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# Write a Matlab code to compute and plot the forced response of a finite element model

INSTRUCTIONS TO CANDIDATES

Write a Matlab code to compute and plot the forced response of a finite element model (50 elements) of a uniform torsion bar (I = 1, J = 1, G = 1) of length L = 5, subjected to a step torque Toat the right hand end and fixed at the left hand end, over the time range 0 ≤t ≤40, for zero initial conditions and To= 0.01.

Assume proportional damping with β = 0.001. Plot the rotational displacement (θ) at the right hand end and the angular velocity ( ̇θ) at the right hand end over the specified simulation time range. Use ode45 to compute your solution. Use the mandatory plotting syntax posted on Canvas, which also includes the exact solution, so that you may check your results. Background information on the application of FEM to the torsion bar problem is provided in the handout Torsion

BarModelFEM.pdf posted on Canvas. NOTES: You may not use any software other than Matlab. You may not use any built-in Matlab functions except the “inv” function. Your Matlab code must use explicit loops and subscripted variables in all calculations,

except: (a) in the subroutine you provide to ‘ode45’ where you may use vector and matrix notation to describe the differential equations which you are integrating, (b) in plotting commands, where you may refer to vector or matrix variables, and (c) in subroutine calls/returns, where you may refer to vector or matrix variables. Do not use colons (:). •Plotted results (two plots on one page).

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