solution

A square region undergoes deformation as shown in Fig. P1.25 . The displacements x , y at the corners are given as u = 0, v = 0 at points A , C and D , and u = -0.01, v = 0.01 at B . x , y coordinates of the points are A (0, 0), B (1, 0), C (1, 1), D (0, 1), Q (0.5, 0.5).

(a) Develop a displacement field that describes the above deformation. That is develop functions u ( x , y ), v ( x , y ) that satisfy the specified corner values.

(b) From (a), determine the shear strain at points B and Q .