Abaqus Verification Guide  


1.4.4 Shell, membrane, and truss stress/displacement elements

Product: Abaqus/Standard  

I. Axisymmetric shells

Problem description

Model:

Length10.0
Radius5.0
Thickness0.5
Centrifugal axis of rotation(0, 1, 0) through origin
Gravity load vector(0, 1, 0)

Material:

Young's modulus3 × 106
Poisson's ratio0.3
Density1.0

Initial conditions:

Hydrostatic pressure datum12.0
Hydrostatic pressure elevation0.0

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.

SAX2 element load tests:


esa3sxd1.inp

BR, BZ, GRAV, CENT, CENTRIF, P, HP.

II. Axisymmetric membranes

Problem description

Model:

Length10.0
Radius5.0
Thickness0.5
Centrifugal axis of rotation(0, 1, 0) through origin
Gravity load vector(0, 1, 0)

Material:

Young's modulus3 × 106
Poisson's ratio0.3
Density1.0

Initial conditions:

Hydrostatic pressure datum12.0
Hydrostatic pressure elevation0.0

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.

MAX2 element load tests:


ema3srd1.inp

BR, BZ, GRAV, CENT, CENTRIF, P, HP.

MGAX1 element load tests:


emg2srd1.inp

BR, BZ, GRAV, CENT, CENTRIF, P, HP.

MGAX2 element load tests:


emg3srd1.inp

BR, BZ, GRAV, CENT, CENTRIF, P, HP.

III. CYLINDRICAL membranes

Problem description

Model:

Length10.0
Radius5.0
Thickness0.5
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 modulus3 × 106
Poisson's ratio0.3
Density1.0

Initial conditions:

Hydrostatic pressure datum12.0
Hydrostatic pressure elevation0.0

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.

MCL9 element load tests:


emc9srd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP.

IV. General shells and membranes: general element loading

Problem description

Model:

Square dimensions7 × 7
Thickness2.0
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 modulus3 × 106
Poisson's ratio0.3
Density1.0
Coefficient of thermal expansion.0001

Initial conditions:

Initial temperatureALL, –10
Hydrostatic pressure datum7.0
Hydrostatic pressure elevation0.0
Initial velocityALL, 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.

esf3sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S4 element load tests:


ese4sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

ese4sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S4R element load tests:


esf4sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

esf4sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S4R5 element load tests:


es54sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es54sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S8R element load tests:


es68sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es68sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S8R5 element load tests:


es58sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es58sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

S9R5 element load tests:


es59sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es59sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

STRI3 element load tests:


es63sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es63sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

STRI65 element load tests:


es56sgd1.inp

BX, BY, BZ, GRAV, CENT, P, HP, *TEMPERATURE.

es56sxd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D3 element load tests:


em33sfd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D4 element load tests:


em34sfd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D4R element load tests:


em34srd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D6 element load tests:


em36sfd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D8 element load tests:


em38sfd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D8R element load tests:


em38srd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D9 element load tests:


em39sfd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

M3D9R element load tests:


em39srd1.inp

BX, BY, BZ, GRAV, CENT, CENTRIF, P, HP, *TEMPERATURE.

V. 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:

Length0.405
Radius0.2875
Thickness0.05

Material:

Coefficient of thermal expansion4.87 × 10–6

Initial conditions:

Initial temperatureALL, 70.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

VI. Axisymmetric shells with nonlinear asymmetric deformation

Problem description

Model:

Length10.0
Radius5.0
Thickness0.01

Material:

Young's modulus3 × 107
Poisson's ratio0.3
Density1.0

Initial conditions:

Hydrostatic pressure datum1 × 106
Hydrostatic pressure elevation0.0

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.

VII. Truss elements

Problem description

Model:

Length1.0
Area0.1
Centrifugal axis of rotation(0, 1, 0) through (.5, 0, 0)
Gravitational load vector(0, –1, 0)

Material:

Young's modulus3 × 106
Poisson's ratio0.3
Coefficient of thermal expansion.0001
Density5 × 10–5

Initial conditions:

Initial temperatureALL, –10.0
Initial velocityALL, 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.

T2D2H element load tests:


et22shd1.inp

BX, BY, CENT, CENTRIF, GRAV, *TEMPERATURE.

T2D3 element load tests:


et23sfd1.inp

BX, BY, CENT, CENTRIF, GRAV, *TEMPERATURE.

T2D3H element load tests:


et23shd1.inp

BX, BY, CENT, CENTRIF, GRAV, *TEMPERATURE.

T3D2 element load tests:


et32sfd1.inp

BX, BY, BZ, CENT, CENTRIF, GRAV, *TEMPERATURE.

T3D2H element load tests:


et32shd1.inp

BX, BY, BZ, CENT, CENTRIF, GRAV, *TEMPERATURE.

T3D3 element load tests:


et33sfd1.inp

BX, BY, BZ, CENT, CENTRIF, GRAV, *TEMPERATURE.

T3D3H element load tests:


et33shd1.inp

BX, BY, BZ, CENT, CENTRIF, GRAV, *TEMPERATURE.

VIII. 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,” Section 1.2.4 of the Abaqus Benchmarks Guide.

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.