Modal damping ratio reliability-based topology optimization of composite cellular structures

Reducing vibrations in the structure can be performed by damping cellular materials. Maximizing the modal damping ratio (MDR) as a physical characteristic of these materials can serve as an effective strategy, which can be applied through deterministic topology optimization (TO). However, multi-source uncertainties usually preventing from an effective MDR design and therefore the optimized structure may not work in a reliable and safe conditions. Using the reliability-based topology method (RBTO) as a solution, this paper uses the dynamic mean value (DMV) as the reliability-based design optimization (RBDO) method utilizing descent conditions in conjunction with tangent algorithm as a novel methodology to capture ultimate optimized multi-material composite cellular structures. Initially in the Tangent-TO which is a TO optimized loop employing the tangent method and an allowed probabilistic constraint (CU), the optimized volume fraction and thereby the optimized layout are derived. Subsequently, the DMV approach utilizing the same admissible probabilistic constraint and proposed TO, concludes the most probable points (MPPs) in which prior that by employing mean volume fraction to perform a normal TO, the proper elemental results have been obtained to be imported into the DMV step. The Tangent-TO applying the MPPs yields the optimized volume fraction for RBTO solution. A comparative analysis of the TO with the RBTO models is explored for many fundamental modes and different damping models. Especially, analysis is extended to cover some damping characteristics such as Rayleigh damping coefficients and pre-stress effect. The obtained results suggest the importance and effectiveness of using the RBTO concept in optimal design of damped structures as part of the design analysis process. In both of the TO and RBTO solutions the maximization of damping because of maximizing modal damping ratio is seen.