Simultaneous Topology and Material Optimization of Composite Structures under Uncertainty

Sammanfattning: Composite materials are known to have superior stiffness and strength properties per unit weight compared to metallic materials. These properties and the ability to tailor the mechanical properties of composites is the main motivation for choosing composite materials for structural components. Design of composite structures requires consideration of many material, design and manufacturing factors to generate designs with desired behaviour. A promising approach to handle this is to use structural optimization (SO) in the design process to obtain composite structures with optimal performance. However, optimality often comes at the cost of robustness unless consideration is taken to uncertainty in the input data to the optimization problem. It is for example well-known that composite materials can exhibit significant variation of mechanical properties and it is thus important that this is accounted for in the optimization. In this thesis, SO methods for design of composite structures are developed, including continuous and discrete parametrization methods, a method for reducing the impact of cure-induced distortion of composite parts in manufacturing; and methods for handling uncertainty to ensure robustness of optimized designs. The focus has been to extend the SO methodology to handle material uncertainty associated with the mechanical properties of composite materials. An uncertainty parametrization was developed for the stiffness properties of a composite material based on a worst-case, or deterministic, approach. Using this parametrization, an uncertainty quantification was performed to investigate the influence of material uncertainty on the performance of optimized composite structures, indicating that the effect can be significant. Combining a discrete parametrization method with the uncertainty quantification, a deterministic method for handling material uncertainty in SO of composite structures was then proposed. This method consists of a min-max optimization problem that simultaneously solves the design and material uncertainty problems to generate optimized composite designs for worst-case values of the uncertain material properties related to both stiffness and strength. Several numerical test problems are solved to exemplify the applicability of the proposed SO methodologies.