BISTOP

The BISTOP function models a gap element.

Format

Bistop ( x , x ˙ , x 1 , x 2 , k , e , c max , d )

Description

It can be used to model forces acting on a body while moving in the gap between two boundary surfaces, which act as elastic bumpers. The properties of the two boundary surfaces can be tuned as desired.

Arguments

x
The expression used for the independent variable. For example, to use the z-displacement of I marker with respect to J marker as resolved in the reference frame of the RM marker as the independent variable, specify x as DZ({marker_i.idstring}, {marker_j.idstring}, {marker_rm.idstring}).
x ˙
The time derivative of the independent variable. For example, if x is specified as above, then x ˙ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipv0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmiEayaaca aaaa@371D@ will be VZ({marker_i.idstring}, {marker_j. idstring}, {marker_rm.idstring}).
x 1
The lower bound of x . If x is less than x 1 , the bistop function returns a positive value. The value of x 1 must be less than the value of x 2 .
x 2
The upper bound of x . If x is greater than x 2 , the bistop function returns a negative value. The value of x 2 must be greater than the value of x 1 .
k
The stiffness of the boundary surface interaction. It must be non-negative.
e
The exponent of the force deformation characteristic. For a stiffening spring characteristic, e must be greater than 1.0 and for a softening spring characteristic, e must be less than 1.0. It must always be positive.
c max
The maximum damping coefficient. It must be non-negative.
d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipv0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@3700@
The penetration at which the full damping coefficient is applied. It must be positive.

Definition

(1)
Bistop= { max(k*(x 1 -x) e -Step(x,x 1 -d,c max ,x 1 ,0)* x ˙ , 0), if x<x 1 0, if x 1 ≤x≤x 2 min(-k*(x-x 2 ) e -Step(x,x 2 ,0,x 2 +d,c max )* x ˙ , 0), if x>x 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaaeOqaiaabM gacaqGZbGaaeiDaiaab+gacaqGWbGaaeypamaaceaabaqbaeqabiqa aaqaaiacaciC=d3=b2gacGaGac3=W9FGHbGaiaiGW9pC=hiEaiacac iG=d3=bIcacGaGac4=W9FGRbGaiaiGa+pC=hOkaiacaciG=d3=bIca cGaGac4=W9FG4bWaiaiGa+pC=VbaaSqaiaiGa+pC=lacaciG=d3=bg daaeqcaciG=d3=aOGaiaiGa+pC=hylaiacaciG=d3=bIhacGaGac4= W9FGPaWaiaiGa+pC=ZbaaSqajaiGa+pC=hacaciG=d3=cGaGac4=W9 FGLbaaaOGaiaiGa+pC=hylaiacaciG=d3=bofacGaGac4=W9FG0bGa iaiGa+pC=hyzaiacaciG=d3=bchacGaGac4=W9FGOaGaiaiGa+pC=h iEaiacaciG=d3=bYcacGaGac4=W9FG4bWaiaiGa+pC=VbaaSqaiaiG a+pC=lacaciG=d3=bgdaaeqcaciG=d3=aOGaiaiGa+pC=hylaiacac iG=d3=bsgacGaGac4=W9FGSaGaiaiGa+pC=h4yamacaciG=d3=Baaa leacaciG=d3=cGaGac4=W9FGTbGaiaiGa+pC=hyyaiacaciG=d3=bI haaeqcaciG=d3=aOGaiaiGa+pC=hilaiacaciG=d3=bIhadGaGac4= W9=gaaWcbGaGac4=W9VaiaiGa+pC=hymaaqajaiGa+pC=dGccGaGac 4=W9FGSaGaiaiGa+pC=himaiacaciG=d3=bMcacGaGac4=W9FGQaWa iaiGa+pC=FbiaeacaciG=d3=cGaGac4=W9FG4baaleqcaciG=d3=bG aGac4=W9FcLbkacGaiagOiGaaakiacaciG=d3=bYcacGaGac4=W9pM c8UaiaiGa+pC=JPaVlacaciG=d3=bcdacGaGac4=W9FGPaGaiaiGa+ pC=hilaiacaciG=d3=ykW7cGaGac4=W9pMc8UaiaiGa+pC=hyAaiac aciG=d3=bAgacGaGac4=W9FGGaGaiaiGa+pC=hiEaiacaciG=d3=bY dacGaGac4=W9FG4bWaiaaGBaaaleacaaOaiaaGbgdaaeqcaaiaaOab aeqabaGaiaiGaaaKaeimaiacaciaaajabYcacGaGacmaqcqGGaGaia iGaaaKaeyAaiacaciaaajabAgacGaGacmaqcqGGaGaiaiGaaaKaeiE amacaciaaajaBaaaleacaciaaajacGaGacaaqcqGXaaabKaGacaaqc aakiacaciaaajabokacGaGacaaqcqG4bGaiaiGaaaKae4Oaiacacia aajabIhadGaGacaaqcWgaaWcbGaGacaaqcGaiaiGaaaKaeOmaaqaja iGaaaKaaaakeaacaqGTbGaaeyAaiaab6gacaqGOaGaaeylaiaabUga caqGQaGaaeikaiaabIhacaqGTaGaaeiEamaaBaaaleaacaqGYaaabe aakiaabMcadaahaaWcbeqaaiaabwgaaaGccaqGTaGaae4uaiaabsha caqGLbGaaeiCaiaabIcacaqG4bGaaeilaiaabIhadaWgaaWcbaGaae OmaaqabaGccaqGSaGaaeimaiaabYcacaqG4bWaaSbaaSqaaiaabkda aeqaaOGaae4kaiaabsgacaqGSaGaae4yamaaBaaaleaacaqGTbGaae yyaiaabIhaaeqaaOGaaeykaiaabQcadaWfGaqaaiaabIhaaSqabeaa jugOaiacaciiaakabkciaaGccaqGSaGaaGPaVlaaykW7caqGWaGaae ykaiaabYcacaaMc8UaaGPaVlaabMgacaqGMbGaaeiiaiaabIhacaqG +aGaaeiEamaaBaaaleaacaqGYaaabeaaaaaaaOGaay5Eaaaaaa@E9A4@

Example

<Force_Vector_TwoBody
     id                    = "30101"
     type                  = "ForceOnly"
     i_marker_id           = "30102031"
     j_floating_marker_id  = "30101031"
     ref_marker_id         = "30101010"
     fx_expression         = "BISTOP(DX(30102030,30101010,30101010),VX(30102030,30101010,30101010),0.5,9.5,10000000,2.1,1,0.001)"
     fy_expression         = "0"
     fz_expression         = "0"
  />