The boundaryvalue problem for a cantilevered beam can be written as

Assume \(p(x)=x\). Assuming the approximate deflection in the form of \(\tilde{w}(x)=c_{1} \phi_{1}(x)+c_{2} \phi_{2}(x)=c_{1} x^{2}+c_{2} x^{3}\). Solve for the boundaryvalue problem using the Galerkin method. Compare the approximate solution to the exact solution by plotting the solutions on a graph.

Transcribed Image Text:

d+w -p(x)=0, 0x1 dr dw dw dx w(0)=(0)=0, 2 (1)=1, dw dr (1)=-1.