This thesis reports on research into the causes of local optima when optimization algorithms are applied to aerospace structural design. A thorough understanding of local optima will enable the engineers to select the algorithm for optimization or to guide the optimization to ensure either global optima or near optimal solutions are achieved. Therefore, a comprehensive literature review has been conducted and several illustrative examples have been identified to help fully understand the cause and importance of local optima. The first application involved the design of the internal structure of a simplified wing spoiler. MSC.NASTRAN was used to optimize each discretized location of an additional rib with the aid of a Patran Command Language (PCL) algorithm. The objective function of minimum weight was approximated as a multimodal function in a 2D smooth curve where the local and global optima were identified. The theory of continuous rectangular plates was used to explain the phenomena. The second problem considered buckling of a wing rib. A PCL code was written to obtain the rib buckling factors as the position of the center of a square cutout was varied within a constrained area. The rib linear buckling factor versus the centre position O(X, Y) of the square cutout was plotted in a 3D surface contour plot. Load path theory and relevant plate buckling theories were used to explain the local and global maxima identified. The final example considered the maximization of the buckling load of a simply supported composite laminated plate under in-plane loading. A conventional Genetic Algorithm was used to examine the local and global optima of the critical buckling load factor. Many local and global optima were identified and explained and many near-optimal solutions were found in a single run. A significant understanding of local optima in aerospace structural design with the optimal utilization of available software and the appropriate selection of optimization algorithms has been achieved. Further work could either include implementing the proposed global optimization strategies or include implementing rapid methods for identifying multiple local optima.

This thesis reports on research into the causes of local optima when optimization algorithms are applied to aerospace structural design. A thorough understanding of local optima will enable the engineers to select the algorithm for optimization or to guide the optimization to ensure either global optima or near optimal solutions are achieved. Therefore, a comprehensive literature review has been conducted and several illustrative examples have been identified to help fully understand the cause and importance of local optima. The first application involved the design of the internal structure of a simplified wing spoiler. MSC.NASTRAN was used to optimize each discretized location of an additional rib with the aid of a Patran Command Language (PCL) algorithm. The objective function of minimum weight was approximated as a multimodal function in a 2D smooth curve where the local and global optima were identified. The theory of continuous rectangular plates was used to explain the phenomena. The second problem considered buckling of a wing rib. A PCL code was written to obtain the rib buckling factors as the position of the center of a square cutout was varied within a constrained area. The rib linear buckling factor versus the centre position O(X, Y) of the square cutout was plotted in a 3D surface contour plot. Load path theory and relevant plate buckling theories were used to explain the local and global maxima identified. The final example considered the maximization of the buckling load of a simply supported composite laminated plate under in-plane loading. A conventional Genetic Algorithm was used to examine the local and global optima of the critical buckling load factor. Many local and global optima were identified and explained and many near-optimal solutions were found in a single run. A significant understanding of local optima in aerospace structural design with the optimal utilization of available software and the appropriate selection of optimization algorithms has been achieved. Further work could either include implementing the proposed global optimization strategies or include implementing rapid methods for identifying multiple local optima.

This thesis reports on research into the causes of local optima when optimization algorithms are applied to aerospace structural design. A thorough understanding of local optima will enable the engineers to select the algorithm for optimization or to guide the optimization to ensure either global optima or near optimal solutions are achieved. Therefore, a comprehensive literature review has been conducted and several illustrative examples have been identified to help fully understand the cause and importance of local optima. The first application involved the design of the internal structure of a simplified wing spoiler. MSC.NASTRAN was used to optimize each discretized location of an additional rib with the aid of a Patran Command Language (PCL) algorithm. The objective function of minimum weight was approximated as a multimodal function in a 2D smooth curve where the local and global optima were identified. The theory of continuous rectangular plates was used to explain the phenomena. The second problem considered buckling of a wing rib. A PCL code was written to obtain the rib buckling factors as the position of the center of a square cutout was varied within a constrained area. The rib linear buckling factor versus the centre position O(X, Y) of the square cutout was plotted in a 3D surface contour plot. Load path theory and relevant plate buckling theories were used to explain the local and global maxima identified. The final example considered the maximization of the buckling load of a simply supported composite laminated plate under in-plane loading. A conventional Genetic Algorithm was used to examine the local and global optima of the critical buckling load factor. Many local and global optima were identified and explained and many near-optimal solutions were found in a single run. A significant understanding of local optima in aerospace structural design with the optimal utilization of available software and the appropriate selection of optimization algorithms has been achieved. Further work could either include implementing the proposed global optimization strategies or include implementing rapid methods for identifying multiple local optima.