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Question Five (10 points): Consider a simple bar fixed at one end(x=0) and subjected to a concentrated force at the other end(x=180) as shown in Fig. 5. Using the notation given in the figure, the total potential of the structure is: \begin{equation} \Pi = \frac{1}{2} \int_0^{180} EA \left( \frac{du}{dx} \right)^2 dx - 100u \Big|_{x=100} \end{equation} And the essential boundary condition is $u|_{x=0} = 0$. 1.Calculate the exact displacement and stress distributions in the bar. 2. Calculate the displacement and stress distributions using the Ritz method with the following displacement assumptions Cross-sectional area = $\left( 1 + \frac{y}{40} \right)$ cm$^2$ Area = 1 cm$^2$ Figure 5 R = 100 N

          Question Five (10 points):
Consider a simple bar fixed at one end(x=0) and subjected to a concentrated force
at the other end(x=180) as shown in Fig. 5. Using the notation given in the figure, the
total potential of the structure is:
\begin{equation*}
\Pi = \frac{1}{2} \int_0^{180} EA \left( \frac{du}{dx} \right)^2 dx - 100u \Big|_{x=100}
\end{equation*}
And the essential boundary condition is $u|_{x=0} = 0$.
1.Calculate the exact displacement and stress distributions in the bar.
2. Calculate the displacement and stress distributions using the Ritz method with the
following displacement assumptions
Cross-sectional area = $\left( 1 + \frac{y}{40} \right)$ cm$^2$
Area = 1 cm$^2$
Figure 5
R = 100 N

Question Five (10 points):
Consider a simple bar fixed at one end(x=0) and subjected to a concentrated force
at the other end(x=180) as shown in Fig. 5. Using the notation given in the figure, the
total potential of the structure is:

Π = (1)/(2)∫0^180 EA ( (du)/(dx))^2 dx - 100u |x=100

And the essential boundary condition is u|x=0 = 0.
1.Calculate the exact displacement and stress distributions in the bar.
2. Calculate the displacement and stress distributions using the Ritz method with the
following displacement assumptions
Cross-sectional area = ( 1 + (y)/(40)) cm^2
Area = 1 cm^2
Figure 5
R = 100 N

Added by Domingo N.

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