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What is the difference between a discrete beam and a spring ?

A discrete beam (beam formulation 6) has up to 6 degrees-of-freedom (DOF) whereas a spring `*ELEMENT_DISCRETE` has only one DOF. Resultant forces and moments of a discrete beqm are output in the local (r,s,t) coordinate system. This is true of the d3plot, d3thdt, and elout databases.

The length of a discrete beam may be zero or nonzero. A nonzero value of volume (VOL in `*section_beam`) must be provided. The mass of the discrete beam is not related to its length but is the product of the material density and VOL. INER is the mass moment of inertia of the beam about each of its three axes. A nonzero value of INER is required if any of the rotational DOF of the beam are activated. The values CA and OFFSET apply only to cables `*MAT_CABLE_DISCRETE_BEAM`.

Materials that apply to discrete beams are

• `*mat_66` (`*mat_linear_elastic_discrete_beam`)
• `*mat_67` (`*mat_nonlinear_elastic_discrete_beam`)
• `*mat_68` (`*mat_nonlinear_plastic_discrete_beam`)
• `*mat_69` (`*mat_sid_damper_discrete_beam`)
• `*mat_70` (`*mat_hydraulic_gas_damper_discrete_beam`)
• `*mat_71` (`*mat_cable_discrete_beam`)

• `*mat_74` (`*mat_elastic_spring_discrete_beam`)
• `*mat_93` (`*mat_elastic_6dof__spring_discrete_beam`) requires also `*mat_74`
• `*mat_94` (`*mat_inelastic_spring_discrete_beam`)
• `*mat_95` (`*mat_inelastic_6dof__spring_discrete_beam`) requires also `*mat_94`
• `*mat_97` (`*mat_general_joint_discrete_beam`)
• `*mat_119` (`*mat_general_nonlinear_6dof_discrete_beam`)
• `*mat_121` (`*mat_general_nonlinear_1dof_discrete_beam`)
• `*mat_146` (`*mat_1dof_generalized_spring`)
• `*mat_196` (`*mat_general_spring_discrete_beam`) alternative to mats 74,93,94,95
• `*mat_197` (`*mat_seismic_isolator`)

Orientation of a discrete beam is controlled by the values of SCOOR, CID, RRCON, SRCON, and TRCON provided in `*section_beam`.

If the discrete beam is initially of zero length, permissible values of SCOOR are -3, -1, 0, 1, or 3. If SCOOR is -3 or 3, a shear force developed by the finite beams as a result of shear stiffness will produce a beam torque contribution equal to `(shear force * beam length)/2` which is not accounted for by the beam rotational stiffness alone. This torque contribution is necessary to give realistic beam-like behavior. If SCOOR is -1, 0, or 1, equilibrating torques are NOT developed. Thus, to avoid nonphysical rotational constraints on the structure, SCOOR = -3 or 3 is generally recommended. In rare nstances, SCOOR = -1, 0, or 1 may be preferred for discrete beams which otherwise become unstable or which remain very close to zero length throughout the simulation. CID defines the initial orientation of the local (r,s,t) system. If CID = 0, the initial r,s,t directions are aligned with the global X,Y,Z directions, respectively.

If the discrete beam is of finite length, SCOOR should be set to -3, -2, 2, or 3 so that torque contributions develop due to shear forces as in a real beam (see explanation in above paragraph). CID defines the initial orientation of the local (r,s,t) system. If CID = 0, the initial r,s,t directions are aligned with the global X,Y,Z directions, respectively, unless a third node N3 is defined in the beam connectivity. In the case where a third node is defined, the three beam nodes N1, N2, and N3 determine the initial orientation of the beam local system. See the example for an illustration of the effect of SCOOR on finite length discrete beams.

Discrete Beam Local System Update:

RRCON, SRCON, and TRCON may be used to fix any or all of the 3 local directions. The default is that the local directions are updated, not fixed.

If RRCON, SRCON, and TRCON are zero (not fixed), the local system is updated based on the angular velocity of node1, node2, or the average of the two (SCOOR says which). The exception is if the coordinate system identified by CID uses `*define_coordinate_nodes` with FLAG=1. In that case, the beam local system is updated based on the current orientation of the three nodes identified in *define_coordinate_nodes. If SCOOR is set to -2 or 2, a final adjustment is made to the local system so that the r-axis lies along the axis of the beam (node1 to node2).

Orientation of `*element_discrete` (not to be confused with a discrete beam) is controlled by the parameter VID.

If VID = 0 (preferred), the line-of-action of the element remains along the node1 to node2 direction throughout the calculation. If a different orientation is desired, we recommend using a discrete beam with SCOOR set to -3,-2, 2, or 3.

If VID > 0 (NOT recommended owing to the likelihood of developing unwanted rotational constraint), IOP in `*define_sd_orientation` determines the method by which the element orientation is determined. If IOP=0 or 1, the orientation is permanently fixed in space. If IOP=2 or 3, the orientation is updated as the two elements nodes move in space. Further details of `*define_sd_orientation` are provided in the User's Manual.

Remarks on deformable spotweld beams:

For a type 9 beam (spotweld), the User's Manual states that N3 is optional if the section is non-circular. This is a typographical mistake. The correct usage is that N3 is optional if the section is circular; otherwise N3 is required. If the section is circular and N3 is not given (which is permitted), the s and t directions are arbitrary. Thus if you want s and t directions to be known, N3 must be provided. If automatic spotweld generation is used (N2=0), circular sections must be used and the s and t directions remain arbitrary (N3 cannot be assigned).

The following input deck demonstrates use of discrete beams:

`*KEYWORD \$ SCOOR=0,1 >> spring-like behavior (no moments) \$ SCOOR=2,3 >> beam-like behavior *part discrete beams 66,66,66 *mat_linear_elastic_discrete_beam 66,1.e-8, 10000,10000,10000 *section_beam \$        SCOOR 66,6,,,,     2 \$66,6,,,,     0 100,,,,,  0,0,0 *element_beam 1,66,268,304 2,66,269,305 3,66,274,310 4,66,275,311 \$*ELEMENT_BEAM                                                                    \$\$       1     100     213     123     218                                         \$       1     100     213     123   *TITLE SPOTWELD MATERIAL                                                        *CONTROL_structured *CONTROL_TERMINATION \$   ENDTIM    ENDCYC     DTMIN    ENDNEG    ENDMAS   .100E-01         0      .000      .000      .000 *CONTROL_TIMESTEP \$   DTINIT      SCFT      ISDO    TSLIMT      DTMS      LCTM     ERODE     MS1ST       .000      .900         0 *CONTROL_HOURGLASS \$      IHQ        QH          8       *CONTROL_CONTACT \$   SLSFAC    RWPNAL    ISLCHK    SHLTHK    PENOPT    THKCHG     ORIEN       .100                   1         1                             1 \$   USRSTR    USRFAC     NSBCS    INTERM     XPENE          0         0         0         0       *DATABASE_BINARY_D3PLOT \$  DT/CYCL      LCDT    NOBEAM   .500E-03 *DATABASE_EXTENT_BINARY                                        1 *PART                                                                            spotweld beams \$      PID       SID       MID     EOSID      HGID      GRAV    ADPOPT      TMID        100       100       100                                                   *PART                                                                            shells \$      PID       SID       MID     EOSID      HGID      GRAV    ADPOPT      TMID          1         1         1                                                   *PART                                                                            shells \$      PID       SID       MID     EOSID      HGID      GRAV    ADPOPT      TMID          2         1         1                                                   *MAT_ELASTIC \$        i         f         f         f         f         f         f \$      mid        ro         e        pr        da        db         k          1   1.00e-8  100000.0     0.300 *MAT_SPOTWELD        100   1.00e-7  1.00e+08     0.300   1.00e+3   1.00e+6   1.00e-4 \$       .05   0.00E+0                                          .2 \$*CONTACT_spotweld *CONTACT_tied_shell_edge_to_surface \$*CONTACT_tied_shell_edge_to_surface_offset        100       200         3         2  *set_part 200 1,2 *SECTION_BEAM                                                                    \$      SID    ELFORM      SHRF   QR/IRID       CST                                      100         9                             1                     \$      TS1       TS2       TT1       TT2     NSLOC     NTLOC                     \$       2.0       2.0       2.0       2.0                                            2,2 *SECTION_SHELL \$        i         i         f         f         f         f         i \$      sid    elform      shrf       nip     propt   qr/irid     icomp          1        16   0.83333       2.0       3.0 \$        f         f         f         f         f \$       t1        t2        t3        t4      nloc        2.0       2.0       2.0       2.0 *NODE                                                                            \$   NODE               X               Y               Z      TC      RC              123  .600000000E+02  .200000000E+02  .000000000E+00                              213  .600000000E+02  .200000000E+02  .200000000E+01                              218  .700000000E+02  .200000000E+02  .200000000E+01                              236  .400000000E+02  .400000000E+02  .000000000E+00                              237  .400000000E+02  .320000000E+02  .000000000E+00                              238  .400000000E+02  .240000000E+02  .000000000E+00                              239  .400000000E+02  .160000000E+02  .000000000E+00                              240  .400000000E+02  .800000000E+01  .000000000E+00                              241  .400000000E+02  .000000000E+00  .000000000E+00                              242  .200000000E+02  .400000000E+02  .000000000E+00                              243  .200000000E+02  .320000000E+02  .000000000E+00                              244  .200000000E+02  .240000000E+02  .000000000E+00                              245  .200000000E+02  .160000000E+02  .000000000E+00                              246  .200000000E+02  .800000000E+01  .000000000E+00                              247  .200000000E+02  .000000000E+00  .000000000E+00                              248  .000000000E+00  .400000000E+02  .000000000E+00                              249  .000000000E+00  .320000000E+02  .000000000E+00                              250  .000000000E+00  .240000000E+02  .000000000E+00                              251  .000000000E+00  .160000000E+02  .000000000E+00                              252  .000000000E+00  .800000000E+01  .000000000E+00                              253  .000000000E+00  .000000000E+00  .000000000E+00                              254  .800000000E+02  .400000000E+02  .000000000E+00                              255  .800000000E+02  .320000000E+02  .000000000E+00                              256  .800000000E+02  .240000000E+02  .000000000E+00                              257  .800000000E+02  .160000000E+02  .000000000E+00                              258  .800000000E+02  .800000000E+01  .000000000E+00                              259  .800000000E+02  .000000000E+00  .000000000E+00                              260  .720000000E+02  .400000000E+02  .000000000E+00                              261  .720000000E+02  .320000000E+02  .000000000E+00                              262  .720000000E+02  .240000000E+02  .000000000E+00                              263  .720000000E+02  .160000000E+02  .000000000E+00                              264  .720000000E+02  .800000000E+01  .000000000E+00                              265  .720000000E+02  .000000000E+00  .000000000E+00                              266  .640000000E+02  .400000000E+02  .000000000E+00                              267  .640000000E+02  .320000000E+02  .000000000E+00                              268  .640000000E+02  .240000000E+02  .000000000E+00                              269  .640000000E+02  .160000000E+02  .000000000E+00                              270  .640000000E+02  .800000000E+01  .000000000E+00                              271  .640000000E+02  .000000000E+00  .000000000E+00                              272  .560000000E+02  .400000000E+02  .000000000E+00                              273  .560000000E+02  .320000000E+02  .000000000E+00                              274  .560000000E+02  .240000000E+02  .000000000E+00                              275  .560000000E+02  .160000000E+02  .000000000E+00                              276  .560000000E+02  .800000000E+01  .000000000E+00                              277  .560000000E+02  .000000000E+00  .000000000E+00                              278  .480000000E+02  .400000000E+02  .000000000E+00                              279  .480000000E+02  .320000000E+02  .000000000E+00                              280  .480000000E+02  .240000000E+02  .000000000E+00                              281  .480000000E+02  .160000000E+02  .000000000E+00                              282  .480000000E+02  .800000000E+01  .000000000E+00                              283  .480000000E+02  .000000000E+00  .000000000E+00                              290  .800000000E+02  .400000000E+02  .200000000E+01                              291  .800000000E+02  .320000000E+02  .200000000E+01                              292  .800000000E+02  .240000000E+02  .200000000E+01                              293  .800000000E+02  .160000000E+02  .200000000E+01                              294  .800000000E+02  .800000000E+01  .200000000E+01                              295  .800000000E+02  .000000000E+00  .200000000E+01                              296  .720000000E+02  .400000000E+02  .200000000E+01                              297  .720000000E+02  .320000000E+02  .200000000E+01                              298  .720000000E+02  .240000000E+02  .200000000E+01                              299  .720000000E+02  .160000000E+02  .200000000E+01                              300  .720000000E+02  .800000000E+01  .200000000E+01                              301  .720000000E+02  .000000000E+00  .200000000E+01                              302  .640000000E+02  .400000000E+02  .200000000E+01                              303  .640000000E+02  .320000000E+02  .200000000E+01                              304  .640000000E+02  .240000000E+02  .200000000E+01                              305  .640000000E+02  .160000000E+02  .200000000E+01                              306  .640000000E+02  .800000000E+01  .200000000E+01                              307  .640000000E+02  .000000000E+00  .200000000E+01                              308  .560000000E+02  .400000000E+02  .200000000E+01                              309  .560000000E+02  .320000000E+02  .200000000E+01                              310  .560000000E+02  .240000000E+02  .200000000E+01                              311  .560000000E+02  .160000000E+02  .200000000E+01                              312  .560000000E+02  .800000000E+01  .200000000E+01                              313  .560000000E+02  .000000000E+00  .200000000E+01                              314  .480000000E+02  .400000000E+02  .200000000E+01                              315  .480000000E+02  .320000000E+02  .200000000E+01                              316  .480000000E+02  .240000000E+02  .200000000E+01                              317  .480000000E+02  .160000000E+02  .200000000E+01                              318  .480000000E+02  .800000000E+01  .200000000E+01                              319  .480000000E+02  .000000000E+00  .200000000E+01                              320  .400000000E+02  .400000000E+02  .200000000E+01                              321  .400000000E+02  .320000000E+02  .200000000E+01                              322  .400000000E+02  .240000000E+02  .200000000E+01                              323  .400000000E+02  .160000000E+02  .200000000E+01                              324  .400000000E+02  .800000000E+01  .200000000E+01                              325  .400000000E+02  .000000000E+00  .200000000E+01                              326  .120000000E+03  .400000000E+02  .200000000E+01                              327  .120000000E+03  .320000000E+02  .200000000E+01                              328  .120000000E+03  .240000000E+02  .200000000E+01                              329  .120000000E+03  .160000000E+02  .200000000E+01                              330  .120000000E+03  .800000000E+01  .200000000E+01                              331  .120000000E+03  .000000000E+00  .200000000E+01                              332  .100000000E+03  .400000000E+02  .200000000E+01                              333  .100000000E+03  .320000000E+02  .200000000E+01                              334  .100000000E+03  .240000000E+02  .200000000E+01                              335  .100000000E+03  .160000000E+02  .200000000E+01                              336  .100000000E+03  .800000000E+01  .200000000E+01                              337  .100000000E+03  .000000000E+00  .200000000E+01                         *ELEMENT_SHELL                                                                   \$    EID     PID      N1      N2      N3      N4                                      101       1     236     242     243     237                                      102       1     237     243     244     238                                      103       1     238     244     245     239                                      104       1     239     245     246     240                                      105       1     240     246     247     241                                      106       1     242     248     249     243                                      107       1     243     249     250     244                                      108       1     244     250     251     245                                      109       1     245     251     252     246                                      110       1     246     252     253     247                                      111       1     254     260     261     255                                      112       1     255     261     262     256                                      113       1     256     262     263     257                                      114       1     257     263     264     258                                      115       1     258     264     265     259                                      116       1     260     266     267     261                                      117       1     261     267     268     262                                      118       1     262     268     269     263                                      119       1     263     269     270     264                                      120       1     264     270     271     265                                      121       1     266     272     273     267                                      122       1     267     273     274     268                                      123       1     268     274     275     269                                      124       1     269     275     276     270                                      125       1     270     276     277     271                                      126       1     272     278     279     273                                      127       1     273     279     280     274                                      128       1     274     280     281     275                                      129       1     275     281     282     276                                      130       1     276     282     283     277                                      131       1     278     236     237     279                                      132       1     279     237     238     280                                      133       1     280     238     239     281                                      134       1     281     239     240     282                                      135       1     282     240     241     283                                      201       2     290     296     297     291                                      202       2     291     297     298     292                                      203       2     292     298     299     293                                      204       2     293     299     300     294                                      205       2     294     300     301     295                                      206       2     296     302     303     297                                      207       2     297     303     304     298                                      208       2     298     304     305     299                                      209       2     299     305     306     300                                      210       2     300     306     307     301                                      211       2     302     308     309     303                                      212       2     303     309     310     304                                      213       2     304     310     311     305                                      214       2     305     311     312     306                                      215       2     306     312     313     307                                      216       2     308     314     315     309                                      217       2     309     315     316     310                                      218       2     310     316     317     311                                      219       2     311     317     318     312                                      220       2     312     318     319     313                                      221       2     314     320     321     315                                      222       2     315     321     322     316                                      223       2     316     322     323     317                                      224       2     317     323     324     318                                      225       2     318     324     325     319                                      226       2     326     332     333     327                                      227       2     327     333     334     328                                      228       2     328     334     335     329                                      229       2     329     335     336     330                                      230       2     330     336     337     331                                      231       2     332     290     291     333                                      232       2     333     291     292     334                                      233       2     334     292     293     335                                      234       2     335     293     294     336                                      235       2     336     294     295     337                                 *SET_NODE_LIST                                                                   \$      SID       DA1       DA2       DA3       DA4                                        1                                                                       \$     NID1      NID2      NID3      NID4      NID5      NID6      NID7      NID8        326       327       328       329       330       331                     *BOUNDARY_SPC_NODE                                                               \$ NID/NSID       CID      DOFX      DOFY      DOFZ     DOFRX     DOFRY     DOFRZ        248         0         1         1         1         0         0         0        249         0         1         1         1         0         0         0        250         0         1         1         1         0         0         0        251         0         1         1         1         0         0         0        252         0         1         1         1         0         0         0        253         0         1         1         1         0         0         0        326         0         0         1         1         0         0         0        327         0         0         1         1         0         0         0        328         0         0         1         1         0         0         0        329         0         0         1         1         0         0         0        330         0         0         1         1         0         0         0        331         0         0         1         1         0         0         0 *DEFINE_CURVE \$        i         i         f         f         f         f \$     lcid      sidr      scla      sclo      offa      offo          1 \$                  f                   f \$           abscissa            ordinate               0.0000                 0.0               0.0200                40.0 *BOUNDARY_PRESCRIBED_MOTION_SET \$        i         i         i         i         f         i \$      nid       dof       vad      lcid        sf       vid          1         1         2         1       0.5         0 *END`