Properties of the filler
The volume fraction of fibre in the composite layers will be specified
The thickness of each of the fibre layers is assummed to be the same
The thickness of the sandwich core will be specified
We shall define the application of the force resultants (N, force per unit width) and the bending moments (M, force per unit width * distance) recalling that clockwise moments and tensile forces are positive.
We now need to calculate the uniform strains and bending curvatures (=F*NM) and evaluate the total strain as a function of distance from the centre (
To detect when a ply fails in the laminate we need to determine the value of the Halpin-Tsai failure criterion at each vertical extreme of each ply and then find the value of the imposed stress such that all but one of the values is less than unity, the remaining value being unity.
Input some initial guesses for the applied tensile stress and bending moments
The strength in uniaxial tension is found by setting all the values in NM to zero except N
We can establish which ply (or plies) failed by checking the value of the Halpin-Tsai function for each ply at the imposed failure stress
The strength in bending is found by setting all the values in NM to zero except M4, which will be solved for. The strength is then determined from the product of the applied moment and the maximum vertical displacement, divided by the moment of inertia of a rectangular plate of unit width.
Again we can determine which of the plies in the laminate failed by checking the value of the Halpin-Tsai function at the imposed bending failure stress.
To describe the behaviour of the beam we first need to establish whether the beam is narrow or wide. Wide beams have no strain in the width of the beam and thus deform under plane strain (
The offset of the plane of zero bending strain from the geometric centre of the beam is given by
The effective flexural rigidity per unit width is given by
Flexural Modulus is
Tensile Modulus is