Term ‘iso-parametric’ is derived from the use of the same shape functions (or interpolation functions) to define the element's geometric shape as those used to define the variation of unknown field within an element. Iso-parametric element equations are formulated using a ‘natural’ (or ‘intrinsic’) co-ordinate system defined by the element geometry. The intrinsic co-ordinates normally vary from −1 to +1, regardless of the element's dimensions. Thus, use of such a co-ordinate system becomes very attractive, especially when all the matrices need to be integrated numerically.

The concept of iso-parametric formulation is explained below in the context of a line (bar) element and is extended later to a two-dimensional, ...

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