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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- Spring '08
- Frequency, 1%, Mode shape, prestressed