See the attached image 1) A long rod in the shape of a circular cone is rotating with constant angular velocity c about an axis located at the left end of the rod as shown in the figure below. The bar has length L, major and minor diameters D and d, respectively, and its material has linear elastic behavior with modulus of elasticity E. The values of the problem parameters must be defined by the student a) From the balance of a differential member of the bar, derive the differential equation of balance for the bar. Solve the equation analytically to obtain the bar displacement field, U(X). Give the expression for the displacement at the free end of the member. b) Implement a computational code in MATLAB (or any other software) to solve this problem with "n" two-node bar finite elements. c) Run different simulations by increasing the number of finite elements in each simulation. At each simulation, obtain the displacement of the free end of the member. Graphically compare your results with the analytical solution, and analyze the convergence of your numerical solution with increasing number of elements. d) From the simulations conducted in part (c), obtain the axial stress at the fixed end of the bar. Graphically compare your results obtained with the analytical solution. I need the step by step explanations of the activity to learn
See the attached image
1) A long rod in the shape of a circular cone is rotating with constant angular velocity c about an axis located at the left end of the rod as shown in the figure below. The bar has length L, major and minor diameters D and d, respectively, and its material has linear elastic behavior with modulus of elasticity E.
The values of the problem parameters must be defined by the student
a) From the balance of a differential member of the bar, derive the differential equation of balance for the bar. Solve the equation analytically to obtain the bar displacement field, U(X). Give the expression for the displacement at the free end of the member.
b) Implement a computational code in MATLAB (or any other software) to solve this problem with "n" two-node bar finite elements.
c) Run different simulations by increasing the number of finite elements in each simulation. At each simulation, obtain the displacement of the free end of the member. Graphically compare your results with the analytical solution, and analyze the convergence of your numerical solution with increasing number of elements.
d) From the simulations conducted in part (c), obtain the axial stress at the fixed end of the bar. Graphically compare your results obtained with the analytical solution.
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