Question

Derive the reduced stiffness matrix Qxy relating stress_xy to strain_xy

Derive the reduced compliance matrix relating strain_xy to stress_xy  

Determine the Ex, Ey, nu_xy, Gxy, in the reference frame (x and y) as a function of angle 0 and 45 degrees for a unidirectional lamina having the properties

What are your observations of the values increasing or decreasing with respect to the 0 degree lamina when the lamina is rotated to 45 degrees.

E₁=181 GPa; E₂=10.3 GPa; u₁₂=0.28; G₁₂=7.17 GPa

please explain in detail. thanks!

Answer 1

Dear Kindly find the value of reduced stiffness matrix as well as the value of reduced compliance matrix.

also check the value of transformed reduced stiffness matrix for 0 degree and 45 degree.

from the given value it is observed that stiffness matrix is decreasing from zero degree to 45 degree. You can check the given matrix of Qij for 0 and 45 degree.

I am attachng a MATLAB coding to understand these values.  

For the last part of the given problem I have take the stacking sequence of of laminate [45/-45/0/-45/45] and found the value engineering constant. Please go through the attachment and coding file for more detail.

for any doubt kindly comment me.