hw-3-assignment - Homework 3 problem 1 Solve for the...

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Unformatted text preview: Homework 3, problem 1 Solve for the approximate deflection of a simply-supported prestressed cable with triangular static distributed load using the finite element Galerkin method. Use a mesh of four equal-length finite elements, and number the nodes and the elements left to right. (a) Compare the midpoint deflection computed analytically and approximately. (b) Compute the transverse force analytically and compare with the finite element result. Homework 3, problem 2 Find the natural frequencies and normal mode shapes for the roller-pin supported cable with uniform mass density using a mesh of three finite elements of equal length. Number the nodes and the elements left to right. Integrate element wise quantities exactly. (a) Plot the normal mode shapes. (b) Calculate the relative error of the natural frequencies. Homework 3, problem 3 Consider the free vibration of a pin-pin supported cable. Construct the “SolidWorks Simulation” finite element model to compute the seventh natural frequency of free vibration using the cable-uniaxial rod analogy. Use both draftand high-quality tetrahedra. Find the uniform mesh size necessary for attaining accuracy better than 1% in angular frequency. Compare the numerical results to the analytical formulas for the prestressed cable free vibration. Produce a brief report. 1 ...
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