6. Examples

The test cases selected illustrate the different possible uses of discrete elements.

6.1. Mass elements

• Modeling a point mass M_T_D_N

  

  Fig. 6.1 Release with a simple spring weight.

  Test case:

  • SDLD34 [V2.01.034]

  • Modelling:

    • SDLD34A DIS_T/M_T_D_N

    • SDLD34B DIS_T/M_T_D_N

• Modeling a rotating M_TR_D_N point

  

  Fig. 6.2 Frequency of a simplified shaft line with gyroscopy.

  Test case:

  • SDLL123 [V2.02.123]

  • Modelling:

    • SDLL123A DIS_TR/M_TR_D_N

    • SDLL123B DIS_TR/M_TR_D_N

    • SDLL123C DIS_TR/M_TR_D_N

    • SDLL123D DIS_TR/M_TR_D_N

    • SDLL123E DIS_TR/M_TR_D_N

    • SDLL123F DIS_TR/M_TR_D_N

• Eccentric mass modelling

  

  Fig. 6.3 Slender, free-embedded beam with eccentric mass or inertia.

  Test case:

  • SDLL15 [V2.02.015]

  • Modelling:

    • SDLL15A DIS_TR/M_TR_D_N

6.2. Stiffness elements

• Support stiffness modelling

  

  Fig. 6.4 Beam subject to a wind speed field.

  Test case:

  • SDNL102 [V5.02.102]

  • Modelling:

    • SDNL102A DIS_T/K_T_D_L

• Modeling of non-symmetric stiffness and damping matries

  

  Fig. 6.5 Harmonic response of a rotor with two disks and two non-symmetric bearings, subject to the gyroscopic effect.

  Test case:

  • SHLL103A [V2.06.103]

  • Modelling:

    • SHLL103A DIS_TR/K_TR_N/A_TR_N

• Modeling simple structural elements

  

  Fig. 6.6 Identification of fluid forces on a wire structure.

  Test case:

  • SDLS139A [V2.03.139]

  • Modelling:

    • SDLS139A DIS_TR/K_TR_D_N

• Modeling of distributed ground stiffness

  

  Fig. 6.7 Response of a rigid circular foundation to a seismic excitation that varies in space.

  Test case:

  • SDLS118 [V2.03.118]

  • Modelling:

    • SDLS118C DIS_TR/K_TR_D_N

    • SDLS118D DIS_TR/K_TR_D_N

• Modeling of distributed ground stiffness with detachment

  

  Fig. 6.8 Non-deformable plate on a spring mat.

  Test case:

  • SSNL130 [V6.02.130]

  • Modelling:

    • SSNL130A DIS_T/K_T_D_L

    • SSNL130B 2D_DIS_T/K_T_D_L

  Note:

  Use of the DIS_CHOC law

• Modeling a bolted assembly

  

  Fig. 6.9 Determination of the ruin loads of the console MEKELEC.

  Test case:

  • SSNL135 [V3.03.020]

  • Modelling:

    • SSNL135A DIS_TR

    • SSNL135B DIS_TR

    • SSNL135C DIS_TR

  Note:

  Each bolt is represented by a discrete element of zero length and its stiffness K_TR_D_L.

• Modeling a rotor crack

  

  

  Fig. 6.10 Rotating cracked rotor, subjected to a bending force.

  Test case:

  • SDNL133 [V5.02.133]

  • Modelling:

    • SDNL133A DIS_TR

  Note:

  See the documentation Instructions for implementing rotor calculations [U2.06.32].

6.3. Damping elements

The documentation for modeling mechanical damping is:

• [R5.05.04] Modeling damping in linear dynamics

• [U2.06.03] Mechanical damping modeling instructions

Viscous damping modelling

Fig. 6.11 Transient dynamic response of a harmonic oscillator with variable damping

Test case:

• SDLD321 [V2.01.321]

• Modelling:

  • SDLD321A DIS_T/K_T_D_L M_T_L A_T_D_L

  • SDLD321B DIS_T/K_T_D_L M_T_L A_T_D_L

  • SDLD321C DIS_T/K_T_D_L M_T_L A_T_D_L

Hysteretic damping modelling

Fig. 6.12 2 degrees of freedom spring mass system with hysteretic damping

Test case:

• SDLD313 [V2.01.313]

• Modelling:

  • SDLD313A DIS_T/K_T_D_L M_T_L

6.4. Other uses

6.4.1. Charging application or point boundary conditions.

• Cracked cylinder under multiple loads

  

  Fig. 6.13 Cracked cylinder under multiple loads

  Test case:

  • SSNV166 [V6.04.166]

  • Modelling: zero stiffness and mass

    • SSNV166A DIS_TR/K_TR_D_N M_TR_D_N

    • SSNV166B DIS_TR/K_TR_D_N M_TR_D_N

    • SSNV166C DIS_TR/K_TR_D_N M_TR_D_N

  In this 3D model, a loading of torsional and flexure is applied to the upper face of the cylinder via a POI1 mesh and a LIAISON_ELEM connection.

• Dynamic response of a free-standing recessed pipe girder.

  

  Fig. 6.14 Dynamic response of a free-standing recessed pipe girder.

  Test case:

  • SDLL135 [V2.02.135]

  • Modelling: zero stiffness and mass

    • SDLL135F DIS_TR/K_TR_D_N M_TR_D_N

  In this model DKT, the nodes located in section A are linked (LIAISON_ELEM) to a discrete element DIS_TR (dot type mesh POI1 located in A) with 6 degrees of freedom, which is totally fixed to it.

• Modeling a model made up of nodes for the projection of results

  

  Fig. 6.15 Simulation of a strain gauge using the OBSERVATION command.

  Test case:

  • SDLV131 [V2.04.131]

  • Modelling: zero stiffness and mass

    • SDLV131A DIS_T

    • SDLV131B DIS_T

    • SDLV131C DIS_T

    • SDLV131D DIS_T

6.4.2. Creation of a numerical model for the comparison of experimental results.

• SDLS112B: Extrapolation of measurements on a 2D model (GARTEUR test)

• SDLV122A: Extrapolation of local measurements onto a complete (3D) model [V2.04.122].

• SDLD104A /B: Extrapolation of local measurements on a complete (discrete) model.

Taking into account the contact (via operator DEFI_CONTACT) between two POI1 meshes of zero stiffness.

Fig. 6.16 Embedded plate subjected to bending by beams in contact with the free edge.

Test case:

• SSNL107 [V2.04.131]

• Modelling:

  • SSNL107A DIS_TR

  • SSNL107B DIS_TR

  • SSNL107C DIS_TR