Hi Nasibeh, imagine two bars (or rods) a and b in serie. Rod a has cross section area A, length La and material stiffness ka, rod b is anlogous. Let's define rod extension dL, strain e, stress s and apply force F.
F <--- o ---rod a--- o ----rod b--- o ---> F e = dL/L s = k.e = F / A kL = k.A / L is rod stifness because rods are in serie, Fa = Fb = F -> sa = sb = F/A = s dLa = s.La / ka = F / kaL dLb = s.Lb / kb = F / kbL dL = dLa + dLb = s.(La / ka + Lb / kb) = F.(1 / kaL + 1 / kbL) from now, there are two ways how to define equivalent stiffness: a) equivalent rod stifness kL = F / dL = F / [ F.(1 / kaL + 1 / kbL) ] = kaL.kbL / (kaL + kbL) b) equivalent material stifness k = s.L / dL = s.(La + Lb) / [s.(La / ka + Lb / kb)] = = (La + Lb) / (La / ka + Lb / kb) under assumption La = Lb k = 2.ka.kb / (ka + kb) Is this explanation at least a little understandable and useful? :-) an example: let's have two springs (rods) made of steel with Young's modulus Ea=10. the rod stiffness of each spring is kLa = EaA / La = 10*2/5 = 4. If You put them into a serie and apply force F, the extension of such system would be twice as big as the extension of one spring. The rod stifness of the system is halved: kL = kLa/2 = 2. On the other hand, the value of the material stiffness E remains the same, E... You can try to apply aforementioned formulas :-) In Yade, (I suppose :-) the stiffness is considered as the material stiffness, and therefore the value of the contact stiffness is computed using harmonic mean.. Best wishes Honza ______________________________________________________________ > Od: "Nasibeh Moradi" <[email protected]> > Komu: [email protected] > Datum: 19.04.2010 10:54 > Předmět: [Yade-users] harmonic average of stiffness > >hi, > >in contact law, harmonic average is used for computing kn and ks in contact >between 2 body, why harmonic average? >in some papers, the springs are in serie, then k=ka*kb/(ka+kb), >but in harmonic average k=2*ka*kb/(ka+kb) > >Nasibeh Moradi > >_______________________________________________ >Mailing list: https://launchpad.net/~yade-users >Post to : [email protected] >Unsubscribe : https://launchpad.net/~yade-users >More help : https://help.launchpad.net/ListHelp > > _______________________________________________ Mailing list: https://launchpad.net/~yade-users Post to : [email protected] Unsubscribe : https://launchpad.net/~yade-users More help : https://help.launchpad.net/ListHelp
