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The article presents an efficient solution method for structural topology optimization aimed at maximizing the fundamental frequency of vibration. Nowadays, this is still a challenging problem mainly because of the high computational cost required by spectral analyses. The proposed method relies on replacing the eigenvalue problem with a frequency response one, which can be tuned and efficiently solved by a multilevel procedure. Connections of the method with multigrid eigenvalue solvers are discussed in details. Several applications demonstrating more than 90% savings of the computational time are presented as well.

This article confirms the superior performance of topology optimized heat sinks compared to lattice designs and suggests simpler manufacturable pin-fin design interpretations. The development is driven by the wide adoption of light-emitting-diode (LED) lamps for industrial and residential lighting. Even for advanced lighting technology as LEDs, a large fraction of the input power is still converted to heat. Thus, efficient thermal control lowers energy waste, increases lifetime and reduces maintenance costs of this rapidly growing, expectedly soon to be governing, illumination technology. The presented heat sink solutions are generated by topology optimization, a computational morphogenesis approach with ultimate design freedom, relying on high-performance computing and simulation. Optimized devices exhibit complex and organic-looking topologies which are realized with the help of additive manufacturing. To reduce manufacturing cost, a simplified interpretation of the optimized design is produced and validated as well. Numerical and experimental results agree well and indicate that the obtained designs outperform lattice geometries by more than 21%, resulting in a doubling of life expectancy and 50% decrease in operational cost.

Topology optimised designs for passive cooling of light-emitting diode (LED) lamps are investigated through extensive numerical parameter studies. The designs are optimised for either horizontal or vertical orientations and are compared to a lattice-fin design as well as a simple parameter optimised commercial pin fin design. The different orientations result in significant differences in topologies. The optimisation favours placing material at outer boundaries of the design domain, leaving a hollow core that allows the buoyancy forces to accelerate the air to higher speeds. Investigations show that increasing design symmetry yields performance with less sensitivity to orientation with a minor loss in mean performance. The topology-optimised designs of heat sinks for natural convection yield a 26% lower package temperature using around 12% less material compared to the lattice-fin design, while maintaining low sensitivity to orientation. Furthermore, they exhibit several defining features and provide insight and general guidelines for the design of passive coolers for LED lamps.

A new suite of computational procedures for stress-constrained continuum topology optimization is presented. In contrast to common approaches for imposing stress constraints, herein it is proposed to limit the maximum stress by controlling the length scale of the optimized design. Several procedures are formulated based on the treatment of the filter radius as a design variable. This enables to automatically manipulate the minimum length scale such that stresses are constrained to the allowable value, while the optimization is driven to minimizing compliance under a volume constraint – without any direct constraints on stresses. Numerical experiments are presented that incorporate the following : 1) Global control over the filter radius that leads to a uniform minimum length scale throughout the design; 2) Spatial variation of the filter radius that leads to local manipulation of the minimum length according to stress concentrations; and 3) Combinations of the two above. The optimized designs provide high-quality trade-offs between compliance, stress and volume. From a computational perspective, the proposed procedures are efficient and simple to implement: essentially, stress-constrained topology optimization is posed as a minimum compliance problem with additional treatment of the length scale.

The goal of this article is to demonstrate the applicability and to discuss the advantages and disadvantages of automatic differentiation in topology optimization. The technique makes it possible to wholly or partially automate the evaluation of derivatives for optimization problems and is demonstrated on two separate, previously published types of problems in topology optimization. Two separate software packages for automatic differentiation, CoDiPack and Tapenade are considered, and their performance and usability trade-offs are discussed and compared to a hand coded adjoint gradient evaluation process. Finally, the resulting optimization framework is verified by applying it to a non-trivial unsteady flow topology optimization problem.

Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can provide competitive designs in terms of cost, materials and functionality under a wide set of constraints. However, the optimized topologies are often considered as conceptual due to loosely defined topologies and the need of postprocessing. Subsequent amendments can affect the optimized design performance and in many cases can completely destroy the optimality of the solution. Therefore, the goal of this paper is to review recent advancements in obtaining manufacturable topology-optimized designs. The focus is on methods for imposing minimum and maximum length scales, and ensuring manufacturable, well-defined designs with robust performances. The overview discusses the limitations, the advantages and the associated computational costs. The review is completed with optimized designs for minimum compliance, mechanism design and heat transfer.

A density-based topology optimization approach is proposed to design structures with strict minimum length scale. The idea is based on using a filtering-threshold topology optimization scheme and computationally cheap geometric constraints. The constraints are defined over the underlying structural geometry represented by the filtered and physical fields. Satisfying the constraints leads to a design that possesses user-specified minimum length scale. Conventional topology optimization problems can be augmented with the proposed constraints to achieve minimum length scale on the final design. No additional finite element analysis is required for the constrained optimization. Several benchmark examples are presented to show the effectiveness of this approach.

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.

The objective of this work is to present benets and challenges of using robust topology optimization techniques for minimizing the sound pressure in interior acoustic problems. The focus is on creating designs which maintain high performance under uniform spatial variations. This work takes offset in previous work considering topology optimization for interior acoustic problems, [1]. However in the previous work the robustness of the designs was not considered.

The aim of this work is to present a method to design material microstructures with high dissipation using topology optimization. In order to compute the macroscopic energy dissipation in periodic structures, we focus both on capturing the physical dissipation mechanism and to find the effective macroscopic dissipation. The effective elastic material properties of a periodic structure can be found numerically using homogenization as describe in e.g. (Guedes and Kikuchi, 1990). For dissipative materials a quasi-static approach can be used to find the homogenized complex elasticity tensor, and thereby the material’s loss factor, however, only for large wave lengths (small wave numbers) and constant material parameters (Andreasen et al., 2012). An alternative way to determine the material’s loss factor is to consider the material’s band diagram (Sigalas and Economou, 1992), from which the loss factor can be deduced. Designs obtained by e.g. maximizing the material’s loss factor for a given frequency range will be presented. The method will be demonstrated both using base cells consisting of continuum elements and base cells consisting of beam elements. The beam element base cell is included with inspiration from experimental results in (Schaedler, 2011), where a highly energy absorbing material, constructed from structural elements with a small cross sectional area but large area moment of inertia, is presented. Furthermore, the applicability of multiscale finite element methods (Efendiev, 2009) to account for boundary conditions of periodic structures that possess a finite extent is investigated.

The aim of this article is to introduce a new topology optimisation formulation for optimal robust design of Micro Electro Mechanical Systems. Mesh independence in topology optimisation is most often ensured by using filtering techniques, which result in transition grey regions difficult to interpret in practical realisations. This problem has been alleviated recently by projection techniques, but these destroy the mesh independence introduced by the filters and result in single node connected hinges. Such features in the design are undesirable as they are not robust with respect to geometric manufacturing errors (such as under/over etching). They can be avoided by optimising for several design realisations which take into account the possible geometry errors. The design variations are modelled with the help of random variables. The proposed stochastic formulation for the design variations results in nearly black and white mechanism designs, robust with respect to uncertainties in the production process, i.e. without any hinges or small details which can create manufacturing difficulties.

This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem. (C) 2011 Elsevier B.V. All rights reserved. ispartof: Computer Methods in Applied Mechanics and Engineering vol:200 issue:49 pages:3613-3627 status: published