Multilevel optimum design of large laminated composite structures - Watkins, R. I. (Cranfield University, 1986)
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.