Studies in Composites
Homework 5
1.- Consider a transversally isotropic laminate plate loaded in plane stress conditions and obtain the
differential equation governing the deflection of the plate in terms of the curvatures from the stressstrain relations and the condition of mechanical equilibrium.
2.- Consider a transversally isotropic laminate plate loaded in plane stress conditions and obtain the
equation giving the elastic energy of the strained plate.
3.- Consider a specially orthotropic four layer [90/0/0/90] cross ply graphite-epoxy laminate square
plate (a x b) loaded by a uniform pressure q0 normal to the plane of the plate and simply supported.
Write down the differential equation governing the deflection of the plate in terms of the curvatures
and solve it by inspection after assuming that the deflection can be expressed as
w(x,y) =
ΣΣ C
m,n
sin(m π x/a) sin(n π y/b)
Assume lamina thickness = 0.003 m; a = b = 0.1 m , q0 = 1e6 Pa and E1 = 148 GPa, E2 = 9.65 GPa, G12 =
4.55 GPa, ν12. Calculate the deflection of the plate using first only one term in the series, then four.
4.- Consider the same laminate as in the previous problem. Write down an expression for the total
energy of the plate (elastic – external). Then assume a solution of the form
w(x,y) =
ΣΣ C
m,n
sin(m π x/a) sin(n π y/b)
and use the Ritz method of minimizing the total energy to determine the values of the coefficients Cm,n
and calculate the deflection. Compare with the results of the previous problem.
5.- Consider now instead a symmetric angle ply four layer [45/-45]S graphite-epoxy laminate square
plate under the same loading conditions of the previous problem. Write down an expression for the
total energy of the plate (elastic – external). Use the Ritz method of minimizing the total energy to
determine the values of the coefficients Cm,n and calculate the deflection. Compare with the previously
obtained results.