The nodal displacements of the triangular element are given in the table below.

a. It is intended to use the polynomial \(u(x, y)=a_{1}+a_{2} x+a_{3} \mathrm{y}\) to interpolate the \(u\) displacements in the triangular element. Calculate the constants \(a_{1}, a_{2}\), and \(a_{3}\).

b. What is the strain \(\varepsilon_{x X}\) at the centroid of the triangle?

c. Derive an expression for \(u\) displacements of points on the edge 2-3 as a function of \(\xi\). That is, derive an expression for \(u(\xi)\).

Transcribed Image Text:

Node (x, y) uv 1 (0, 0) 06 2 (3,0) 35 3 (0, 4) 84