3.4.12 Substructures with large rotations

Product: Abaqus/Standard  

I. Substructures moving as rigid bodies

Features tested

Substructure's ability to move as a rigid body. The substructures undergo large rotation motions in analyses that generate negligible strain/stress in the substructure. Both static and direct-integration implicit dynamic analyses are verified.

Problem description

A rectangular substructure is formed. The substructure is subjected to boundary conditions and concentrated loads specified at the retained degrees of freedom that create negligible strain in the substructure but generate large rotations of the model. In the static analyses the substructure is constrained using springs to prevent numerical singularities.

A second identical mesh is defined without substructures. The displacements, rotations, and reaction forces should be nearly identical between the two equivalent analyses.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_rbm_solid2d_sta.inp

Large rotations, static, two-dimensional analysis using substructures.

substr_rbm_solid2d_dyn.inp

Large rotations, direct-integration implicit dynamic, two-dimensional analysis using substructures.

substr_rbm_solid2d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_rbm_solid2d_sta.inp

Large rotations, static, two-dimensional analysis without substructures.

nosubstr_rbm_solid2d_dyn.inp

Large rotations, direct-integration implicit dynamic, two-dimensional analysis without substructures.

substr_rbm_solid3d_sta.inp

Large rotations, static, three-dimensional analysis using substructures.

substr_rbm_solid3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis using substructures.

substr_rbm_solid3d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_rbm_solid3d_sta.inp

Large rotations, static, three-dimensional analysis without substructures.

nosubstr_rbm_solid3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis without substructures.

substr_rbm_beam2d_sta.inp

Large rotations, static, two-dimensional analysis using substructures.

substr_rbm_beam2d_dyn.inp

Large rotations, direct-integration implicit dynamic, two-dimensional analysis using substructures.

substr_rbm_beam2d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_rbm_beam2d_sta.inp

Large rotations, static, two-dimensional analysis without substructures.

nosubstr_rbm_beam2d_dyn.inp

Large rotations, direct-integration implicit dynamic, two-dimensional analysis without substructures.

substr_rbm_beam3d_sta.inp

Large rotations, static, three-dimensional analysis using substructures.

substr_rbm_beam3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis using substructures.

substr_rbm_beam3d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_rbm_beam3d_sta.inp

Large rotations, static, three-dimensional analysis without substructures.

nosubstr_rbm_beam3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis without substructures.

II. Small-deformation substructures in large rotations

Features tested

Substructures that are subject to elastic small-deformations but undergo large rotations. Both static and direct-integration implicit dynamic analyses are verified.

Problem description

The modes to be used are specified, and a rectangular mesh is formed. The loading and boundary contions specified at the retained degrees of freedom are such that elastic small-strain-inducing defomations occur on top of large rotations of the substructure. In the static analyses additional springs are used to prevent numerical singularities. Results are then compared to results obtained from equivalent analyses that do not use substructures.

Results and discussion

All results in the analyses using substructures are nearly identical to the results obtained in the analyses using a regular mesh.

Input files

substr_smdef_solid2d_sta.inp

Elastic, small-strain, large rotations, static, two-dimensional analysis using substructures.

substr_smdef_solid2d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, two-dimensional analysis using substructures.

substr_smdef_solid2d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_smdef_solid2d_sta.inp

Elastic, small-strain, large rotations, static, two-dimensional analysis without substructures.

nosubstr_smdef_solid2d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, two-dimensional analysis without substructures.

substr_smdef_solid3d_sta.inp

Elastic, small-strain, large rotations, static, three-dimensional analysis using substructures.

substr_smdef_solid3d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, three-dimensional analysis using substructures.

substr_smdef_solid3d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_smdef_solid3d_sta.inp

Elastic, small-strain, large rotations, static, three-dimensional analysis without substructures.

nosubstr_smdef_solid3d_dyn.inp

Elastic small-strain large rotations direct-integration implicit dynamic three-dimensional analysis without substructures.

substr_smdef_beam2d_sta.inp

Elastic, small-strain, large rotations, static, two-dimensional analysis using substructures.

substr_smdef_beam2d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, two-dimensional analysis using substructures.

substr_smdef_beam2d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_smdef_beam2d_sta.inp

Elastic, small-strain, large rotations, static, two-dimensional analysis without substructures.

nosubstr_smdef_beam2d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, two-dimensional analysis without substructures.

substr_smdef_shell3d_sta.inp

Elastic, small-strain, large rotations, static, three-dimensional analysis using substructures.

substr_smdef_shell3d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, three-dimensional analysis using substructures.

substr_smdef_shell3d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_smdef_shell3d_sta.inp

Elastic, small-strain, large rotations, static, three-dimensional analysis without substructures.

nosubstr_smdef_shell3d_dyn.inp

Elastic, small-strain, large rotations, direct-integration implicit dynamic, three-dimensional analysis without substructures.

III. User-specified rotation/mirroring and transformations

Features tested

User-rotated or mirrored substructures that also exhibit elastic small-strain deformation in addition to large rotations.

Problem description

A rectangular mesh is formed. At the usage level the substructure is either translated and rotated or mirrored.

A second identical mesh is defined without using substructures but accounting for the user-specified rotation/mirroring. The displacements, rotations, and stresses should be nearly identical between the two equivalent analyses.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_urot_shell3d_sta.inp

User-rotated substructure with large rotation motions, static, three-dimensional analysis.

nosubstr_urot_shell3d_sta.inp

Equivalent regular mesh static three-dimensional analysis.

substr_umir_shell3d_sta.inp

User-mirrored substructure with large rotation motions, static, three-dimensional analysis.

nosubstr_umir_shell3d_sta.inp

Equivalent regular mesh static three-dimensional analysis.

substr_user_shell3d_gen.inp

Substructure generation file referenced in files substr_urot_shell3d_sta.inp and substr_umir_shell3d_sta.inp.

IV. Multi-level substructures in large rotations

Features tested

Multi-level substructures that undergo large rotations.

Problem description

Three levels of substructures are created for this particular analysis. The lowest level is a 2 × 2 mesh of CPE4 elements. The next level comprises two of the first-level substructures, and the third level is the actual structure. The use of unsorted retained degrees of freedom is tested during the creation levels. The loading and boundary conditions specified at the retained degrees of freedom are such that elastic small-strain-inducing defomations occur in addition to the large rotations of the substructure. A second identical mesh is defined without substructures and the results are compared.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_multi_solid2d_gen1.inp

Lowest level substructure generation file.

substr_multi_solid2d_gen2.inp

Second level substructure generation file.

substr_multi_solid2d_gen3.inp

Third level substructure generation file.

substr_multi_solid2d_sta.inp

Large rotations, static, two-dimensional analysis.

nosubstr_multi_solid2d_sta.inp

Large rotations, static, two-dimensional analysis without substructures.

V. Substructures and gravity loads

Features tested

Substructures subjected to fixed direction gravity loads.

Problem description

A rectangular substructure is formed. A gravity load is then applied by accounting for the substructure's gravity load vectors during generation and by specifying a distributed load type GRAV at the substructure usage level. The loading is such that the substructure undergoes large rotations. An equivalent regular mesh is also created, and the results are compared.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_grav_solid2d_sta.inp

Large rotations, gravity-loaded, static, two-dimensional analysis using substructures.

substr_grav_solid2d_dyn.inp

Large rotations, gravity-loaded, direct-integration implicit dynamic, two-dimensional analysis using substructures.

substr_grav_solid2d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_grav_solid2d_sta.inp

Large rotations, gravity-loaded, static, two-dimensional analysis without substructures.

nosubstr_grav_solid2d_dyn.inp

Large rotations, gravity-loaded, direct-integration implicit dynamic, two-dimensional analysis without substructures.

substr_grav_shell3d_sta.inp

Large rotations, gravity-loaded, static, three-dimensional analysis using substructures.

substr_grav_shell3d_dyn.inp

Large rotations, gravity-loaded, direct-integration implicit dynamic, three-dimensional analysis using substructures.

substr_grav_shell3d_gen.inp

Substructure generation file referenced in the two files above.

nosubstr_grav_shell3d_sta.inp

Large rotations, gravity-loaded, static, three-dimensional analysis without substructures.

nosubstr_grav_shell3d_dyn.inp

Large rotations, gravity-loaded, direct-integration implicit dynamic, three-dimensional analysis without substructures.

VI. Substructures, connector elements, Coupling constraints, and rigid body constraints

Features tested

Multiple substructures connected with connector elements and coupling constraints in large motions. Substructures included in a rigid body constraint in large rotations. How to switch quickly from a rigid body model of a part to a small-strain large-motion representation of the same part.

Problem description

The common 4-bar mechanism is analyzed (see Overconstraint checks, Section 35.6.1 of the Abaqus Analysis User's Guide). The two-dimensional rigid bodies are meshed using CPE4 elements. The coupling constraints are used to attach connection nodes to the ends of each bar, and connector elements are used to enforce the appropriate kinematic constraints between the bars. The bars are gravity loaded, and the mechanism is driven by prescribing the available components of relative motion in connector elements. Since the four bars are identical in shape, only one substructure is generated. The substructure is then translated, mirrored, and rotated at the usage level to create four copies of the substructure in the appropriate locations. Results from both static and direct-integration implicit dynamic analyses are verified against equivalent analyses that do not use substructures.

In addition, at the usage level one of the substructures is turned into a rigid part. The attached input files illustrate how one can very efficiently switch from a rigid (faster to run) model (substr_4barrb_solid2d_sta.inp and nosubstr_4barrb_solid2d_sta.inp) to a small-deformation large-rotations efficient subtructure representation of the same model (substr_4bar_solid2d_sta.inp). The substructure analysis is typically significantly faster to run than the regular mesh models (nosubstr_4bar_solid2d_sta.inp).

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_4bar_solid2d_gen.inp

Substructure generation file for one bar in the mechanism.

substr_4bar_solid2d_sta.inp

Static analysis of the gravity-loaded 4-bar mechanism using substructures.

substr_4barrb_solid2d_sta.inp

Direct-integration implicit dynamic analysis of the 4-bar multibody with one substructure included in a rigid body definition.

nosubstr_4bar_solid2d_sta.inp

Static analysis of the gravity-loaded 4-bar mechanism without substructures.

nosubstr_4barrb_solid2d_sta.inp

Direct-integration implicit dynamic analysis of the 4-bar multibody using four separate rigid bodies and no substructures.

substr_4bar_solid2d_dyn.inp

Direct-integration implicit dynamic analysis of the gravity-loaded 4-bar multibody using substructures.

nosubstr_4bar_solid2d_dyn.inp

Direct-integration implicit dynamic analysis of the gravity-loaded 4-bar multibody without substructures.

VII. Substructures and contact

Features tested

Large rotation substructures and contact.

Problem description

A rectangular substructure is formed. The applied loads and boundary conditions are such that the substructure exhibits large rotations. After a 45° rotation, impact with a rigid surface occurs. Results are compared with results from an equivalent model without substructures.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_contact_solid3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis using substructures and contact.

substr_contact_solid3d_gen.inp

Substructure generation reference in the file above.

nosubstr_contact_solid3d_dyn.inp

Large rotations, direct-integration implicit dynamic, three-dimensional analysis without substructures and contact.

VIII. Miscellaneous tests

Features tested

Substructures with large rotations with multi-point constraints, model change, prescribed initial conditions, and restart analysis.

Problem description

Several input files are created to test various features with large rotation substructures. Results are compared with equivalent models that do not use substructures.

Results and discussion

All results in the substructure are nearly identical to the results in the regular mesh.

Input files

substr_misc_solid2d_gen.inp

Substructure generation referenced in the files below.

substr_misc_solid2d_dyn.inp

Direct-integration implicit dynamic, two-dimensional analysis using substructures, multi-point constraints, and initial conditions.

nosubstr_misc_solid2d_dyn.inp

Direct-integration implicit dynamic, two-dimensional analysis without substructures and *MPCs and initial conditions.

substr_misc_solid2d_res.inp

Restart analysis from substr_misc_solid2d_dyn.inp using substructure.

nosubstr_misc_solid2d_res.inp

Restart analysis from nosubstr_misc_solid2d_dyn.inp without substructures.

substr_misc_solid2d_modelch.inp

Model change analysis using substructures.

nosubstr_misc_solid2d_modelch.inp

Model change analysis without substructures.

substr_misc_beam_1node_gen.inp

Substructure generation referenced in the file below.

substr_misc_beam_1node.inp

One retained node analysis using substructures.

nosubstr_misc_beam_1node.inp

Equivalent analysis without substructures.

substr_misc_pert_gen.inp

Substructure generation referenced in the files below.

substr_misc_nlgrot_pert.inp

Perturbation step after a geometrically nonlinear static rotation.

substr_misc_urot_pert.inp

Perturbation step after a user-specified rotation.