USNCCM 15: US National Congress on Computational Mechanics
Reza Pejman presented at the USNCCM15: US National Congress on Computational Mechanics, July 28-August 1, Austin, Tx.
Title:
Reliability-based and Robust Design Optimization of Microvascular Materials for Active Cooling Applications
Authors:
Reza Pejman, Vahid Keshavarzzadeh, Ahmad Raeisi Najafi
Abstract:
We present a systematic approach for topology/shape optimization of microvascular materials under uncertainty. The emphasis of this presentation is placed on the efficient approach which combines the topology/shape optimization scheme with non-intrusive polynomial chaos expansion (PCE) method to produce a reliable/robust network design of microvascular materials. We develop a novel hybrid topology/shape optimization scheme for microvascular materials which simultaneously can perform the topological change as well as the shape optimization. In this study, Interface-enriched Generalized Finite Element Method (IGFEM) is used wherein the design geometry is projected onto a stationary mesh. This method eliminates the mesh distortion present in conventional Lagrangian shape optimization methods, as well as the essence of remeshing. In addition, very efficient simplified thermal and hydraulic models are implemented to obtain the thermal response of microvascular composites. Having an efficient model with small computational cost facilitate solving of much more complicated optimization problems such as optimization under uncertainty.
The non-intrusiveness of this method allows almost any source of uncertainty to be included virtually in the design optimization process. In the current study, we have introduced uncertainty on loads, material properties, and geometry to address the variability on the working conditions and manufacturing process. Response metrics such as p-norm temperature and pressure drop are characterized as PCE of the underlying uncertain parameters, enabling precise and efficient estimation of statistical moments, failure probabilities and their sensitivities. The sensitivity analysis of the statistical moments and failure probability are conducted by means of PCE in which the necessary gradients on quadrature points are obtained via the adjoint method. A smooth approximation of the indicator function is introduced to facilitate the sensitivity analysis of failure probabilities.
Different sets of application problems have been solved to demonstrate the advantages of using the suggested scheme rather than deterministic optimization method for microvascular materials. The comparison of results shows that as opposed to the optimum configurations obtained by Reliability-based and Robust design optimization, the deterministic designs violate the probabilistic constraints and hence represent non-optimal designs in presence of uncertainty.