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Derive the shape function in natural co-ordinate system for eight nodded quadrilateral element.
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Serendipity elements:
They are the rectangulars element which have no interior nodes i.e all nodes lie on the boundary of element only.

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Shape Function for eight noded element.
Considder a quadrilateral element with eight node as shown in Fig.

Now to determine ϕ1 we note that ϕ1 vanishes along lines. …

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