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The purpose of this paper is to compare between two methods of volume control in the context of topological derivative-based structural optimization of Kirchhoff plates.

The compliance topology optimization of Kirchhoff plates subjected to volume constraint is considered. In order to impose the volume constraint, two methods are presented. The first one is done by means of a linear penalization method. In this case, the penalty parameter is the coefficient of a linear term used to control the amount of material to be removed. The second approach is based on the Augmented Lagrangian method which has both, linear and quadratic terms. The coefficient of the quadratic part controls the Lagrange multiplier update of the linear part. The associated topological sensitivity is used to devise a structural design algorithm based on the topological derivative and a level-set domain representation method. Finally, some numerical experiments are presented allowing for a comparative analysis between the two methods of volume control from a qualitative point of view.

The linear penalization method does not provide direct control over the required volume fraction. In contrast, through the Augmented Lagrangian method it is possible to specify the final amount of material in the optimized structure.

A strictly simple topology design algorithm is devised and used in the context of compliance structural optimization of Kirchhoff plates under volume constraint. The proposed computational framework is quite general and can be applied in different engineering problems.

The purpose of this study is sensitivity analysis of the L²-norm and H¹-seminorm of the solution of a diffusive–convective–reactive problem to topological changes of the underlying material.

The topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method.

Remarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization.

The topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.

The purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.

The resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.

Numerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.

The novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

The purpose of this study is to explore the optimum design of bending plate compliant mechanisms subjected to pure mechanical excitations using topological-derivative-based topology optimization. The main objective is to design the reinforcement in a plate of base material.

The optimum design is performed by means of a level-set representation method guided by topological derivatives. Kirchhoff and Reissner–Mindlin models are used to solve the linear bending plate problem. A qualitative comparison has been carried out between the optimal obtained topologies for each model.

The proposed methodology was able to design reinforcement in a plate of the base material. The obtained reinforcements notably improve the device’s behavior. The shape and topology of the reinforcements vary depending on the mechanical plate model considered. In fact, in the Reissner–Mindlin solutions, very thin flexo-torsional hinges connecting big zones of the reinforcement material are designed.

Up to date, the synthesis of ortho-planar mechanisms by means of continuum topology optimization was only boarded within a multi-physics context. In this work, the optimal design of pure ortho-planar compliance actuators is addressed. The best performance is found by analyzing the results for two classical mechanical plate models.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

The purpose of this paper is to propose a level set method (LSM) for topology optimization of an electromagnetic system.

The classical shape optimization method has a meshing problem for shape changes and so the level set method is employed to overcome this difficulty, due to its efficient representation of evolving geometry. The velocity field is required to solve the level set equation of the Hamilton‐Jacobi equation. It is obtained using the continuum shape sensitivity in a closed form by the material derivative concept. The optimization problem is modeled as a coupled system of Poisson's equation and the level set equation. They are solved using a standard FEM in the time domain.

Numerical examples are shown to test an optimization problem in the electric and magnetic field system. The design goal is to obtain the maximum torque for an operating electrostatic actuator and synchronous reluctance motor (SynRM), respectively. The results of the optimal shape and topology for electromagnetic system are presented.

This paper presents a theoretical algorithm and numerical techniques for topology optimization of an electromagnetic system to generate the maximum torque using the level set method and design sensitivity analysis.

The purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.

The incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.

In the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.

The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based Eulerian fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted.

Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures.

While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics.

It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an Eulerian setting.

The paper presents the topology optimization method to design the rotor and the tooth base in the stator of the permanent magnet (PM) excited machine with the improved high-speed features. The topological and shape sensitivity through the Multi-Level Set Method (MLSM) have been used to attain an innovative design of both the rotor and stator made of different materials.

This framework is based on the application of the topological and the shape derivative, obtained by incorporating the AVM into the multi-level set method for the magnetoquasistatic system. The representation of the shape and their evolution during the iterative optimization process are obtained by the multi-level set method.

To find the optimal configuration of a PM machine, the stator and rotor poles were simultaneously optimized by redistributing the iron and the magnet material over the design domains. In this way, it was possible to obtain an innovative design which allows to reduce mechanical vibration and the acoustic noise caused by the Cogging Torque, while taking the back-EMF into account.

The novelty of the proposed method is to apply the modified multi-level-set algorithm with the Total Variation (TV) to the magnetoquasistatic optimization problem. Given the eddy currents phenomenon in the model of a PM machine, it was possible not only to optimize the structure of a PM machine but also to analyse electromagnetic losses distribution.

The purpose of this paper is to find an optimized thin-film amorphous silicon solar cell design by numerically optimizing the light trapping efficiency of a pyramid-structured back-reflector using a frequency-domain finite element Maxwell solver. For this purpose short circuit current densities and absorption spectra within the investigated solar cell model are systematically analyzed. Furthermore, the authors employ a topology simulation method to accurately predict the material layer interfaces within the investigated solar cell model. The method simulates the chemical vapor deposition (CVD) process that is typically used to fabricate thin-film solar cells by combining a ballistic transport and reaction model (BTRM) with a level-set method in an iterative approach. Predicted solar cell models are far more realistic compared to solar cell models created assuming conformal material growth. The purpose of the topology simulation method is to increase the accuracy of thin-film solar cell models in order to facilitate highly accurate simulation results in solar cell design optimizations.

The authors perform numeric optimizations using a frequency domain finite element Maxwell solver. Topology simulations are carried out using a BTRM combined with a level-set method in an iterative fashion.

The simulation results reveal that the employed pyramid structured back-reflectors effectively increase the light path in the absorber mainly by exciting photonic waveguide modes. In using the optimization approach, the authors have identified solar cell models with cell periodicities around 480 nm and pyramid base widths around 450 nm to yield the highest short circuit current densities. Compared to equivalent solar cell models with flat back-reflectors, computed short circuit current densities are significantly increased. Furthermore, the paper finds that the solar cell models computed using the topology simulation approach represent a far more realistic approximation to a real solar cell stack compared to solar cell models computed by a conformal material growth assumption.

So far in the topology simulation approach the authors assume CVD as the material deposition process for all material layers. However, during the fabrication process sputtering (i.e. physical vapor deposition) will be employed for the Al:ZnO and ITO layers. In the framework of this ongoing research project the authors will extend the topology simulation approach to take the different material deposition processes into account. The differences in predicted material interfaces will presumably be only minor compared to the results shown here and certainly be insignificant relative to the differences the authors observe for solar cell models computed assuming conformal material growth.

The authors systematically investigate and optimize the light trapping efficiency of a pyramid nano-structured back-reflector using rigorous electromagnetic field computations with a 3D finite element Maxwell solver. To the authors’ knowledge such an investigation has not been carried out yet in the solar cell research literature. The topology simulation approach (to the best of the authors’ knowledge) has previously not been applied to the modelling of solar cells. Typically a conformal layer growth assumption is used instead.