Consider two triangular elements as shown in Figure 731 If t

Consider two triangular elements as shown in Figure 7.31. If the exact temperature field is x^2, can the two elements represent the exact solution? Explain.

Solution

Since the triangualr element has 3 nodes. the field it will represent will be linear. For 1st element with nodes 1,2,4

f\'(x,y)=N1*f1+N2*f2+N3*f3

where Ni= ai+bi*x+ci*y

So the resulting solution will be liner function of x.

Now since we only have 1 element along x direction at y=0 and y=1. A linear function will not be able represent the exact solution which is a quadractic (x^2)