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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)

Some recent additions are

  • *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