Elements of Higher Order

Figure 23.1: A four noded quadrilateral

For the higher-order elements, the interpolation will be performed using higher-order polynomials. For instance, for a 4-noded quadrilateral Fig. 23.1 the interpolation for temperature can be written as

The shape functions and for such a case will be obtained from

(23.9)

Similarly, for a 6-noded traingle the shape functions can be obtained through

(23.10)

with the temperature interpolation given by

(23.11)

The size of the elemental matrices will also be different for higher-order elements. For instance, for a 4-noded quadrilateral element will be a 4 × 4 matrix. The evaluation of these matrices for the higher-order shape functions have to be performed using numerical integration. All the other procedures are similar to the problem that used 3-noded triangular elements. Finally, the assembled global matrix equations can be solved to get the field variable at all nodes.

Congratulations, you have finished Lecture 23. To view the next lecture select it from the left hand side menu of the page or click the next button.