Shell submodeling

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

This page discusses:

Bending tests
Membrane tests
Heat transfer test
Thermal-stress analysis
Finite rotation test
Continuum shell elements

ProductsAbaqus/StandardAbaqus/Explicit

Bending tests

Elements tested

S3R

S3RS

S4R

S4RS

S4RSW

S8R

STRI3

Features tested

The submodeling capability is applied to various shell elements, with 6 degrees of freedom per node, subject to a bending load. Various combinations for both the global and submodel analyses are tested: in Abaqus/Standard general static and static perturbation procedures are used, and in Abaqus/Explicit the analyses are dynamic and quasi-static.

Problem description

Model:

All global models have dimensions 10.0 × 3.0 in the x–y plane and use five section points through the thickness of 0.001.

Material:


Young's modulus	1 × 10⁶
Poisson's ratio	0.3
Density	10

Loading and boundary conditions

Except for the problem defined in files pgsf4srsgm.inp and pssf4sr1gm.inp, the global model is constrained such that all displacement and rotation degrees of freedom for nodes along the y-axis are suppressed. All elements in the model are then subject to a uniform pressure load of 1 × 10⁻⁷ in the positive z-direction. In Abaqus/Explicit the elements are subject to a uniform pressure load of 1 × 10⁻² in the positive z-direction. The global models using triangular shells in Abaqus/Explicit have three steps; however, the submodel analyses have one step that is driven from the third global step. This is valid because the inertial forces are not significant during the first two steps (the process is quasi-static).

The model considered in Abaqus/Standard files pgsf4srsgm.inp and pssf4sr1gm.inp and in Abaqus/Explicit input files using quadrilateral shells has two shell elements through the thickness in part of the region. One end of the model is fixed, while displacements in the z-direction are applied to the other end: in the positive z-direction for one layer of shells and in the opposite direction for the other layer. This is a special situation, which, in general, necessitates the use of multiple submodels to ensure that driven nodes are assigned to the correct global elements.

General:

Gauss integration is used for the shell cross-section in input files pgsf3srm.inp and pssf3sr1.inp.

Results and discussion

The amplitudes of all driven variables in the submodel analysis are correctly identified in the global analysis file output and applied at the driven nodes in the submodel analysis.

Input files

Abaqus/Standard input files

pgsf3srm.inp: S3/S3R elements; global analysis.
pssf3sr1.inp: S3/S3R elements; submodel analysis.
pgsf3srmg.inp: S3/S3R elements; SUBMODEL, GLOBAL ELSET; global analysis.
pssf3sr1g.inp: S3/S3R elements; SUBMODEL, GLOBAL ELSET; submodel analysis.
pgse4sfs.inp: S4 elements; global analysis.
psse4sf5.inp: S4 elements; submodel analysis.
pgsf4srs.inp: S4R elements; global analysis.
pssf4sr1.inp: S4R elements; submodel analysis.
pgsf4srsgm.inp: S4R elements; multiple SUBMODEL options; global analysis.
pssf4sr1gm.inp: S4R elements; multiple SUBMODEL options; submodel analysis.
pgs68srm.inp: S8R elements; global analysis.
pss68sr1.inp: S8R elements; submodel analysis.
pgs63sfs.inp: STRI3 elements; global analysis.
pss63sf1.inp: STRI3 elements; submodel analysis.

Abaqus/Explicit input files

submodelshell_g_gel_s3r_xpl.inp: S3R elements; SUBMODEL, GLOBAL ELSET; global analysis.
submodelshell_s_gel_s3r_xpl.inp: S3R elements; SUBMODEL, GLOBAL ELSET; submodel analysis.
submodelshell_g_s3r_xpl.inp: S3R elements; global analysis.
submodelshell_s_s3r_xpl.inp: S3R elements; submodel analysis.
submodelshell_g_s3rs_xpl.inp: S3RS elements; global analysis.
submodelshell_s_s3rs_xpl.inp: S3RS elements; submodel analysis.
submodelshell_g_s4_xpl.inp: S4 elements; global analysis.
submodelshell_s_s4_xpl.inp: S4 elements; submodel analysis.
submodelshell_g_s4r_xpl.inp: S4R elements; global analysis.
submodelshell_s_s4r_xpl.inp: S4R elements; submodel analysis.
submodelshell_g_m_s4r_xpl.inp: S4R elements; multiple SUBMODEL options; global analysis.
submodelshell_s_m_s4r_xpl.inp: S4R elements; multiple SUBMODEL options; submodel analysis.
submodelshell_g_m_s4rs_xpl.inp: S4RS elements; multiple SUBMODEL options; global analysis.
submodelshell_s_m_s4rs_xpl.inp: S4RS elements; multiple SUBMODEL options; submodel analysis.
submodelshell_g_m_s4rsw_xpl.inp: S4RSW elements; multiple SUBMODEL options; global analysis.
submodelshell_s_m_s4rsw_xpl.inp: S4RSW elements; multiple SUBMODEL options; submodel analysis.

Membrane tests

Elements tested

S4R5

Features tested

The submodeling capability is applied to two patches of shell elements, with 5 degrees of freedom per node, subject to membrane-type loading. General static and static perturbation procedures are used in various combinations for both the global and submodel analyses.

Problem description

Model:

The global models have dimensions 0.24 × 0.12 in the x–y plane and use five section points through the thickness of 0.001.

Material:


Young's modulus	1 × 10⁶
Poisson's ratio	0.25

Loading and boundary conditions

$u_{x}$ =10⁻³ $(x + y / 2)$ , $u_{y}$ =10⁻³ $(y + x / 2)$ , at all exterior nodes. $u_{z}$ =0 at all nodes.

Results and discussion

The amplitudes of all driven variables (translational degrees of freedom in this case) in the submodel analysis are correctly identified in the file output for the global analysis and applied at the driven nodes in the submodel analysis.

Input files

pgs54srs.inp: S4R5 elements; global analysis.
pss54sr1.inp: S4R5 elements; submodel analysis.
pgs54srsg.inp: S4R5 elements; SUBMODEL, GLOBAL ELSET; global analysis.
pss54sr1g.inp: S4R5 elements; SUBMODEL, GLOBAL ELSET; submodel analysis.

Heat transfer test

Elements tested

DS3

DS6

DS8

Features tested

The submodeling capability is applied to a mesh of shell elements in a heat transfer analysis.

Problem description

Model:

The global model has dimensions 10.0 × 3.0 in the x–y plane and uses three section points through the thickness of 0.001.

Material:


Thermal conductivity	1.0

Loading and boundary conditions

T=0.0 along x=y=0; and T=100.0 along x=10.0, y=3.0.

Results and discussion

The amplitudes of temperature in the submodel analysis are correctly identified in the global analysis file output and applied at the driven nodes in the submodel analysis.

Input files

pgs33dfh.inp: DS3 elements; global analysis.
pss33df1.inp: DS3 elements; submodel analysis.
pgs36dfh.inp: DS6 elements; global analysis.
pss36df1.inp: DS6 elements; submodel analysis.
pgs38dfh.inp: DS8 elements; global analysis.
pss38df1.inp: DS8 elements; submodel analysis.

Thermal-stress analysis

Elements tested

DS4

S4R

Features tested

A sequentially coupled thermal-stress analysis using the submodeling technique is tested.

Problem description

Model:

The global model has dimensions 3.0 × 2.0 in the x–z plane and uses three section points through the thickness of 0.001.

Material:


Young's modulus	1.0 × 10⁶
Poisson's ratio	0.3
Thermal conductivity	4.85 × 10⁻⁴
Coefficient of thermal expansion ( $α$ )	1.0 × 10⁻⁶

Loading and boundary conditions

In the global heat transfer analysis a linear through-thickness temperature gradient is developed in the model by specifying T=0 at all nodes on the top face of the plate and T=100 at all nodes on the bottom face. The global model for the thermal-stress analysis is constrained such that $u_{x}$ =0 for x=0, $u_{y}$ =0 for x=0 and x=3, and $u_{z}$ =0 for x=y=z=0.

Results and discussion

Submodeling of a sequentially coupled thermal-stress analysis can be accomplished by any one of three methods in Abaqus. Whenever interpolation of temperature as a field variable is required between models because of mesh dissimilarities, temperatures must be read from the output database, since temperature interpolation is not supported with the results file. Driven variables can be interpolated using either the results file or the output database.

Method 1

Run the heat transfer analysis on the global model, and output the nodal temperatures.
Run the thermal-stress analysis on the global model, reading (and possibly interpolating) temperatures as field variables from the previous global heat transfer analysis. Output the nodal temperatures and displacements.
Run the submodel analysis reading (and possibly interpolating) temperatures as field variables and displacements from the global thermal-stress analysis.

Method 2

Run the heat transfer analysis on the global model, and output the nodal temperatures.
Run the thermal-stress analysis on the global model, reading (and possibly interpolating) temperatures as field variables from the previous global heat transfer analysis. Output the nodal temperatures and displacements.
Run the thermal-stress submodel analysis, reading (and possibly interpolating) temperatures as field variables from the global heat transfer analysis and displacements from the global thermal-stress analysis.

Method 3

Run the heat transfer analysis on the global model, and output the nodal temperatures.
Run a heat transfer submodel analysis, reading temperatures as driven from the global model. Output the nodal temperatures.
Run the thermal-stress submodel analysis, reading (and possibly interpolating) temperatures as field variables from the previous heat transfer submodel analysis.

The first two methods make use of the dissimilar mesh interpolation technique.

The amplitudes of all driven variables in the submodel analysis are correctly identified in the global analysis and applied at the driven nodes in the submodel analysis.

Input files

pgs34dfq.inp: DS4 elements; global heat transfer analysis.
pss34df1.inp: DS4 elements; submodel heat transfer analysis.
pgse4sfsc.inp: S4 elements; global static thermal-stress analysis.
psse4sf5.inp: S4 elements; submodel static thermal-stress analysis.
pgsf4srq.inp: S4R elements; global static thermal-stress analysis.
pssf4sr2.inp: S4R elements; submodel static thermal-stress analysis.
pssf4sr2_inter1.inp: Submodel thermal-stress analysis that interpolates temperatures from the global heat transfer analysis.
pssf4sr2_inter2.inp: Submodel thermal-stress analysis that interpolates temperatures from the global thermal-stress analysis.
pssf4sr2_2odb_inter.inp: Submodel thermal-stress analysis that interpolates temperatures from two different output database files representing heat transfer analyses.

Finite rotation test

Elements tested

S4R

Features tested

The submodeling capability is applied to a shell element, with 6 degrees of freedom per node, subjected to rotation boundary conditions in a large-displacement analysis. In Abaqus/Standard general static procedures are used for both the global and submodel analyses. In Abaqus/Explicit dynamic procedures are used for both analyses.

Problem description

Model:

Both the global model and the submodel use a single element with dimensions 10.0 × 3.0 in the x–y plane, with a thickness of 0.001.

Material:


Young's modulus	1 × 10⁶
Poisson's ratio	0.3
Density	10

Boundary conditions:

The global model is constrained such that all displacement and rotation degrees of freedom for nodes along the y-axis are suppressed. The rotation degrees of freedom at the remaining nodes are given finite rotation boundary conditions in all three rotation components using different amplitude functions.

Results and discussion

The amplitudes of all driven variables in the submodeled analysis are correctly identified in the global analysis file output and applied at the driven nodes in the submodel analysis.

Input files

Abaqus/Standard input files

pgsf4srr.inp: S4R elements; global analysis.
pssf4sr3.inp: S4R elements; submodel analysis.

Abaqus/Explicit input files

submodelshell_grot_s4r_xpl.inp: S4R elements; global analysis.
submodelshell_srot_s4r_xpl.inp: S4R elements; submodel analysis.

Continuum shell elements

Elements tested

C3D8I
SC6R
SC8R
S4
CSS8

Features tested

The submodeling capability is tested for continuum shell elements. The general static procedure is used for the global model as well as the submodel.

Problem description

In all the problems the global model is a cantilever beam loaded by concentrated loads at one end and fixed at the other end. The submodel consists of a partial cantilever beam that includes the fixed end.

Results and discussion

The amplitudes of all the driven variables in the submodel analysis are correctly identified in the global analysis output database and applied at the driven nodes in the submodel analysis.

Input files

global_sc8r_c3d8i.inp: SC8R elements; global analysis.
sub_sc8r_c3d8i.inp: C3D8I elements; submodel analysis.
global_sc6r_c3d8i.inp: SC6R elements; global analysis.
sub_sc6r_c3d8i.inp: C3D8I elements; submodel analysis.
global_shell_sc8r.inp: S4 elements; global analysis.
sub_shell_sc8r.inp: SC8R elements; submodel analysis.
global_sc8r_css8.inp: CSS8 elements; global analysis.
sub_sc8r_css8.inp: CSS8 elements; submodel analysis.