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Shape function for beam element

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Old   February 3, 2017, 07:20
Default Shape function for beam element
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I have a question about the shape function for a beam element in natural coordinates. Generally, if we add all shape functions, it should give UNITY. But, for shape functions for Beam element is not giving unity? Kindly clarify the doubt. The follwing are the shape functions for beam element.
N1 = (1 − ξ)^2 (2 + ξ),
N2 =  (1 − ξ)^2 (1 + ξ),
N3 = (1 + ξ)^2 (2 − ξ),
N4 = (1 + ξ)^2 (1 − ξ).
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beam element, fem, shape functions

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