1) through origin
Gravity load vector	(0, 0, 1)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	1.0
Coefficient of thermal expansion	.0001

Initial conditions


Initial temperature	ALL, −10
Hydrostatic pressure datum	7.0
Hydrostatic pressure elevation	0.0
Initial velocity	ALL, 1, 10.0
(Coriolis loading)	ALL, 2, 5.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

S3/S3R element load tests:

esf3sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
esf3sgdi.inp: P, HP, TEMPERATURE.
esf3sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
esf3sxdi.inp: P, HP, TEMPERATURE.
esf3sxdr.inp: ROTA.

S4 element load tests:

ese4sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
ese4sgdi.inp: P, HP, TEMPERATURE.
ese4sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
ese4sxd8.inp: F.
ese4sxda.inp: CORIO.
ese4sxdi.inp: P, HP, TEMPERATURE.

S4R element load tests:

esf4sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
esf4sgdi.inp: P, HP, TEMPERATURE.
esf4sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
esf4sxd8.inp: F.
esf4sxda.inp: CORIO.
esf4sxdi.inp: P, HP, TEMPERATURE.
esf4sxdr.inp: ROTA.

S4R5 element load tests:

es54sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es54sgdi.inp: P, HP, TEMPERATURE.
es54sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es54sxd8.inp: F.
es54sxda.inp: CORIO.
es54sxdi.inp: P, HP, TEMPERATURE.
es54sxdr.inp: ROTA.

S8R element load tests:

es68sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es68sgdi.inp: P, HP, TEMPERATURE.
es68sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es68sxd8.inp: F.
es68sxda.inp: CORIO.
es68sxdi.inp: P, HP, TEMPERATURE.
es68sxdr.inp: ROTA.

S8R5 element load tests:

es58sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es58sgdi.inp: P, HP, TEMPERATURE.
es58sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es58sxd8.inp: F.
es58sxda.inp: CORIO.
es58sxdi.inp: P, HP, TEMPERATURE.
es58sxdr.inp: ROTA.

S9R5 element load tests:

es59sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es59sgdi.inp: P, HP, TEMPERATURE.
es59sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es59sxd8.inp: F.
es59sxda.inp: CORIO.
es59sxdi.inp: P, HP, TEMPERATURE.
es59sxdr.inp: ROTA.

STRI3 element load tests:

es63sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es63sgdi.inp: P, HP, TEMPERATURE.
es63sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es63sxd8.inp: F.
es63sxda.inp: CORIO.
es63sxdi.inp: P, HP, TEMPERATURE.
es63sxdr.inp: ROTA.

STRI65 element load tests:

es56sgd1.inp: BX, BY, BZ, GRAV, CENT, P, HP, TEMPERATURE.
es56sgdi.inp: P, HP, TEMPERATURE.
es56sxd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
es56sxd8.inp: F.
es56sxda.inp: CORIO.
es56sxdi.inp: P, HP, TEMPERATURE.
es56sxdr.inp: ROTA.

M3D3 element load tests:

em33sfd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em33sfd8.inp: F.
em33sfda.inp: CORIO.
em33sfdi.inp: P, HP, TEMPERATURE.
em33sfdr.inp: ROTA.

M3D4 element load tests:

em34sfd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em34sfd8.inp: F.
em34sfda.inp: CORIO.
em34sfdi.inp: P, HP, TEMPERATURE.
em34sfdr.inp: ROTA.

M3D4R element load tests:

em34srd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em34srd8.inp: F.
em34srda.inp: CORIO.
em34srdi.inp: P, HP, TEMPERATURE.
em34srdr.inp: ROTA.

M3D6 element load tests:

em36sfd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em36sfd8.inp: F.
em36sfda.inp: CORIO.
em36sfdi.inp: P, HP, TEMPERATURE.
em36sfdr.inp: ROTA.

M3D8 element load tests:

em38sfd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em38sfd8.inp: F.
em38sfda.inp: CORIO.
em38sfdi.inp: P, HP, TEMPERATURE.
em38sfdr.inp: ROTA.

M3D8R element load tests:

em38srd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em38srd8.inp: F.
em38srda.inp: CORIO.
em38srdi.inp: P, HP, TEMPERATURE.
em38srdr.inp: ROTA.

M3D9 element load tests:

em39sfd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em39sfd8.inp: F.
em39sfda.inp: CORIO.
em39sfdi.inp: P, HP, TEMPERATURE.
em39sfdr.inp: ROTA.

M3D9R element load tests:

em39srd1.inp: BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, TEMPERATURE.
em39srd8.inp: F.
em39srda.inp: CORIO.
em39srdi.inp: P, HP, TEMPERATURE.
em39srdr.inp: ROTA.

General shells and membranes: unconstrained thermal expansion

Problem description

Unconstrained expansion of a hollow cylinder subject to uniform thermal loading is investigated. One-quarter of the cylinder is modeled with a 6 × 6 mesh of quadrilateral elements with appropriate boundary conditions applied along lines of symmetry. A similar discretization is used (with the diagonals crossed on the quadrilaterals) to test triangular elements.

Model:


Length	0.405
Radius	0.2875
Thickness	0.05

Material:


Coefficient of thermal expansion	4.87 × 10⁻⁶

Initial conditions


Initial temperature	ALL, 70.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

esf3sxdg.inp: S3/S3R: TEMPERATURE.
ese4sgdg.inp: S4: TEMPERATURE.
ese4sxdg.inp: S4: TEMPERATURE.
esf4sxdg.inp: S4R: TEMPERATURE.
es54sxdg.inp: S4R5: TEMPERATURE.
es68sxdg.inp: S8R: TEMPERATURE.
es58sxdg.inp: S8R5: TEMPERATURE.
es59sxdg.inp: S9R5: TEMPERATURE.
es63sxdg.inp: STRI3: TEMPERATURE.
es56sxdg.inp: STRI65: TEMPERATURE.

Axisymmetric shells with nonlinear asymmetric deformation

Problem description

Model:


Length	10.0
Radius	5.0
Thickness	0.01

Material:


Young's modulus	3 × 10⁷
Poisson's ratio	0.3
Density	1.0

Initial conditions


Hydrostatic pressure datum	1 × 10⁶
Hydrostatic pressure elevation	0.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

esnssxd1.inp: SAXA11: BX, BZ, HP, P.
esntsxd1.inp: SAXA12: BX, BZ, HP, P.
esnusxd1.inp: SAXA13: BX, BZ, HP, P.
esnvsxd1.inp: SAXA14: BX, BZ, HP, P.
esnwsxd1.inp: SAXA21: BX, BZ, HP, P.
esnxsxd1.inp: SAXA22: BX, BZ, HP, P.
esnysxd1.inp: SAXA23: BX, BZ, HP, P.
esnzsxd1.inp: SAXA24: BX, BZ, HP, P.

Truss elements

Problem description

Model:


Length	1.0
Area	0.1
Centrifugal axis of rotation	(0, 1, 0) through (.5, 0, 0)
Gravitational load vector	(0, −1, 0)

Material:


Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Coefficient of thermal expansion	.0001
Density	5 × 10⁻⁵

Initial conditions


Initial temperature	ALL, −10.0
Initial velocity	ALL, 1, 10.0
(Coriolis loading)	ALL, 2, 5.0
(3D only)	ALL, 3, 2.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

T2D2 element load tests:

et22sfd1.inp: BX, BY, CENT, CENTRIF, GRAV, TEMPERATURE.
et22sfda.inp: CORIO.
et22sfdc.inp: CORIO.
et22sfdr.inp: ROTA.

T2D2H element load tests:

et22shd1.inp: BX, BY, CENT, CENTRIF, GRAV, TEMPERATURE.
et22shda.inp: CORIO.
et22shdr.inp: ROTA.

T2D3 element load tests:

et23sfd1.inp: BX, BY, CENT, CENTRIF, GRAV, TEMPERATURE.
et23sfda.inp: CORIO.
et23sfdc.inp: CORIO.
et23sfdr.inp: ROTA.

T2D3H element load tests:

et23shd1.inp: BX, BY, CENT, CENTRIF, GRAV, TEMPERATURE.
et23shda.inp: CORIO.
et23shdr.inp: ROTA.

T3D2 element load tests:

et32sfd1.inp: BX, BY, BZ, CENT, CENTRIF, GRAV, TEMPERATURE.
et32sfda.inp: CORIO.
et32sfdc.inp: CORIO.
et32sfdr.inp: ROTA.

T3D2H element load tests:

et32shd1.inp: BX, BY, BZ, CENT, CENTRIF, GRAV, TEMPERATURE.
et32shda.inp: CORIO.
et32shdr.inp: ROTA.

T3D3 element load tests:

et33sfd1.inp: BX, BY, BZ, CENT, CENTRIF, GRAV, TEMPERATURE.
et33sfda.inp: CORIO.
et33sfdc.inp: CORIO.
et33sfdr.inp: ROTA.

T3D3H element load tests:

et33shd1.inp: BX, BY, BZ, CENT, CENTRIF, GRAV, TEMPERATURE.
et33shda.inp: CORIO.
et33shdr.inp: ROTA.

Field expansion tests

Problem description

Model:

This section lists a number of simple tests that verify the field expansion capability. In most cases a single element or a small assembly of elements is loaded using the field expansion capability.

Material:

All tests use a linear elastic material model. In all cases a field expansion coefficient is defined and associated with at least one, and in some cases more than one, predefined field variable.

Initial conditions

In all tests the initial value of all relevant field variables is assumed to be zero at all the nodes.

Results and discussion

The results for loading based on field expansion match those obtained from a similar model using thermal expansion. The one-dimensional elements are subjected to field and thermal expansion while fully constrained, and the results have been verified by analytical means.

Input files

fieldexp_s4r.inp: S4R element using a linear elastic material model and loaded with both field and thermal expansion.
fieldexp_sc8r.inp: SC8R element using a linear elastic material model and loaded with field expansion driven by a single field variable. Tests nonlinear static and linear perturbation steps.
fieldexp_m3d4.inp: M3D4R element using a linear elastic material model and loaded with both field and thermal expansion.
buckleplate_s8r5_fieldexpan_riks.inp: S8R5 element using an elastic material model loaded with field expansion driven by a single field variable. Tests Riks procedure and produces same result as buckleplate_s8r5_riks.inp in Buckling of a simply supported square plate.
fieldexp-t2d2-multfld.inp: T2D2 element using a linear elastic material model loaded with both field and thermal expansions. The field expansion behavior is driven by three different field variables. Tests proper interpolation of temperature and predefined field-variable-dependent material data defining field expansion coefficient.
fieldexp-t2d2-reftemp.inp: T2D2 element using a linear elastic material model loaded with both field and thermal expansions. The field expansion behavior is driven by two different field variables. The thermal expansion coefficient and the two field expansion coefficients are assumed to be associated with a nonzero reference temperature and nonzero reference field variable values, respectively.
uexpan1x_field.inp: T2D2 element using a linear elastic material model loaded with field expansion defined using user subroutine UEXPAN.