Shape Functions in Natural Coordinate

Using the mapping function of section 11.1, shape functions of any order can be expressed as functions of the natural coordinate x . Thus

(11.8)

Since the mapping function is linear in , a polynomial of degree p in coordinate x will get converted to the polynomial of the same degree in . Next paragraph describes the derivation of the shape functions in terms of for the approximations of various orders.

• Linear Approximation (p = 1)
• Quadratic Approximation ( p = 2)
• Approximation of Order p

We'll discuss them in the following three slides