Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Boundary velocity control of incompressible flow with an application to viscous drag reduction
SIAM Journal on Control and Optimization
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Optimal Control of Distributed Parameter Systems
Optimal Control of Distributed Parameter Systems
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Shape-topology optimization for Navier-Stokes problem using variational level set method
Journal of Computational and Applied Mathematics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Optimal design for non-Newtonian flows using a topology optimization approach
Computers & Mathematics with Applications
On projection methods, convergence and robust formulations in topology optimization
Structural and Multidisciplinary Optimization
Heaviside projection based topology optimization by a PDE-filtered scalar function
Structural and Multidisciplinary Optimization
Topology optimization of unsteady incompressible Navier-Stokes flows
Journal of Computational Physics
Structural and Multidisciplinary Optimization
| Hi-index | 31.45 |
This paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control. In the presented method, the material topology is determined using the SIMP (Solid Isotropic Material with Penalization) method, which has been popularly used in topology optimization. In the SIMP method, the design variable is relaxed and bounded in the interval [0,1], and the evolution of the design variable is usually implemented by the method of moving asymptotes (MMA), which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable. In the combination of topology optimization and optimal control method, the control variable appears along with the design variable. In order to evolve the control variable and design variable using MMA simultaneously, the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval [0,1], which is the same as the bound constraint of the design variable. The optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity. During the optimization procedure, the design and control variables are filtered by the Helmholtz filters to ensure the smoothness of the distribution. To ensure the minimum scale length and remove the gray area in the material topology, the filtered design variable is projected by the threshold method. The feasibility and robustness of the combination of these two methods are demonstrated by several test problems, including heat transfer, fluid flow and compliance minimization.