In this paper, design strategies are developed to explore better approaches of enforcing local layer-wise curvature constraints in the optimization of variable stiffness laminates in order to ensure the manufacturability of optimized designs based on the limitations of automated fiber placement. The methods developed here aim to improve an existing approach of imposing the curvature constraint directly on the fiber angles (i.e., direct control method) and are suitable for a design framework that uses lamination parameters as primary design variables. One approach developed here, termed the indirect control method, enforces the curvature constraint indirectly with better computational efficiency through the spatial gradient of the lamination parameters. It is shown that the curvature constraint on the actual fiber angles can also be satisfied with a sufficiently stringent upper bound albeit it produces overly conservative designs. Alternatively, an enhanced approach, termed the hybrid control method, is developed by combining the direct method and a relaxed version of the indirect control method. The case studies of minimum compliance design indicate that it provides the best manufacturable design among the three methods in the context of variable stiffness laminates using lamination parameters.

A way to approximate the compliance of composites for optimisation is described. A two-level approximation scheme is proposed inspired by traditional approximation concepts such as force approximations and convex linearisation. In level one, an approximation in terms of the reciprocal in-plane stiffness matrix is made. In level two, either the lamination parameters, or the nodal fibre angle distribution are used as design variables. A quadratic approximation is used to build the approximations in terms of the fibre angles. The method of conservative, convex separable approximations is used for the optimisation. Conservativeness is guaranteed by adding a convex damping function to the approximations. Two numerical examples, one optimisng the compliance of a plate clamped on the left, loaded downwards on the bottom right, another one optimising the compliance of a plate loaded with a shear force and a moment show the computational efficiency of the proposed optimisation algorithm.

Optimisation algorithms used to automatically size structural members commonly involve stress constraints to avoid material failure. Therefore the cost of optimisation grows rapidly as the number of structural members is increased due to the corresponding increase in the number of constraints. In this work, an efficient method for large scale stress constrained structural sizing optimisation problems is proposed. A convex, separable, and scalable approximation for stress constraints which splits the approximation into a local fully stressed term and a global load distribution term is introduced. Predictor-corrector interior point method, an excellent option for large scale optimization problem, is chosen to solve the approximate subproblems. The core idea in this work is to achieve computational efficiency in the optimization procedure by avoiding the construction and the solution of the Schur complement system generated by the interior point method. Avoiding the Schur complement, and explicit sensitivity analysis, eliminates the high cost of solving stress constrained problems within the interior point optimisation. This is achieved using the preconditioned conjugate gradient method, and a new preconditioner is proposed specifically for stress constrained problems. The proposed method is applied to a number of beam sizing problems. Numerical results show that optimal complexity is achieved by the algorithm, the computational cost being linearly proportional to the number of sizing variables.