Abstract:
A general method for the optimal design of large laminated
composite structures, that allows full design variable (ply
thickness and orientation) freedom, has been developed .. The
number of variables and constraints, and hence the problem
size, being dealt with at any given moment in the
optimization process is kept within reasonable bounds by
using a multilevel optimization scheme.
The optimization process is split into a system level and an
element level. At the system level the entire structure is
considered and the individual laminae thicknesses (not ply
angles) are sized so as to minimize the total structural
weight within the constraints placed on the system. These
constraints can include strain, displacement, buckling and
gauge limits. Once the design has converged at this level
the optimization process then switches to the element level.
The objective function at the element level combines a
weight function and a strain energy change function into a
utility function which is minimized and in which the
relative importance of each part is reflected by weighting
coefficients. Minimizing the change in strain energy
ensures load path continuity when switching between the two
levels of optimization, and so decouples the problems at the
two levels. Continuous lamina thickness and ply-angle
variation is used to minimize the element level objective
function while satisfying strain, buckling and gauge constraints. In this way optimum use is made of the
material in each element, without changing the the load
paths in the overall structure and thereby ensuring that the
constraints at the system level are still satisfied. The
procedure switches between the two levels until overall
convergence has been achieved.
Structures representative of straight, forward swept and
delta wings are used to illustrate the effectiveness of the
system and to show that the optimal designs produced are
feasible and realistic, and compare favourably with designs
obtained by more conventional and intuitive methods.