Shape functions of commonly used finite elements

2 Shape functions of commonly used finite elements 

Variations of a continuous function over this element can be represented by a complete first-order (linear) polynomial as 

By the insertion of the nodal coordinates into Equation (2.5) nodal values of / can be found. This is shown as 

24 WEIGHTED RESIDUAL FINITE ELEMENT METHODS - AN OUTLINE hence a = 

In the outlined procedure the derivation of the shape functions of a three-noded (linear) triangular element requires the solution of a set of algebraic equations, generally shown as Equation (2.7). 

---