Macromechanical Analysis of Laminates

Question 1

What does the laminate code assume?

Answer 1

All ply’s are made form the same material and have the same thickness.

Question 2

What does a plate experience during in-plane loads?

Answer 2

1) Shear and axial forces
2) Bending and twisting moments

Question 3

What are the 6 assumptions of the Classical Laminate Theory?

Answer 3

1) Each lamina is elastic and orthotropic
2) Each lamina is homogenous
3) A line straight and perpendicular to the middle of the surface remains straight and perpendicular to the middle surface during deformation
4) The laminate is thin and is loaded only in its plane (plane stress).
5) Displacements are continuous and small throughout the laminate were h is the laminate thickness.
6) No slip occurs between the lamina interfaces.

Question 4

What does the Kirchhoff-Love hypothesis state?

Answer 4

Any line that was originally straight and perpendicular to the x-axis also remains straight and perpendicular to the deformed geometry midplane of the laminate.

Question 5

How do we represent midplane displacements?

Answer 5

1) u0 (x,y) - x direction
2) v0 (x,y) - y-direction
3) w0 (x,y) - z-direction

Question 6

What are the 6 steps for analysing a laminated composite subjected to applied forces and moments?

Answer 6

1) Find the value of the reduced stiffness matrix Q for each ply using its four elastic moduli: E1, E2, Nu12 and G12.
2) Find the value of the transformed reduced stiffness matrix Q bar for each ply using the Q matrix and the angle of ply.
3) Knowing the thickness t, of each ply, find the coordinate of the top ply and bottom surface of each ply.
4) Use the matricies from step 2 and the location of each ply from step 3 to find the three stiffness matricies A, B and D.
5) Substitute the stiffness matrix values found in step 4 and the applied forces and moments into the forces and moment matrix equation and solve the six simultaneous equations to find the midplane strains and curvatures
6) Find the global strains, then the global stresses using the stress-strain equation, local stresses and strains using the transformation equation and then local stresses