Boyan Stefanov Lazarov

Giga-voxel computational morphogenesis for structural design

In the design of industrial products ranging from hearing aids to automobiles and aeroplanes, material is distributed so as to maximize the performance and minimize the cost. Historically, human intuition and insight have driven the evolution of mechanical design, recently assisted by computer-aided design approaches. The computer-aided approach known as topology optimization enables unrestricted design freedom and shows great promise with regard to weight savings, but its applicability has so far been limited to the design of single components or simple structures, owing to the resolution limits of current optimization methods. Here we report a computational morphogenesis tool, implemented on a supercomputer, that produces designs with giga-voxel resolution—more than two orders of magnitude higher than previously reported. Such resolution provides insights into the optimal distribution of material within a structure that were hitherto unachievable owing to the challenges of scaling up existing modelling and optimization frameworks. As an example, we apply the tool to the design of the internal structure of a full-scale aeroplane wing. The optimized full-wing design has unprecedented structural detail at length scales ranging from tens of metres to millimetres and, intriguingly, shows remarkable similarity to naturally occurring bone structures in, for example, bird beaks. We estimate that our optimized design corresponds to a reduction in mass of 2–5 per cent compared to currently used aeroplane wing designs, which translates into a reduction in fuel consumption of about 40–200 tonnes per year per aeroplane. Our morphogenesis process is generally applicable, not only to mechanical design, but also to flow systems, antennas, nano-optics and micro-systems.

Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner

Abstract This paper applies topology optimisation to the design of structures with periodic and layered microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all microstructural details, as compared to the often used homogenisation approach. The approach takes boundary conditions into account and ensures connected and macroscopically optimised microstructures regardless of the difference in micro- and macroscopic length scales. This results in microstructures tailored for specific applications rather than specific properties. Manufacturability is further ensured by the use of robust topology optimisation. Dealing with the complete macroscopic structure and its response is computationally challenging as very fine discretisations are needed in order to resolve all microstructural details. Therefore, this paper shows the benefits of applying a contrast-independent spectral preconditioner based on the multiscale finite element method (MsFEM) to large structures with fully-resolved microstructural details. It is shown that a single preconditioner can be reused for many design iterations and used for several design realisations, in turn leading to massive savings in computational cost. The density-based topology optimisation approach combined with a Heaviside projection filter and a stochastic robust formulation is used on various problems, with both periodic and layered microstructures. The presented approach is shown to allow for the topology optimisation of very large problems in Matlab , specifically a problem with 26 million displacement degrees of freedom in 26 hours using a single computational thread.

Topology optimization of unsteady flow problems using the lattice Boltzmann method

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

Topology Optimization Using Multiscale Finite Element Method for High-Contrast Media

The focus of this paper is on the applicability of multiscale finite element coarse spaces for reducing the computational burden in topology optimization. The coarse spaces are obtained by solving a set of local eigenvalue problems on overlapping patches covering the computational domain. The approach is relatively easy for parallelization, due to the complete independence of the subproblems, and ensures contrast independent convergence of the iterative state problem solvers. Several modifications for reducing the computational cost in connection to topology optimization are discussed in details. The method is exemplified in minimum compliance designs for linear elasticity.

Reducing Wind Turbine Load Simulation Uncertainties by Means of a Constrained Gaussian Turbulence Field

We demonstrate a method for incorporating wind measurements from multiple-point scanning lidars into the turbulence fields serving as input to wind turbine load simulations. The measurement values are included in the analysis by applying constraints to randomly generated turbulence fields. A numerical study shows the application of the constrained turbulence method to load simulations on a 10MW wind turbine model, using two example lidar patterns – a 5-point pattern forming a square with a central point, and a circular one. Based on the results of this study, we assess the influence of applying the proposed method on the statistical uncertainty in wind turbine extreme and fatigue loads.

Tailoring Macroscale Response of Mechanical and Heat Transfer Systems by Topology Optimization of Microstructural Details

The aim of this book chapter is to demonstrate a methodology for tailoring macroscale response by topology optimizing microstructural details. The microscale and macroscale response are completely coupled by treating the full model. The multiscale finite element method (MsFEM) for high-contrast material parameters is proposed to alleviate the high computational cost associated with solving the discrete systems arising during the topology optimization process. Problems within important engineering areas, heat transfer and linear elasticity, are considered for exemplifying the approach. It is demonstrated that it is important to account for the boundary effects to ensure prescribed behavior of the macrostructure. The obtained microstructures are designed for specific applications, in contrast to more traditional homogenization approaches where the microstructure is designed for specific material properties.

Combined Length Scale and Overhang Angle Control in Minimum Compliance Topology Optimization for Additive Manufacturing

This paper focusses on topology optimization for additive manufacturing. Two manufacturing constraints are considered: minimum length scale and maximum overhang angle. The first is needed to ensure that the condition on minimal printable feature sizes is satisfied, while the second eliminates the need for a temporary support structure. Filtering schemes have been proposed in the literature to ensure either a minimum length scale or a maximum overhang angle, but not both simultaneously. In this paper, it is shown that both constraints cannot simultaneously be met by simply applying both filters sequentially, as the effect of the first filter is destroyed by the second. A new, slightly more complex filtering scheme is therefore proposed, which does allow simultaneous control over length scale and overhang angle in a minimum compliance topology optimization problem. The method is successfully applied to a 2D benchmark problem.

TOPOLOGY OPTIMIZATION OF TWO-DIMENSIONAL WAVE BARRIERS FOR THE REDUCTION OF GROUND VIBRATION TRANSMISSION

Abstract. This paper studies topology optimization as a tool for designing barriers for ground vibration transmission. A two-dimensional problem is considered where material is stiffened in the design domain, located in the transmission path between the wource and the receiver. The two-dimensional homogeneous halfspace is excited at the surface. The response at the receiver is minimized for a harmonic load by distributing a stiffened material in the design domain using topology optimization. The performance is compared to a wall barrier which has the same volume of material and has a depth equal to the depth of the design domain. At low frequencies, where the wavelengths are large compared to the height of the domain, the optimized wave barrier reflects and guides waves away from the surface. At high frequencies, destructive interference is obtained that leads to high values of the insertion loss. The presence of small features in the designs makes the performance sensitive to deviations in the geometry. In order to obtain a design which is robust with respect to geometric imperfections, a worst case approach is followed. The resulting design not only outperforms the wall barrier, but is also robust with respect to deviations in the geometry. This paper also shows that the robust design can be used to develop simplified design solutions.

Topology optimization of ultra‐fast nano‐photonic switches

The aim of this paper is to demonstrate 1D switch designs obtained by topology optimization which show better performance than the designs considered in the literature. Such devices are non‐linear and their performance depends on the efficiency of light‐matter interaction. Simple optical switches can be designed using physical considerations and intuition. Alternatively the proposed topology optimization scheme provides a systematic methodology for obtaining and optimizing the layout of the devices. It is shown that the algorithm can efficiently handle more than two materials and that the obtained switches possess excellent performance.