Show that the weak form of is given by d +2x=0 on 1...

 

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Show that the weak form of is given by d +2x=0 on 1<x<3, dr σ(1)= E du = 0.1, dx u(3)=0.001 3 ++/2wd 2.xwdr Vw with w(3) = 0. dw du AEdx=-0.1(WA)- + dr dr Problem 3.2 Show that the weak form in Problem 3.1 implies the strong form. Problem 3.3 Consider a trial (candidate) solution of the form u(x)=0+x(x-3) and a weight function of the same form. Obtain a solution to the weak form in Problem 3.1. Check the equilibrium equation in the strong form in Problem 3.1; is it satisfied? Check the natural boundary condition; is it satisfied? Problem 3.4 Repeat Problem 3.3 with the trial solution u(x) = 20 +1(x-3) + 2(x-3)². Show that the weak form of is given by d +2x=0 on 1<x<3, dr σ(1)= E du = 0.1, dx u(3)=0.001 3 ++/2wd 2.xwdr Vw with w(3) = 0. dw du AEdx=-0.1(WA)- + dr dr Problem 3.2 Show that the weak form in Problem 3.1 implies the strong form. Problem 3.3 Consider a trial (candidate) solution of the form u(x)=0+x(x-3) and a weight function of the same form. Obtain a solution to the weak form in Problem 3.1. Check the equilibrium equation in the strong form in Problem 3.1; is it satisfied? Check the natural boundary condition; is it satisfied? Problem 3.4 Repeat Problem 3.3 with the trial solution u(x) = 20 +1(x-3) + 2(x-3)².