We formulate and develop gradient-based shape optimization scheme that projects the design geometry on a fixed mesh and we used our advanced FEM for analysis. Our approach eliminates the mesh distortion present in conventional Lagrangian shape optimization methods, as well as the need for remeshing. To perform our optimization method, we have formulated a novel analytic sensitivity by introducing new terms involving the sensitivity of shape functions and their spatial derivatives that we must consider for a full analytical sensitivity analysis. We implement our optimization method to a broad range of multiscale/multiphysics problems.
First Example: Optimal design of a cantilever beam
A benchmark structural problem: cantilever beam design. This work was done in collaboration with Dr. Safdari (Illinois Rocstar Startup), Dr. Geubelle and Dr. Tortorelli (UIUC).
See the design evolution in the following videos. The first video shows the results obtained using our NIGFEM-based shape optimization, while the second video is for topology optimization.
Second Example: Design of actively-cooled microvascular composite panels
Gradient-based design of actively-cooled microvascular composite panels for temperature regulation and structural protection in a battery packaging scheme which is used in electric vehicles. This work was done in collaboration with Dr. Tan, Dr. Pety, Dr. White and Dr. Geubelle (UIUC).
The following animation illustrates the change in microvascular network design during optimization over a fixed mesh.
Related Publications
- Raeisi Najafi A., Safdari M., Tortorelli D., Geubelle P.H.; “Shape Optimization Using a NURBS-based Interface-enriched Generalized FEM” International Journal for Numerical Methods in Engineering, vol. 111, pp. 927-954, 2017.
- Pety, S.J., Tan M.H.Y., Raeisi Najafi A., Barnett P.R., Sottos N. R., Geubelle P.H., White S. R.; “Carbon Fiber Composites with 2D Microvascular Networks for Battery Cooling”, International Journal of Heat and Mass Transfer, vol. 115, pp. 513-522, 2017.
- Pety, S.J., Tan M.H.Y., Raeisi Najafi A., Gendusa C.G., Barnett P.R., Sottos N. R., Geubelle P.H., White S. R.; “Design of redundant microvascular cooling networks for blockage tolerance”, Applied Thermal Engineering, accepted.
- Tan M.H.Y., Raeisi Najafi A., Pety, S.J., White S. R., Geubelle P.H.; “Gradient-based Design of Actively-cooled Microvascular Composite Panels”, International Journal of Heat and Mass Transfer, vol. 103, pp. 594-606, 2016.
- Tan M.H.Y., Raeisi Najafi A., Pety, S.J., White S. R., Geubelle P.H.; “Multi-objective design of microvascular panels subject to operating constraints”, (Submitted).
- Raeisi Najafi A., Safdari M., Tortorelli D., Geubelle P.H.; “A Gradient-based Shape Optimization Scheme Using an Interface-enriched Generalized FEM” Computer Methods in Applied Mechanics and Engineering, vol. 296, pp. 1-17, 2015.