Manufacturing cost and reliability-based shape optimization of plate structures

A novel methodology is presented for the manufacturing cost and reliability-based optimization of plate structures with the boundary element method (BEM), with the aim of improving the accuracy, robustness, and efficiency of the optimization of aircraft structures. The BEM plate formulations with respect to plate thickness are derived for the first time, and used as part of an implicit differentiation method (IDM), enabling the full shape optimization of plate structures with the BEM. These implicit derivatives are validated against derivatives obtained from the finite difference method (FDM) and from an analytical solution. Results indicate that the IDM is more robust than the FDM and in excellent agreement with the analytical solution, and more accurate than the FDM for most of the step-sizes investigated. To demonstrate the full shape optimization of plates with the newly developed IDM, a numerical example involving reliability-based design optimization and manufacturing cost optimization is presented for a plate structure. Results show that the newly developed IDM is more efficient than the FDM when performing this optimization.