Blending

• Large composite panels are usually subjected to loads that vary across the panel. Such panels are divided into regions called elements, for the purpose of analysis. 

• The loads are assumed to be constant for each element but may vary between different elements. 

• For a certain load distribution the key element representing the load concentration can be identified. Each ply starts from the key element and may cover any number of elements as long as they are adjecent to one another. 

• The abrupt change of fiber direction within one ply is not allowed. 

• Blending ensures that a panel is manufacturable by allowing controlled ply drops and consistent fiber angles across the panel. 

Two optimization problem formulations were introduced to incorporate blending rules.
 

t - Formulation

t_i(j,k)- binary thickness variable indicating presence of a ply i in an element (j,k)
 

                                                 minimize    f(q,t)

                                         subject to        g_l(q,t) > 0   l = 1,...,m
                                                                t_i(j,k) > t_i(j,k+1)
                                                                t_i(j,k) > t_{i(j+1,k)  i = 1,...,N   j = 1,...,P   k = 1,...Q}
 

d-Formulation

d_i(j) - distance variable indicating number of elements a ply i occupies ina row j
 

                                                  minimize    f(q,d)

                                         subject to        g_l(q,t) > 0   l = 1,...,m
                                                                d_i(j) > t_{i(j+1)   i = 1,...,N   j = 1,...,P}
 

N = maximum number of plies in each element
P = number of elements in a row
Q = number of elements in a column

Sample 4x3 panel