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##### 5.4 TWO-DIMENSIONAL ELEMENTS

Triangular, rectangular and quadrilateral elements are most widely used for two-dimensional finite element modelling. Various properties of these elements and related interpolation functions are discussed in this section.

#### 5.4.1 Triangular Element: Linear Interpolation Function in Cartesian Co-ordinates

The triangular element was formulated by Turner et al. (1956). It is commonly used element shape for two-dimensional problems. Triangular elements can be used when the field variable is a function of two independent variables, namely x and y. Variation of field variable ɸ over the domain of an element can be written in polynomial form as

where α1, α2 and α3 are the coefficients to be evaluated.

Let the nodes ...

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