Material uncertainty quantification for optimized composite structures with failure criteria

We propose a method to analyze effects of material uncertainty in composite laminate structures optimized using a simultaneous topology and material optimization approach. The method is based on computing worst -case values for the material properties and provides an efficient way of handling variation in material properties of composites for stiffness driven optimization problems. An analysis is performed to evaluate the impact of material uncertainty on designs from two design problems: Maximization of stiffness and minimization of a failure criteria index, respectively. The design problems are solved using different loads, boundary conditions and manufacturing constraints. The analysis indicates that the influence of material uncertainty is dependent on the type of optimization problem. For compliance problems the impact on the objective value is proportional to the changes of the constitutive properties and the effect of material uncertainty is consistent and predictable for the generated designs. The strength-based problem shows that material uncertainty has a significant impact on the response, and the effects of material uncertainty is not consistent and changes for different design requirements. In addition, the results show an increase of up to 25% of the maximum failure index when considering the worst-case deviation of the constitutive properties from their nominal values.