3.9.2 Analysis of cyclic symmetric models

Product: ABAQUS/Standard  

Elements tested

B21    B22    B32   

C3D8R    C3D20    CPE4H    CPE4R    CPE8R    CPS4R    CPS8R   

DC2D4    DC2D8    DC3D8   

S4R    S8R    SC8R   

Features tested

Natural frequency extraction for two-dimensional and three-dimensional models that exhibit cyclic symmetry.

Element-based and node-based cyclic symmetric surface definitions on matched and mismatched meshes.

Use of *MPC and *TRANSFORM with *CYCLIC SYMMETRY MODEL.

Application of preload prior to natural frequency extraction.

Modal-based steady-state dynamic analysis for models that exhibit cyclic symmetry.

Heat transfer analysis for models that exhibit cyclic symmetry.

Problem description

The models consist of 1 × 2 and 2 × 2 element meshes. There are no boundary conditions and loads, except for preload tests. Preloading of the model is done with both concentrated and distributed loads and for heat transfer analysis with temperature assigned to the chosen set of nodes.

Results and discussion

The results for the natural frequency extraction of the cyclic symmetric models are the same as those obtained for a corresponding 360° model.

Input files

Beam elements

cyclicsym_b21_nn.inp

Two-element mesh with node-type slave surface and node-type master surface.

cyclicsym_b21_360.inp

Full model corresponding to two-element mesh of B21 elements.

cyclicsym_b22_nn.inp

Single-element mesh with node-type slave surface and node-type master surface.

cyclicsym_b22_360.inp

Full model corresponding to single-element mesh of B22 elements.

cyclicsym_b31_nn.inp

Single-element mesh with node-type slave surface and node-type master surface.

cyclicsym_b31_360.inp

Full model corresponding to single-element mesh of B31 elements.

cyclicsym_b32_nn.inp

Single-element mesh with node-type slave surface and node-type master surface.

cyclicsym_b32_360.inp

Full model corresponding to single-element mesh of B32 elements.

Continuum elements

cyclicsym_c3d8r_ee.inp

1 × 2 mesh with element-type slave surface and element-type master surface.

cyclicsym_c3d8r_en.inp

1 × 2 mesh with element-type slave surface and node-type master surface.

cyclicsym_c3d8r_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface.

cyclicsym_c3d8r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_c3d8r_360.inp

Full model corresponding to 1 × 2 mesh of C3D8R elements.

cyclicsym_c3d8r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_c3d8r_360_ref.inp

Full model corresponding to 2 × 2 mesh of C3D8R elements.

cyclicsym_c3d8r_mis_map_ee.inp

2 × 2 mismatched mesh with element-type slave surface and element-type master surface.

cyclicsym_c3d8r_mis_map_ne.inp

2 × 2 mismatched mesh with node-type slave surface and element-type master surface.

cyclicsym_c3d8r_mis_map_360.inp

Full model corresponding to 2 × 2 mismatched mesh of C3D8R elements.

cyclicsym_c3d20_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface.

cyclicsym_c3d20_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_c3d20_360.inp

Full model corresponding to 1 × 2 mesh of C3D20 elements.

cyclicsym_c3d20_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_c3d20_360_ref.inp

Full model corresponding to 2 × 2 mesh of C3D20 elements.

cyclicsym_cpe4h_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cpe4h_360.inp

Full model corresponding to 1 × 2 mesh of CPE4H elements.

cyclicsym_cpe4r_ee.inp

1 × 2 mesh with element-type slave surface and element-type master surface.

cyclicsym_cpe4r_en.inp

1 × 2 mesh with element-type slave surface and node-type master surface.

cyclicsym_cpe4r_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface type.

cyclicsym_cpe4r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cpe4r_360.inp

Full model corresponding to 1 × 2 mesh of CPE4R elements.

cyclicsym_cpe4r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cpe4r_360_ref.inp

Full model corresponding to 2 × 2 mesh of CPE4R elements.

cyclicsym_cpe4r_mis_map_ee.inp

2 × 2 mismatched mesh with element-type slave surface and element-type master surface.

cyclicsym_cpe4r_mis_map_ne.inp

2 × 2 mismatched mesh with node-type slave surface and element-type master surface type.

cyclicsym_cpe4r_mis_map_360.inp

Full model corresponding to 2 × 2 mismatched mesh of CPE4R elements.

cyclicsym_cpe8r_ee.inp

1 × 2 mesh with element-type slave surface and element-type master surface.

cyclicsym_cpe8r_en.inp

1 × 2 mesh with element-type slave surface and node-type master surface.

cyclicsym_cpe8r_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface.

cyclicsym_cpe8r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cpe8r_360.inp

Full model corresponding to 1 × 2 mesh of CPE8R elements.

cyclicsym_cpe8r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cpe8r_360_ref.inp

Full model corresponding to 2 × 2 mesh of CPE8R elements.

cyclicsym_cps4r_ee.inp

1 × 2 mesh with element-type slave surface and element-type master surface.

cyclicsym_cps4r_en.inp

1 × 2 mesh with element-type slave surface and node-type master surface.

cyclicsym_cps4r_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface.

cyclicsym_cps4r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cps4r_360.inp

Full model corresponding to 1 × 2 mesh of CPS4R elements.

cyclicsym_cps4r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cps4r_360_ref.inp

Full model corresponding to 2 × 2 mesh of CPS4R elements.

cyclicsym_cps4r_mis_map_ee.inp

2 × 2 mismatched mesh with element-type slave surface and element-type master surface.

cyclicsym_cps4r_mis_map_ne.inp

2 × 2 mismatched mesh with node-type slave surface and element-type master surface type.

cyclicsym_cps4r_mis_map_360.inp

Full model corresponding to 2 × 2 mismatched mesh of CPS4R elements.

cyclicsym_cps8r_ee.inp

1 × 2 mesh with element-type slave surface and element-type master surface.

cyclicsym_cps8r_en.inp

1 × 2 mesh with element-type slave surface and node-type master surface.

cyclicsym_cps8r_ne.inp

1 × 2 mesh with node-type slave surface and element-type master surface.

cyclicsym_cps8r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cps8r_360.inp

Full model corresponding to 1 × 2 mesh of CPS8R elements.

cyclicsym_cps8r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_cps8r_360_ref.inp

Full model corresponding to 2 × 2 mesh of CPS8R elements.

Continuum shell elements

cyclicsym_sc8r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_sc8r_360.inp

Full model corresponding to 1 × 2 mesh of SC8R elements.

Shell elements

cyclicsym_s4r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_s4r_360.inp

Full model corresponding to 1 × 2 mesh of S4R elements.

cyclicsym_s4r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_s4r_360_ref.inp

Full model corresponding to 2 × 2 mesh of S4R elements.

cyclicsym_s4r_mis_map_ne.inp

2 × 2 mismatched mesh with node-type slave surface and element-type master surface.

cyclicsym_s4r_mis_map_360.inp

Full model corresponding to 12 × 2 mismatched mesh of S4R elements.

cyclicsym_s8r_nn.inp

1 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_s8r_360.inp

Full model corresponding to 1 × 2 mesh of S8R elements.

cyclicsym_s8r_nn_ref.inp

2 × 2 mesh with node-type slave surface and node-type master surface.

cyclicsym_s8r_360_ref.inp

Full model corresponding to 2 × 2 mesh of S8R elements.

Other features tested

cyclicsym_c3d8r_ee_cload_x.inp

Frequency extraction after a preloading step in which a *CLOAD is applied in the global x-direction.

cyclicsym_c3d8r_ee_cload_y.inp

Frequency extraction after a preloading step in which a *CLOAD is applied in the global y-direction.

cyclicsym_c3d8r_360_cload.inp

Full model corresponding to the application of a *CLOAD before frequency extraction.

cyclicsym_c3d8r_ee_dload.inp

Frequency extraction after a preloading step in which a *DLOAD is applied.

cyclicsym_c3d8r_360_dload.inp

Full model corresponding to the application of a *DLOAD before frequency extraction.

cyclicsym_c3d8r_nn_mpc.inp

Cyclic symmetric model with an *MPC option.

cyclicsym_c3d8r_360_mpc.inp

Full model corresponding to the use of an *MPC option.

cyclicsym_c3d8r_nn_single_node_x.inp

Cyclic symmetric model with a single node at one end and the cyclic symmetry axis parallel to the global x-axis.

cyclicsym_c3d8r_nn_single_node_y.inp

Cyclic symmetric model with a single node at one end and the cyclic symmetry axis parallel to the global y-axis.

cyclicsym_c3d8r_nn_single_node_z.inp

Cyclic symmetric model with a single node at one end and the cyclic symmetry axis parallel to the global z-axis.

cyclicsym_c3d8r_360_single_node.inp

Full model corresponding to the cyclic symmetric model with a single node at one end.

cyclicsym_c3d8r_nn_trans.inp

Cyclic symmetric model with a *TRANSFORM option.

cyclicsym_c3d8r_360_trans.inp

Full model corresponding to the use of a *TRANSFORM option.

cyclicsym_c3d8r_ss.inp

Cyclic symmetric model with a preloading step using the *VISCO option, frequency extraction, and steady-state modal-based dynamic analysis.

cyclicsym_c3d8r_360_ss.inp

Full model corresponding to the use of a preloading step with the *VISCO option, frequency extraction, and steady-state modal-based dynamic analysis.

cyclicsym_cpe4r_nn_basis.inp

Cyclic symmetric model with a static nonlinear step that forms the basis for the analysis in cyclicsym_cpe4r_nn_rezone.inp.

cyclicsym_cpe4r_nn_rezone.inp

Cyclic symmetric model with a frequency extraction step following the mapping of the solution from the analysis in cyclicsym_cpe4r_nn_basis.inp.

cyclicsym_cpe4r_360_basis.inp

Full model with a static nonlinear step that forms the basis for the analysis in cyclicsym_cpe4r_360_rezone.inp.

cyclicsym_cpe4r_360_rezone.inp

Full model with a frequency extraction step following the mapping of the solution from the analysis in cyclicsym_cpe4r_360_basis.inp.

cyclicsym_cpe4r_nn_multi_step.inp

Cyclic symmetric model with multiple frequency extraction steps.

cyclicsym_cpe4r_nn_restart.inp

Cyclic symmetric model with multiple frequency extraction steps performed as a restart analysis after the first step in the analysis in cyclicsym_cpe4r_nn_multi_step.inp.

cyclicsym_cps4r_nn_sub.inp

Cyclic symmetric model with the *SUBMODEL option.

cyclicsym_cps4r_nn_full.inp

Full cyclic symmetric model used in the analysis in cyclicsym_cps4r_nn_sub.inp.

cyclicsym_s4r_nn_mdl_change.inp

Cyclic symmetric model with the *MODEL CHANGE option.

cyclicsym_cpe4r_ss.inp

Cyclic symmetric model with a nonlinear preloading static step, frequency extraction, and modal-based steady-state dynamic analysis (one nodal diameter) using the *DLOAD and *DSLOAD options.

cyclicsym_cpe4r_360_ss.inp

Full model with a nonlinear preloading static step, frequency extraction, and modal-based steady-state dynamic analysis (one nodal diameter) using the *DLOAD and *DSLOAD options.

cyclicsym_cpe4r_ss2.inp

Cyclic symmetric model with frequency extraction and modal-based steady-state dynamic analysis (two nodal diameters) using the *DLOAD and *DSLOAD options.

cyclicsym_cpe4r_360_ss2.inp

Full model with frequency extraction and modal-based steady-state dynamic analysis (two nodal diameters) using the *DLOAD and *DSLOAD options.

cyclicsym_cpe4r_cl_ss.inp

Cyclic symmetric model with a nonlinear preloading static step, frequency extraction, and two modal-based steady-state dynamic analyses (one and two nodal diameters) using the *CLOAD, *DLOAD, and *TRANSFORM options.

cyclicsym_cpe4r_360_cl_ss.inp

Full model with a nonlinear preloading static step, frequency extraction, and two modal-based steady-state dynamic analyses (one and two nodal diameters) using the *CLOAD, *DLOAD, and *TRANSFORM options.

cyclicsym_dc2d4_mis_heat.inp

Cyclic symmetric model with a transient heat transfer analysis.

cyclicsym_dc2d4_mis_heat_360.inp

Full model with a transient heat transfer analysis.

cyclicsym_dc2d8_nn_heat.inp

Cyclic symmetric model with a steady-state heat transfer analysis.

cyclicsym_dc2d8_heat_360.inp

Full model with a steady-state heat transfer analysis.

cyclicsym_dc3d8_nn_heat.inp

Cyclic symmetric model with a steady-state heat transfer analysis.

cyclicsym_dc3d8_heat_360.inp

Full model with a steady-state heat transfer analysis.

cyclicsym_dcc2d4_nn_loads.inp

Cyclic symmetric model with all thermal loads (*FILM, *CFILM, *SFILM, *CFLUX, *DFLUX, *DSFLUX, *RADIATE, *CRADIATE, and *SRADIATE).

cyclicsym_dc2d4_heat_nonlin.inp

Cyclic symmetry model with a nonlinear heat transfer analysis.

cyclicsym_dc2d4_heat_nonlin_360.inp

Full model corresponding to nonlinear heat transfer analysis.

cyclicsym_dc2d4_mis_heat_ee.inp

Cyclic symmetry model with a heat transfer analysis. Mismatched mesh with element-type slave surface and element-type master surface.

cyclicsym_dc2d4_mis_heat_ne.inp

Cyclic symmetry model with a heat transfer analysis. Mismatched mesh with node-type slave surface and element-type master surface.

cyclicsym_dc2d4_mis_360.inp

Full model corresponding to mismatched mesh of DC2D4 elements.

cyclicsym_dc2d8_heat2D.inp

Cyclic symmetry model with a heat transfer analysis using DC2D8 elements.

cyclicsym_dc2d8_heat2D_360.inp

Full model corresponding to the heat transfer analysis using DC2D8 elements.

cyclicsym_dc3d8_heat_CFLUX.inp

Cyclic symmetry model with a heat transfer analysis (*CFLUX).

cyclicsym_dc3d8_heat_CFLUX_360.inp

Full model with a heat transfer analysis (*CFLUX).

cyclicsym_dc3d8_heat_DFLUX.inp

Cyclic symmetry model with a heat transfer analysis (*DFLUX).

cyclicsym_dc3d8_heat_DFLUX_360.inp

Full model with a heat transfer analysis (*DFLUX).

cyclicsym_dc3d8_heat_DSFLUX.inp

Cyclic symmetry model with a heat transfer analysis (*DSFLUX).

cyclicsym_dc3d8_heat_DSFLUX_360.inp

Full model with a heat transfer analysis (*DSFLUX).

cyclicsym_dc3d8_heat_FILM.inp

Cyclic symmetry model with a heat transfer analysis (*FILM).

cyclicsym_dc3d8_heat_FILM_360.inp

Full model with a heat transfer analysis (*FILM).

cyclicsym_dc3d8_heat_RAD.inp

Cyclic symmetry model with a heat transfer analysis (*RADIATE).

cyclicsym_dc3d8_heat_RAD_360.inp

Full model with a heat transfer analysis (*RADIATE).

cyclicsym_dc3d8_heat_SFILM.inp

Cyclic symmetry model with a heat transfer analysis (*SFILM).

cyclicsym_dc3d8_heat_SFILM_360.inp

Full model with a heat transfer analysis (*SFILM).

cyclicsym_dc3d8_heat_SRAD.inp

Cyclic symmetry model with a heat transfer analysis (*SRADIATE).

cyclicsym_dc3d8_heat_SRAD_360.inp

Full model with a heat transfer analysis (*SRADIATE).

cyclicsym_dc3d8_heat_XYZ.inp

Cyclic symmetry model with a heat transfer analysis. The symmetry axis is a linear combination of the X, Y, and Z axes.

cyclicsym_dc3d8_heat_XYZ_360.inp

Full model with a heat transfer analysis. The symmetry axis is a linear combination of the X, Y, and Z axes.

cyclicsym_dc3d8_heat_axisY.inp

Cyclic symmetry model with a heat transfer analysis. The symmetry axis is parallel to the Y-axis.

cyclicsym_dc3d8_heat_axisY_360.inp

Full model with a heat transfer analysis. The symmetry axis is parallel to the Y-axis.