Fig. 1: Multiscale topological optimum for force inverter (4 x 4 zones of unique microstructures are allowed).
Multiscale Structural-Material Topology Optimization is being developed to optimize both the macroscopic structures and material topology coupled via periodic homogenization. The unique novelty of our method is that it allows for spatial tailoring of material microstructures throughout the macroscopic domain.
We have developed a generic problem decomposition strategy for the multiscale problem into a set macroscopic and each microscopic optimization problems. This decomposition strategy is applicable to a range of problems beyond the traditional compliance minimization problem and ensures that the multiscale problem is scalable and computationally tractable.
The figure above shows the optimum solutions for macro (blue) and microstructures (red) of a force inverter. We gratefully acknowledge the support of Engineering and Physical Sciences Research Council (EPSRC) fellowship for this research.
Fig. 2: Topology optimization for buckling constraints for a cantilevered beam with uniformly distributed vertical loads.
Buckling Constrained Topology Optimization has long been considered a challenging problem. We investigate some of these challenges for 3D level set method based topology optimization. We collaborate with Dr Ovtchinnikov and Dr Scott, the Numerical Analysis Group of the Rutherford Appleton Laboratory and use their block Jacobi conjugate gradient (BJCG) eigenvalue method with favorable features such as optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts to efficiently and robustly compute a large number of buckling eigenmodes which are used to carry out topology optimization. For the problem shown in figure, we use 25 buckling constraints. We gratefully acknowledge the support of Engineering and Physical Sciences Research Council (EPSRC) fellowship for this research.
Fig. 3: Topology optimization for a p-norm stress constraint for a L-beam.
Stress Constrained Topology Optimization is developed using our level set topology optimization method. Figure 3 shows the well-know benchmark L-beam problem where the acute stress concentration at the re-entrant corner of the initial design domain (left) presents a challenge to topology optimization. The optimum solution obtained after 150 iterations shown a more uniformly distributed stress with the rounded corner and the stress constraint is successfully met. Our investigation shows that our level set stress optimization consistently finds equivalent solutions (objective function with negligible differences) with different starting designs. We gratefully acknowledge the support of the European Office of Aerospace Research and Development, Air Force Office of Scientific Research for this research.
Fig. 4: Optimum internal configuration of the CRM wing box for flutter.
Topology optimization for aeroelastic wing is studied for a range of problems. The aerodynamics of the wing is computed using the doublet lattice method and the 3D finite element method is applied to the internal structure. The coupling of aerodynamic load distribution and displacement is considered for optimization and the level set method is applied to a solid wing. Figure 4 shows the minimum weight solution for aeroelastic flutter where the wing is essentially hollowed out pushing material onto the skin. The wing is stiffened effectively by the skin distribution inducing a bend-twist coupling behavior and aeroelastically tailoring the wing. We gratefully acknowledge the support of the European Office of Aerospace Research and Development, Air Force Office of Scientific Research and NASA Langley for this research.