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Isoparametric elements are those in which we use the same shape functions to interpolate both the displacement field and the geometry of the element. The displacement of a point within an element can be expressed in terms of nodal degree(s) of freedom and the shape functions [N] which are functions of reference coordinates. Similarly the global coordinates of a point within the element can be expressed in terms of global nodal positions and the same shape functions [N].

We have a bar element of 3 nodes represented in the reference coordinate system as shown in Fig. 1a. The actual element in the global coordinate system is shown in Fig. 1b. In the reference coordinate system, nodes 1 and 3 always lie at ξ = −1 and at ξ = 1 respectively, regardless of the physical length of the element. Whereas node 2 always lie at ξ = 0, the center of mapped element....

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