Optimisation of a 4-layer laminated cylindrical shell to meet given cross-sectional stiffness properties

The design of a 4-layer laminated cylindrical shell is considered as an optimisation problem in which the objective is determined as the N-dimensional Euclidean distance between current and target value of various cross-sectional stiffness properties (where N is the number of cross-sectional stiffness properties to be matched).The optimisation problem is made convex by appropriate choice of design variables, allowing a deterministic solution method to be employed. Although such deterministic methods are usually based on linear approximations of the objective function with respect to the design variables, it is found that the optimisation efficiency can be significantly improved by making a linear approximation with respect to each of the cross-sectional properties in turn (rather than the single objective function). The resulting simultaneous linear equations may be easily solved via matrix methods, and a solution to the linearised problem may be obtained directly. Successive iterations remove any discrepancy between the linearised and actual behaviours of the problem.