/PROP/TYPE12 (SPR_PUL)

Block Format Keyword The pulley spring property set (with one translational DOF) is used to model a pulley.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/PROP/TYPE12/prop_ID/unit_ID or /PROP/SPR_PUL/prop_ID/unit_ID
prop_title
Mass       sens_ID Isflag Ileng Fric
K1 C1 A1 B1 D1
fct_ID11 H1 fct_ID21 fct_ID31 fct_ID41   δmin1 δmax1
F1 E1 Ascale1 Hscale1    
fct_IDfr Ifr Yscale_F Xscale_F F_min F_max

Definitions

Field Contents SI Unit Example
prop_ID Property identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
prop_title Property title

(Character, maximum 100 characters)

 
Mass Mass.
If Ileng= 0
M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbaaaa@3730@
If Ileng= 1
M l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbGaey yXICTaamiBamaaBaaaleaacaaIWaaabeaaaaa@3B51@

(Real)

[ kg ] or [ kgm ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai GacUgacaGGNbGaeyyXICTaaiyBaaGaay5waiaaw2faaaaa@3D67@
sens_ID Sensor identifier.

(Integer)

 
Isflag Sensor flag. 4 5
=0
Spring element activated.
=1
Spring element deactivated.
=2
Spring element activated or deactivated.

(Integer)

 
Ileng Input per unit length flag.
= 0
Force in the spring is computed.
= 1
All input are per unit length.

(Integer)

 
Fric Coulomb friction. 6

(Real)

 
K1 Stiffness K MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbaaaa@372E@ with Ileng= 0.
If fct_ID11= 0
Stiffness for linear spring.
If fct_ID11≠ 0
Unloading stiffness for nonlinear spring.

(Real)

[ N s ]
Stiffness K l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai aadUeaaeaacaWGSbWaaSbaaSqaaiaaicdaaeqaaaaaaaa@3915@ with Ileng= 1.
If fct_ID11= 0
Stiffness for linear spring.
If fct_ID11≠ 0
Unloading stiffness for nonlinear spring.

(Real)

[ N ms ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaam aalaaabaGaaiOtaaqaaiGac2gacqGHflY1caGGZbaaaaGaay5waiaa w2faaaaa@3D66@
C1 Damping C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbaaaa@372E@ with Ileng= 0.

(Real)

[ Ns m ]
Damping C l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai aadUeaaeaacaWGSbWaaSbaaSqaaiaaicdaaeqaaaaaaaa@3915@ with Ileng= 1.

(Real)

[ Ns ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai aac6eacaGGZbaacaGLBbGaayzxaaaaaa@3A19@
A1 Coefficient for strain rate effect in tension (homogeneous to a force).

Default = 1.0 (Real)

[ N ]
B1 Logarithmic coefficient for strain rate effect in tension (homogeneous to a force).

(Real)

[ N ]
D1 Scale coefficients for elongation velocity.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
fct_ID11 Stiffness function identifier defining f ( δ ) with Ileng= 0 or f ( ε ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGMbWaae WaaeaacqaH1oqzaiaawIcacaGLPaaaaaa@3A7A@ with Ileng= 1.
= 0
Linear spring.

(Integer)

 
H1 Hardening flag for nonlinear spring.
= 0
Nonlinear elastic spring.
= 1
Nonlinear elastic plastic spring with isotropic hardening.
= 2
Nonlinear elasto-plastic spring with decoupled hardening in tension.
= 4
Nonlinear elastic plastic spring with “kinematic” hardening.
= 5
Nonlinear elasto-plastic spring with nonlinear unloading.
= 6
Nonlinear elasto-plastic spring with isotropic hardening + nonlinear unloading.
= 7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID21 Function defining the change in force with spring displacement (or rotation) rate in g ( δ ˙ ) with Ileng= 0 or g ( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGNbWaae WaaeaacuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@3A84@ with Ileng=1.

(Integer)

 
fct_ID31 Function used only for unloading.

If H1=4: Function identifier defining lower yield curve.

If H1=5: Function identifier defining residual displacement vs maximum displacement.

If H1=6: Function identifier defining nonlinear unloading curve.

If H1=7: Function identifier defining nonlinear unloading curve.

(Integer)

 
fct_ID41 Function to consider velocity or deformation velocity dependency damping in h ( δ ˙ ) with Ileng= 0 or h( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGObWaae WaaeaacuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@3A85@ with Ileng=1.

(Integer)

 
δ min 1 Negative failure displacement (if Ileng=0), or

Negative failure displacement multiply l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGSbWaaSbaaSqaaiaaicdaaeqaaaaa@3AAE@ if Ileng=1).

Default = -1030 (Real)

[ m ]
δ max 1 Positive failure displacement (if Ileng=0), or

Positive failure displacement multiply l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGSbWaaSbaaSqaaiaaicdaaeqaaaaa@3AAE@ if Ileng=1).

Default = 1030 (Real)

[ m ]
F1 Scale factor for δ or ε ˙ (abscissa of fct_ID21 function for g ( δ ˙ ) or g ( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGNbWaae WaaeaacuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@3A84@ ).

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
E1 Scale factor for g( δ ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGNbWaae WaaeaacuaH0oazgaGaaaGaayjkaiaawMcaaaaa@3A83@ or g( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGNbWaae WaaeaacuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@3A84@ (fct_ID21 function) which is coefficient for strain rate effect (homogeneous to a force).

(Real)

[ N ]
Ascale1 Scale factor for δ or ε (abscissa of fct_ID11 function for f ( δ ) or f ( ε ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGMbWaae WaaeaacqaH1oqzaiaawIcacaGLPaaaaaa@3A7A@ ).

(Real)

[ m ]
Hscale1 Scale factor for h ( δ ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGObWaae WaaeaacuaH0oazgaGaaaGaayjkaiaawMcaaaaa@3A83@ or h ( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGObWaae WaaeaacuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@3A85@ (fct_ID41 function) homogeneous to a force.

Default = 1.0 (Real)

 
fct_IDfr Function identifier defining scaling of friction coefficient Fric as function of force difference between left and right arms of the pulley.

(Integer)

 
Ifr Friction model flag. 6
=0 (Default)
Symmetrical friction model.
=1
Non-symmetrical friction model with limits.

(Integer)

 
Yscale_F Ordinate scale for function fct_IDfr.

Default = 1.0 (Real)

 
Xscale_F Abscissa scale for function fct_IDfr.

Default = 0.0 (Real)

[ N ]
F_min Negative limit force for non-reversible friction model.

Used only for Ifr = 1. 6

Default = -1030 (Real)

[ N ]
F_max Positive limit force for non-reversible friction model.

Used only for Ifr = 1. 6

Default = 1030 (Real)

[ N ]

Example

/UNIT/2
unit for prop
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/PROP/SPR_PUL/1/2
pulley spring example with friction
#               Mass                               sensor_ID    Isflag     Ileng                Fric
              2.7e-5                                       0         0         0                   1
#                  K                   C                   A                   B                   D
               10000                .001                   0                   0                   0
#funct_ID1         H funct_ID2 funct_ID3 funct_ID4                     delta_min           delta_max
         1         0         0         0         0                             0                   0
#            Fscale1                   E             Ascalex                  H4
                   0                   0                   0                   0
# Fct_IDfr       Ifr            Yscale_F            Xscale_F               F_MIN               F_MAX
         2         1                   0                   0                -800                4500
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
non-linear elastic
#              Disp.               Force
#                  X                   Y
                  -1                -0.1                                                            
                   0                   0
                   1               10000				   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
friction function 
#              Force                Fric
#                  X                   Y
               -1000                 0.2                                                            
                1000                 0.2
                2000                 0.3                                                            
                4000                 0.9
                5000                 1.0
               10000                 1.0				
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

  1. This property is modeled using a 3 node /SPRING element where node 1 and node 3 are the ends of the rope and node 2 is the pully location.


    Figure 1.
    Once node 1 slides to node 2 locking occurs as if there is a knot at node 1 that cannot move through the pully.


    Figure 2.
  2. Force computation:
    • In case of Ileng =0 (flag Ileng is defined in Line 3), the force in the spring is computed as:(1)
      F = f ( δ 1 A s c a l e 1 ) [ A 1 + B 1 ln ( max ( 1 , | δ ˙ 1 D 1 | ) ) + E 1 g ( δ ˙ 1 F 1 ) ] + C 1 δ ˙ 1 + H s c a l e 1 h ( δ ˙ 1 F 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0JaciOzamaabmaabaWaaSaaaeaacqaH0oazdaahaaWcbeqaaiaa igdaaaaakeaacaWGbbGaam4CaiaadogacaWGHbGaamiBaiaadwgada WgaaWcbaGaaGymaaqabaaaaaGccaGLOaGaayzkaaWaamWaaeaacaWG bbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSIaamOqamaaBaaaleaaca aIXaaabeaakiGacYgacaGGUbWaaeWaaeaaciGGTbGaaiyyaiaacIha daqadaqaaiaaigdacaGGSaWaaqWaaeaadaWcaaqaaiqbes7aKzaaca WaaWbaaSqabeaacaaIXaaaaaGcbaGaamiramaaBaaaleaacaaIXaaa beaaaaaakiaawEa7caGLiWoaaiaawIcacaGLPaaaaiaawIcacaGLPa aacqGHRaWkcaWGfbWaaSbaaSqaaiaaigdaaeqaaOGaci4zamaabmaa baWaaSaaaeaacuaH0oazgaGaamaaCaaaleqabaGaaGymaaaaaOqaai aadAeadaWgaaWcbaGaaGymaaqabaaaaaGccaGLOaGaayzkaaaacaGL BbGaayzxaaGaey4kaSIaam4qamaaBaaaleaacaaIXaaabeaakiqbes 7aKzaacaWaaWbaaSqabeaacaaIXaaaaOGaey4kaSIaamisaiaadoha caWGJbGaamyyaiaadYgacaWGLbWaaSbaaSqaaiaaigdaaeqaaOGaci iAamaabmaabaWaaSaaaeaacuaH0oazgaGaamaaCaaaleqabaGaaGym aaaaaOqaaiaadAeadaWgaaWcbaGaaGymaaqabaaaaaGccaGLOaGaay zkaaaaaa@7785@

      With l 0 < δ 1 < +

      Where, δ = l l 0 is the difference between the current length and the initial length of the spring element.

    • If Ileng=1, all input are per unit length.

      Spring mass = M l 0

      Spring stiffness = K l 0

      Spring damping = C l 0

      Spring inertia = I l 0

      Where, l 0 is the spring reference length.

    • The value of force in the spring is computed as:(2)
      F = f ( ε A s c a l e 1 ) [ A 1 + B 1 ln ( max ( 1 , | ε ˙ D 1 | ) ) + E 1 g ( ε ˙ F 1 ) ] + C 1 ε ˙ + H s c a l e 1 h ( ε ˙ F 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0JaciOzamaabmaabaWaaSaaaeaacqaH1oqzaeaacaWGbbGaam4C aiaadogacaWGHbGaamiBaiaadwgadaWgaaWcbaGaaGymaaqabaaaaa GccaGLOaGaayzkaaWaamWaaeaacaWGbbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamOqamaaBaaaleaacaaIXaaabeaakiGacYgacaGGUb WaaeWaaeaaciGGTbGaaiyyaiaacIhadaqadaqaaiaaigdacaGGSaWa aqWaaeaadaWcaaqaaiqbew7aLzaacaaabaGaamiramaaBaaaleaaca aIXaaabeaaaaaakiaawEa7caGLiWoaaiaawIcacaGLPaaaaiaawIca caGLPaaacqGHRaWkcaWGfbWaaSbaaSqaaiaaigdaaeqaaOGaci4zam aabmaabaWaaSaaaeaacuaH1oqzgaGaaaqaaiaadAeadaWgaaWcbaGa aGymaaqabaaaaaGccaGLOaGaayzkaaaacaGLBbGaayzxaaGaey4kaS Iaam4qamaaBaaaleaacaaIXaaabeaakiqbew7aLzaacaGaey4kaSIa amisaiaadohacaWGJbGaamyyaiaadYgacaWGLbWaaSbaaSqaaiaaig daaeqaaOGaciiAamaabmaabaWaaSaaaeaacuaH1oqzgaGaaaqaaiaa dAeadaWgaaWcbaGaaGymaaqabaaaaaGccaGLOaGaayzkaaaaaa@72D5@
      Where, ε is the engineering strain:(3)
      ε = δ l 0

      Force functions are given versus engineering strain and engineering strain rate.

      Failure criteria are defined with respect to strain. Input of negative/positive failure limit should be related to initial length l 0

  3. If δ min 1 (resp δ max 1 ) is 0, no failure in the direction. The δ min 1 must be negative. For linear springs, f ( δ ) and g ( δ ˙ ) are null functions and A1, B1 and E1 are not taken into account.
  4. Spring is activated and/or deactivated by sensor:
    • If sens_ID ≠ 0 and Isflag = 0, the spring element is activated by the sens_ID.
    • If sens_ID ≠ 0 and Isflag = 1, the spring element is deactivated by the sens_ID.
    • If sens_ID 0 and Isflag = 2, then:
      • The spring is activated and/or, deactivated by sens_ID. (if sensor is ON, spring is ON; if sensor is OFF, spring is OFF).
      • The spring reference length ( l 0 ) is the distance between spring node N1 and N2 at the time of the sensor's activation.
  5. If a sensor is used for activating or deactivating a spring, the reference length of the spring at sensor activation (or deactivation) is equal to the nodal distance at time =0; except if sensor flag is equal to 2.
  6. Friction models definition:

    clip0120
    Figure 3.
    • If fct_IDfr and Fric = 0 (no friction), then | F 1 | = | F 2 | .
    • If fct_IDfr = 0 and Fric > 0, then constant Coulomb friction coefficient used: μ=Fric=const. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBcq GH9aqpcaWGgbGaamOCaiaadMgacaWGJbGaeyypa0Jaci4yaiaac+ga caGGUbGaai4CaiaacshaciGGUaaaaa@4329@
    • If fct_IDfr > 0, then variable friction is calculated as a function on relative force between two pulley branches:

      Ifr = 0 (symmetrical behavior), Δ F = | F 1 F 2 |

      Ifr = 1 (non-symmetrical behavior), Δ F = F 1 F 2

      Friction force F f r is computed as:(4)
      F f r = min { | Δ F | , max [ 0 , ( F 1 + F 2 ) tanh ( β μ 2 ) ] } s i g ( Δ F ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaahAeadaWgaaWcbaGaamOzaiaadkhaaeqaaOGaeyypa0JaciyB aiaacMgacaGGUbWaaiWaaeaadaabdaqaaiabfs5aejaahAeaaiaawE a7caGLiWoacaGGSaGaciyBaiaacggacaGG4bWaamWaaeaacaaIWaGa aiilamaabmaabaGaaCOramaaBaaaleaacaaIXaaabeaakiabgUcaRi aahAeadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGHflY1 ciGG0bGaaiyyaiaac6gacaGGObWaaeWaaeaadaWcaaqaaiabek7aIj abgwSixlabeY7aTbqaaiaaikdaaaaacaGLOaGaayzkaaaacaGLBbGa ayzxaaaacaGL7bGaayzFaaGaeyyXICTaam4CaiaadMgacaWGNbWaae WaaeaacqqHuoarcaWHgbaacaGLOaGaayzkaaaaaa@6869@
      Where,(5)
      μ = f f r ( Δ F X s c a l e _ F ) Y s c a l e _ F
      β
      Angle (radians unit)
      f f r
      Function of fct_IDfr
    • If Ifr = 1 (non-symmetrical behavior) and when F_min (or F_max) is reached, friction is switching permanently from the function definition to the constant value Fric.


      Figure 4.

      Otherwise, the friction value is defined according to the input function fct_IDfr.