Question 2-1

2-D Four-node Plane Finite Element Method - Interpolation Functions

Consider a first-order four-node rectangular plane element shown in Fig. 2-1, made of steel (E = 207 GPa, ν= 0.3), and its thickness t = 0.1 mm 

Figure 2-1: 2-D Four-node Plane Finite Element

The coordinates of each node in mm are:

(x1, y1) = (10+Q, 30+Q) (x2, y2) = (50+Q, 30+Q)

(x3, y3) = (50+Q, 60+Q) (x2, y2) = (10+Q, 60+Q)

The displacements at each node are found in the FEA as follows:

(u1,v1) = (0.001, 0.005) mm (u2,v2) = (0.0015,0.0006) mm

(u3,v3) = (0.0012,0.0008)mm (u2,v2) = (0.0025,0.001) mm

You are required to determine the displacements at a point with its coordinates (30+Q, 45+Q).