/FUNCT_SMOOTH

Block Format Keyword Defines a smoothstep analytic function to be used with loads.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FUNCT_SMOOTH/fct_ID
fct_title
Ascalex Fscaley Ashiftx Fshifty    
X1 Y1        
X2 Y2        
etc. etc.        
XN YN        

Definitions

Field Contents SI Unit Example
fct_ID Function identifier.

(Integer, maximum 10 digits)

 
fct_title Function title.

(Character, maximum 100 characters)

 
Ascalex Abscissa scale factor.

Default = 1.0 (Real)

 
Fscaley Ordinate scale factor.

Default = 1.0 (Real)

 
Ashiftx Abscissa shift value.

Default = 0.0 (Real)

 
Fshifty Ordinate shift value.

Default = 0.0 (Real)

 
X1 First abscissa for the function definition.

Default = 0 (Real)

 
Y1 First ordinate for the function definition.

Default = 0 (Real)

 
X2 Second abscissa for the function definition.

(Real)

 
Y2 Second ordinate for the function definition.

(Real)

 
XN (Optional) Nth abscissa point.  
YN (Optional) Nth ordinate point.  

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT_SMOOTH/1
Displacement
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#            Ascalex             Fscaley             Ashiftx             Fshifty   

#                  X                   Y  
                   0                   0                                                            
                  .2                  60				   
                  .4                  20				   
                  .5                  70				   
                  .6                  70				   
                  .8                 0.0				   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA


Figure 1. Example Smoothstep Function Based on Input

Comments

  1. Points 1 and 2 are required.
  2. A function and a table cannot share the same identifier.
  3. This function can be used with these options:

    /IMPDISP, /IMPVEL, /IMPACC, /IMPDISP/FGEO, /IMPVEL/FGEO, /IMPVEL/LAGMUL, /PLOAD, /CLOAD, /GRAV, /IMPTEMP, and /IMPFLUX

  4. For an abscissa smaller than X1, the ordinate value is Y1.
  5. For an abscissa larger than XN, the ordinate value is YN.
  6. The function is scaled first and shifted afterwards, as:(1)
    X n e w = X o l d A s c a l e x + A s h i f t x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGUbGaamyzaiaadEhaaeqaaOGaeyypa0JaamiwamaaBaaa leaacaWGVbGaamiBaiaadsgaaeqaaOGaeyyXICTaamyqaiaadohaca WGJbGaamyyaiaadYgacaWGLbWaaSbaaSqaaiaadIhaaeqaaOGaey4k aSIaamyqaiaadohacaWGObGaamyAaiaadAgacaWG0bWaaSbaaSqaai aadIhaaeqaaaaa@4F36@
    (2)
    Y n e w = Y o l d F s c a l e y + F s h i f t y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGUbGaamyzaiaadEhaaeqaaOGaeyypa0JaamywamaaBaaa leaacaWGVbGaamiBaiaadsgaaeqaaOGaeyyXICTaamOraiaadohaca WGJbGaamyyaiaadYgacaWGLbWaaSbaaSqaaiaadMhaaeqaaOGaey4k aSIaamOraiaadohacaWGObGaamyAaiaadAgacaWG0bWaaSbaaSqaai aadMhaaeqaaaaa@4F44@

    Where, X o l d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGVbGaamiBaiaadsgaaeqaaaaa@39CF@ and Y o l d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGVbGaamiBaiaadsgaaeqaaaaa@39CF@ are values from the function.

  7. The ordinate is calculated for each time step which results in a smooth function.
  8. The function is calculated for using two consecutive input data points i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ and i+1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaiabgU caRiaaigdaaaa@3881@ as:

    If  x X 1  then  y = Y 1 If X 1 < x < X N  then  y = y i + ( y i + 1 y i ) d 3 ( 10 15 d + 6 d 2 ) where,  d = x x i x i + 1 x i If  x X N  then  y = Y N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaabccacaWG4bGaeyizImQaamiwamaaBaaaleaacaaIXaaa beaakiaabccacaqG0bGaaeiAaiaabwgacaqGUbGaaeiiaiaadMhacq GH9aqpcaWGzbWaaSbaaSqaaiaaigdaaeqaaaGcbaGaaeysaiaabAga caqGGaGaaeiwamaaBaaaleaacaaIXaaabeaakiabgYda8iaadIhacq GH8aapcaWGybWaaSbaaSqaaiaad6eaaeqaaOGaaeiiaiaabshacaqG ObGaaeyzaiaab6gacaqGGaGaamyEaiabg2da9iaadMhadaWgaaWcba GaamyAaaqabaGccqGHRaWkdaqadaqaaiaadMhadaWgaaWcbaGaamyA aiabgUcaRiaaigdaaeqaaOGaeyOeI0IaamyEamaaBaaaleaacaWGPb aabeaaaOGaayjkaiaawMcaaiaadsgadaahaaWcbeqaaiaaiodaaaGc daqadaqaaiaaigdacaaIWaGaeyOeI0IaaGymaiaaiwdacaWGKbGaey 4kaSIaaGOnaiaadsgadaahaaWcbeqaaiaaikdaaaaakiaawIcacaGL PaaaaeaacaqG3bGaaeiAaiaabwgacaqGYbGaaeyzaiaabYcacaqGGa Gaamizaiabg2da9maalaaabaGaamiEaiabgkHiTiaadIhadaWgaaWc baGaamyAaaqabaaakeaacaWG4bWaaSbaaSqaaiaadMgacqGHRaWkca aIXaaabeaakiabgkHiTiaadIhadaWgaaWcbaGaamyAaaqabaaaaaGc baGaaeysaiaabAgacaqGGaGaamiEaiabgwMiZkaadIfadaWgaaWcba GaamOtaaqabaGccaqGGaGaaeiDaiaabIgacaqGLbGaaeOBaiaabcca caWG5bGaeyypa0JaamywamaaBaaaleaacaWGobaabeaaaaaa@8F78@