Question

1. A bar with uniform cross-sectional area, A, elastic modulus, E, and length, L is loaded with distributed loads q(x). The bar is fixed on the right end and attach to the spring of stiffness, K, which is relaxed when the bar is undeformed. Here, Cross-sectional area, A = .025 m², the Young's modulus, E = 70 GPa, K = 750 kN/m. Governing equation for 1-D bar is as follows: $AE \frac{d^2u}{dx^2} = -q(x); 0 < x < L$ Where, distributed load, q(x), is defined below for the problem: $q(x) = q_0 \left(2 - \frac{2x}{L}\right)$ And the boundary condition for this particular problem is as follows: u(x = 0) = 0, and F = -Ku(x = L) Write a MATLAB program which: [25 points] • Takes as input: length of the bar, L, number of intervals, N, and $q_0$. • Assembles the FD matrices for governing equations and boundary condition. • Plot the displacement solution against the length of bar, i.e., u(x) vs. x. Run your program using test input as L = 20 m, $q_0$ = 50 kN/m, and N = 5. Print out your co-efficient matrix, equation constant vector, and displacement solution.

          1. A bar with uniform cross-sectional area, A, elastic modulus, E, and length, L is loaded with distributed loads q(x). The bar is fixed on the right end and attach to the spring of stiffness, K, which is relaxed when the bar is undeformed.
Here, Cross-sectional area, A = .025 m², the Young's modulus, E = 70 GPa, K = 750 kN/m.
Governing equation for 1-D bar is as follows:
$AE \frac{d^2u}{dx^2} = -q(x); 0 < x < L$
Where, distributed load, q(x), is defined below for the problem: $q(x) = q_0 \left(2 - \frac{2x}{L}\right)$
And the boundary condition for this particular problem is as follows:
u(x = 0) = 0, and F = -Ku(x = L)
Write a MATLAB program which: [25 points]
• Takes as input: length of the bar, L, number of intervals, N, and $q_0$.
• Assembles the FD matrices for governing equations and boundary condition.
• Plot the displacement solution against the length of bar, i.e., u(x) vs. x.
Run your program using test input as L = 20 m, $q_0$ = 50 kN/m, and N = 5. Print out your co-efficient matrix, equation constant vector, and displacement solution.

1. A bar with uniform cross-sectional area, A, elastic modulus, E, and length, L is loaded with distributed loads q(x). The bar is fixed on the right end and attach to the spring of stiffness, K, which is relaxed when the bar is undeformed.
Here, Cross-sectional area, A = .025 m², the Young's modulus, E = 70 GPa, K = 750 kN/m.
Governing equation for 1-D bar is as follows:
AE (d^2u)/(dx^2) = -q(x); 0 < x < L
Where, distributed load, q(x), is defined below for the problem: q(x) = q0 (2 - (2x)/(L))
And the boundary condition for this particular problem is as follows:
u(x = 0) = 0, and F = -Ku(x = L)
Write a MATLAB program which: [25 points]
• Takes as input: length of the bar, L, number of intervals, N, and q0.
• Assembles the FD matrices for governing equations and boundary condition.
• Plot the displacement solution against the length of bar, i.e., u(x) vs. x.
Run your program using test input as L = 20 m, q0 = 50 kN/m, and N = 5. Print out your co-efficient matrix, equation constant vector, and displacement solution.

Added by Fernando R.

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