Consider a 20-mm-diameter, aluminum rod with length 900 mm, subject to a uniform distributed axial load...

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Consider a 20-mm-diameter, aluminum rod with length 900 mm, subject to a uniform distributed axial load of 30 kN/m directed to the left, and fixed at the right end. There is also a concentrated force of 10 N applied to the right at the midpoint of the rod. Determine the displacement and stress distribution along the length of the bar using the finite element method with a uniform mesh of 2-node elements. (a) Using a hand-analysis, determine the finite element approximation for displacement and stress using 4 elements of equal length. (b) Write a Matlab program to compare and discuss accuracy and observed trends in behavior of displacement and stress plots using finite element meshes of 4, 8, and 16 elements. Examples of discussion are: What is percent change for some key quantities of interest in increased number of elements in the mesh. What is the effect of sudden change in loading? Does the solution for displacement and stress distribution show a trend such as linear, parabolic, or other observed behavior such as sudden changes in behavior? Consider a 20-mm-diameter, aluminum rod with length 900 mm, subject to a uniform distributed axial load of 30 kN/m directed to the left, and fixed at the right end. There is also a concentrated force of 10 N applied to the right at the midpoint of the rod. Determine the displacement and stress distribution along the length of the bar using the finite element method with a uniform mesh of 2-node elements. (a) Using a hand-analysis, determine the finite element approximation for displacement and stress using 4 elements of equal length. (b) Write a Matlab program to compare and discuss accuracy and observed trends in behavior of displacement and stress plots using finite element meshes of 4, 8, and 16 elements. Examples of discussion are: What is percent change for some key quantities of interest in increased number of elements in the mesh. What is the effect of sudden change in loading? Does the solution for displacement and stress distribution show a trend such as linear, parabolic, or other observed behavior such as sudden changes in behavior?

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a For a handanalysis the first step is to divide the rod into equal elements with 4 elements of length 225mm each The nodal displacements for each ele... View the full answer