WCSMO13: World Congress of Structural and Multidisciplinary Optimization
Prof. Ahmad R. Najafi will present at the WCSMO13: World Congress of Structural and Multidisciplinary Optimization, May 20-24, Beijing, China.
Title:
Efficient Scheme for IGFEM-based Topology/Shape Optimization of Microvascular Materials Considering Uncertainty in Geometry, Load, and Material Properties
Authors:
Reza Pejman, Marcus H.Y. Tan, Vahid Keshavarzzadeh, Sherif H. Aboubakr, William H. Martin, Jason F. Patrick, Ahmad Raeisi Najafi
Abstract:
The aim of this study is presenting a gradient-based topology/shape optimization approach to design microvascular composites under uncertainty. The focus of this presentation is on an efficient approach which combines the topology/shape optimization scheme with non-intrusive polynomial chaos expansion (PCE) method to produce a reliable/robust design of microchannel network in a microvascular composite. We develop a novel hybrid topology/shape optimization scheme for microvascular composites which simultaneously can carry out the topological change as well as the shape optimization. We previously developed a fully analytical sensitivity analysis of the shape optimization of microvascular composites in Interface-enriched Generalized Finite Element Method (IGFEM) framework over a stationary mesh. The developed analytical sensitivity analysis bypasses the issues often observed in finite differences and semi-analytical sensitivity methods. The developed IGFEM-based Eulerian shape optimization scheme in current work eliminates the mesh distortion present in conventional Lagrangian shape optimization methods, as well as the essence of remeshing.
In the current study, we add two new features to the previously developed shape optimization approach: First, the optimizer is able to appear/disappear the microchannels and change the topology of the network during the optimization process; second, we integrate the non-intrusive polynomial chaos expansion method into our hybrid topology/shape optimization scheme to design a reliable/robust microchannel network for microvascular composites. The first feature is added by introducing a new set of design parameters which act analogous to the penalization factor of Solid Isotropic Material with Penalization (SIMP) method. This set of design parameters is responsible for adding/removing the microchannels based on the prescribed objective function and imposed constraints. The analytical sensitivity of the newly introduced set of design parameters has been developed and their accuracy is verified against the finite difference method. The second feature enables the optimizer to perform Reliability-based/Robust design optimization instead of deterministic optimization. The non-intrusiveness of this method allows for many different sources of uncertainties to be included virtually in the design optimization process. 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 accurate and efficient estimation of statistical moments, failure probabilities and their sensitivities. The sensitivity analysis of the statistical moments and failure probabilities are carried out by means of PCE in which the required gradients on quadrature points are computed via the adjoint method. A smooth approximation of the indicator function is used to facilitate the sensitivity analysis of failure probabilities.
By using the 3D printing method, the microvascular composite is fabricated, and the method has been validated by experiment. An acceptable agreement has been seen between the experimental and numerical results. To demonstrate the abilities of the suggested hybrid topology/shape optimization scheme, four sets of application problems have been solved. First three sets of examples are designed with the aim of showing the benefits of using the topology/shape optimization method rather than only shape optimization approach. In the first set of examples, we have shown that in contrast to the shape optimization scheme the design space in the topology/shape optimization method is not locked down to the topology of the initial configuration. The second set of problems represent the ability of the topology/shape optimization method to handle strict constraints. The third set of examples have illustrated how topological changes and network branching can lead to vascular redundancy, which is of great importance in designing microvascular cooling networks for blockage tolerance. Finally, in the last set of application problems, we demonstrate the ability of the suggested scheme in producing reliable/robust designs. 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 the presence of uncertainty.