Ex. 1(35%): 1) Write down the elastic compliance matrix [a] for anisotropic materials according to the three- dimensional stress-strain relations.(10%) AX 39 35 H =[a] [ay] = 2) How many independent elastic constants in the elastic constant matrix (2.5%) ? What are them? (10.5%) (e) Write down the elastic compliance matrix for a transversely isotropic material? (9%) bbb. A 1 Ex H=1 cm Vay E D [ay] = Pyx Vex Ey E 1 Ey Vz Vyz Ex Ey 1x.yyy Ex nxx Ex Vay E 1 E nayz E Ey nyxz x E Ey xxy lyxy Nexy E Ey E nya,xnxx.xxyx Gry Gys Gz " " Gys Gry xx.xyz Gry Hy Hyys G Gxy (d) Write down the 3 equations that can be derived from the elastic compliance matrix [a] due to symmetry (ay-ap).(3%) yza Gy Gz 1 Gyz Ex. 2 (12%): Consider a 2-D body (a unit squire ABCD) in the y-z plane as shown in the figure below. After deformation, the four corner points move A'. B. C', and D, respectively. Assume that the displacement field is given by L=1 cm 1 Pxy.xx Gyz Gz Gxy Hyzxy Hxz.xy 1 Gyz GE Gry @= 0.03y (1) Calculate the new coordinate of the four points A, B, C, and D. (4%) (2) Draw the 2-D body after deformation by hand directly in the figure shown below. (2%) (3) Calculate all the strain components (6 E) (6%) [a] = B C