Two-dimensional continuum stress/displacement submodeling

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

The following topics are discussed:

Elements tested
Features tested
Problem description
Results and discussion
Input files

ProductsAbaqus/StandardAbaqus/Explicit

Elements tested

CPEG3
CPEG4
CPEG6
CPEG6M
CPEG8

CPE3
CPE4
CPE4H
CPE4R
CPE6
CPE6M
CPE8
CPE8H
CPE8R

CPS3
CPS4
CPS4R
CPS6
CPS6M
CPS8

Features tested

The submodeling capability is applied to two-dimensional continuum stress/displacement elements. In Abaqus/Standard general static and linear perturbation procedures are used in various combinations for both the global and submodel analyses. In Abaqus/Explicit the procedures are quasi-static for both the global and submodel analyses.

Problem description

Model:

All global models have dimensions 8.0 × 1.5 in the x–y plane, with an out-of-plane dimension of 1.0 (plane stress analysis).

Material:

Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	10.0
Rayleigh damping ( $α_{R}$ )	0.2
Rayleigh damping ( $β_{R}$ )	0.4

Loading and boundary conditions

All global models involving static procedures and Abaqus/Explicit quasi-static procedures are subject to the loading and boundary conditions depicted in Figure 1. In Abaqus/Standard the time history of the loading, the time at which the corresponding submodeled analysis is performed, and the requested file output from the global model are unique to each individual analysis. In Abaqus/Explicit the same step time and smooth step loading are used in both the global and submodel analyses.

Figure 1. Global and submodeled domains used with static procedures.

All global models involving dynamic procedures in Abaqus/Standard are subject to the loading and boundary conditions depicted in Figure 2. For the transient simulations using the direct-integration implicit dynamic procedure, different excitation frequencies of the load can be tested by changing the parameters defined in the input files. As in the static analyses the time history of the loading, the time at which the corresponding submodeled analysis is performed, and the requested file output from the global model are unique to each individual analysis.

Figure 2. Global and submodeled domains used with dynamic procedures.

Results and discussion

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

Input files

Abaqus/Standard input files

The following input files test various combinations of static analyses using the static and linear static perturbation procedures:

pgcg4sfs.inp: CPEG3, CPEG4 elements; global analysis.
pscg4sf1.inp: CPEG4 elements; submodel analysis of pgcg4sfs.inp.
pscg4sf1_sb.inp: CPEG4 elements; stress-based submodel analysis of pgcg4sfs.inp.
pscg4sf2.inp: Restart from pscg4sf1.inp.
pscg4sf2_sb.inp: Restart from pscg4sf1_sb.inp.
pgcg8sfs.inp: CPEG6, CPEG8 elements; global analysis.
pscg8sf1.inp: CPEG4 elements; submodel analysis of pgcg8sfs.inp.
pgcg8sks.inp: CPEG6M, CPEG8 elements; global analysis.
pscg8sk1.inp: CPEG4 elements; submodel analysis of pgcg8sks.inp.
pscg8sk1_sb.inp: CPEG4 elements; stress-based submodel analysis of pgcg8sks.inp.
pgce4sfs.inp: CPE3, CPE4 elements; global analysis.
psce4sf1.inp: CPE4 elements; submodel analysis of pgce4sfs.inp.
psce4sf1_sb.inp: CPE4 elements; stress-based submodel analysis of pgce4sfs.inp.
pgce4sfsg.inp: CPE3, CPE4 elements; SUBMODEL, GLOBAL ELSET; global analysis.
psce4sf1g.inp: CPE4 elements; SUBMODEL, GLOBAL ELSET; submodel analysis of pgce4sfsg.inp.
pgce4shm.inp: CPE4H elements; global analysis.
psce4sh1.inp: CPE4 elements; submodel analysis of pgce4shm.inp .
pgce4srm.inp: CPE4R elements; global analysis.
psce4sr1.inp: CPE4 elements; submodel analysis of pgce4srm.inp.
pgce8sfs.inp: CPE6, CPE8 elements; global analysis.
psce8sf1.inp: CPE4 elements; submodel analysis of pgce8sfs.inp.
pgce6sms.inp: CPE6M elements; global analysis.
psce6sm1.inp: CPE6M elements; submodel analysis of pgce6sms.inp.
psce6sm1_sb.inp: CPE6M elements; stress-based submodel analysis of pgce6sms.inp.
pgcs4sfs.inp: CPS3, CPS4 elements; global analysis.
pscs4sf1.inp: CPS4 elements; submodel analysis of pgcs4sfs.inp.
pgcs6sms.inp: CPS6M elements; global analysis.
pscs6sm1.inp: CPS6M elements; submodel analysis of pgcs6sms.inp.

The following input files test various combinations of dynamic analyses using the direct solution steady-state dynamic and direct-integration implicit procedures:

pgce8shd.inp: CPE8H elements; global analysis.
psce8sh1.inp: CPS8 elements; submodel analysis of pgce8shd.inp.
pgce8srd.inp: CPE8R elements; global analysis.
psce8sr1.inp: CPE8 elements; submodel analysis of pgce8srd.inp.
psce8sr1_sb.inp: CPE8 elements; stress-based submodel analysis of pgce8srd.inp.
pgcs8sfd.inp: CPS6, CPS8 elements; global analysis.
pscs8sf1.inp: CPS8 elements; submodel analysis of pgcs8sfd.inp.
pscs8sf1_sb.inp: CPS8 elements; stress-based submodel analysis of pgcs8sfd.inp.
submodel2delem_cpe8h_gd_std.inp: CPE8H elements; global DYNAMIC analysis.
submodel2delem_cps8_sd_std.inp: CPS8 elements; submodel DYNAMIC analysis.

Abaqus/Explicit input files

submodel2delem_cpe_g_xpl.inp: CPE4R, CPE3 elements; global analysis.
submodel2delem_cpe4r_s_xpl.inp: CPE4R elements; submodel analysis.
submodel2delem_cps_g_xpl.inp: CPS4R, CPS3 elements; global analysis.
submodel2delem_cps4r_s_xpl.inp: CPS4R elements; submodel analysis.
submodel2delem_cpe6m_g_xpl.inp: CPE6M elements; global analysis.
submodel2delem_cpe6m_s_xpl.inp: CPE6M elements; submodel analysis.
submodel2delem_cps6m_g_xpl.inp: CPS6M elements; global analysis.
submodel2delem_cps6m_s_xpl.inp: CPS6M elements; submodel analysis.