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For a four noded element while implementing a computer program, the compact representation of shape function is ____

a) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)
b) Nt=(1-ξ)(1-η)
c) Nt=\(\frac{1}{4}\)(1+ξξi)(1+ηηi)
d) Undefined

Answer: c
Explanation: FourNodeQuad is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).

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