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Finite-Element Method Description

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Using Finite-Element Methods, assuming that stiffness of each element is equal to f.

https://brainmass.com/math/finite-element-method/finite-element-method-description-20166

Solution Preview

I have discretized and labelled the nodes and elements as follows.

For element 1, theta = 90 degrees + tan^-1(2/3) = 123.69 degrees

F1 0.307684 -0.46154 -0.30768 0.461535 u1
F2 = f * -0.46154 0.692316 0.461535 -0.692316 u2
F3 -0.30768 0.461535 0.307684 -0.461535 u3
F4 0.461535 -0.69232 -0.46154 0.692316 u4

For element 2, theta = tan^-1(1/3.5) = 15.95 degrees

F3 0.926888 0.26032 -0.92689 -0.26032 u3
F4 = f * 0.26032 0.073112 -0.26032 -0.073112 u4
F5 -0.92689 -0.26032 0.926888 0.26032 u5
F6 -0.26032 -0.07311 0.26032 0.073112 u6

For element 3, theta = tan^-1(4/1.5) = 69.44 degrees
F1 0.123333 0.329748 -0.12333 -0.329748 u1
F2 = f * 0.329748 0.881627 -0.32975 -0.881627 u2
F5 -0.12333 -0.32975 0.123333 0.329748 u5
F6 -0.32975 -0.88163 0.329748 0.881627 u6

For element 4, theta = 360 - ...

Solution Summary

The finite-element method descriptions are given.

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