Finite element wodel of a beam(Euler-Bernollia- governing eQuations EI w- O<x< L W-w n S (displacement bo EIw"=MIon st (nabil or tracion 8c MLQ ?(￥ n approximation insi de elemnet L=1 U e e TEleweut boondary Conditions disputant w(x9)=05W(x)912w(×29w(2
(2 n(Ew1=0(则 X EIw- Q Erw XB Whet do the first and second row represent? potent ial energy for the beam elewer T (we)=Ee e dwe '+we ge dx dx PUe-2(2- ee sele Whot do the last four tems represent? clattoⅥ of ba asis uncoV Need twlce-differentiable, Continuous, continuous- sLope functions. The miniMum polynowisl order should be Hree so that non-end shears are obtained st Hie nodes. The wbic polnowidd also gives us for para eters to fit the four essenti
3 boundary conditions at the nodes I The resulting basis fonctions are the Hermite wbic polynomials e 4° 3 2 。5 4=-S「1- e 2 2 e e e 4俗舒 Finite element equations Replace approxiation I吧4
potential T Ee Ie/Z Ue de2 e d Appt PvPE:Tre=o≈lne。o aus e°|Ee0g 日3+ +930代K-202=0 e oEe A A e K 1=R element stiffness element ne element torce MaTiX displaceMents vector
For the e case in wicn Ee and d Ie ore constant Inside the element, these reduce to 3h lke. 2 2 G 3 6B Re=%oh-h()p P2 2-)6 h)p
