Manufacturing issues
  • 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. 

Blending rule - Plies may be droped in the > direction starting from the key element

Design space

Two optimization problem formulations were introduced to incorporate blending rules.

t - Formulation

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

                                                 minimize    f(q,t)

                                         subject to        gl(q,t) > 0   l = 1,...,m
                                                                ti(j,k) > ti(j,k+1)
                                                                ti(j,k) > ti(j+1,ki = 1,...,N   j = 1,...,P   k = 1,...Q


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

                                                  minimize    f(q,d)

                                         subject to        gl(q,t) > 0   l = 1,...,m
                                                                di(j) > ti(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

Layup for a blended panel using d variables

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