Ole Sigmund

• Professor at Technical University of Denmark

Preemptive identification of potential failure under loading of engineering structures is a critical challenge. Our study presents an innovative approach to design built-in prefailure indicators within multiscale structural designs with optimized load carrying capabilities utilizing the design freedom of topology optimization. The indicators are en...

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e., components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are modeled using a fully coupled non-linear thermo-mechanical finite element framework. To obtain the intricate...

Precise spatial manipulation of particles via optical forces is essential in many research areas, ranging from biophysics to atomic physics. Central to this effort is the challenge of designing optical systems that are optimized for specific applications. Traditional design methods often rely on trial-and-error methods or on models that approximate...

This paper introduces a novel regularization term, denoted ''HuHu-LuLu'', for Third Medium Contact (TMC), and shows its usefulness in 2D and 3D topology optimization problems with frictionless contact. The HuHu-LuLu regularization, where HuHu and LuLu respectively refer to the contraction of the Hessian and Laplacian of the displacement field, is d...

Topology optimization facilitates the automated design of high-performance structures across various engineering fields but, if unconstrained, often produces designs that are complex and difficult to manufacture. A key attribute of the resulting designs is connectivity, which involves controlling the presence of solid and/or void islands of materia...

Metamaterials have shown potential to achieve strong noise or vibration reduction in predefined frequency ranges. Targeting both wave types simultaneously remains, however, a cumbersome design task requiring complex geometries which often only enable a wide bandgap for one type while limited attenuation for the other. To overcome this hurdle, this...

High quality mechanical resonators are critical for driving advances in quantum information technologies, precision sensing, and optomechanics. However, achieving compact resonator designs that maintain high performance is a key challenge. In this study, we present a new class of compact resonators optimized to operate at higher-order eigenmodes, a...

This work presents an 808-line Matlab educational code for combined multi-scale topology optimisation and phasor-based dehomogenisation titled deHomTop808. The multi-scale formulation utilises homogenisation of optimal microstructures to facilitate efficient coarse-scale optimisation. Dehomogenisation allows for a high-resolution single-scale recon...

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for some inverse problems, the benefit for topology optimization has been limited—where the focus of investigations...

Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in recent years, several unanswered questions remain. This paper takes a step towards answering one of the larger q...

Precise spatial manipulation of particles via optical forces is essential in many research areas, ranging from biophysics to atomic physics. Central to this effort is the challenge of designing optical systems that are optimized for specific applications. Traditional design methods often rely on trial-and-error methods, or on models that approximat...

A means of reducing the computational cost in robust topology optimization is discussed. Without proper countermeasures, topology optimization can lead to artificially well-performing solutions for certain design problems, with unrealistic hinges that would break in reality. Enforcement of minimum length scales in both solid and void phases of the...

Optical trapping enables precise control of individual particles of different sizes such as atoms, molecules, or nanospheres. Optical tweezers provide free-space omnidirectional optical trapping of objects in laboratories around the world. As an alternative to standard macroscopic setups based on lenses, which are inherently bound by the diffractio...

This paper presents two MATLAB codes for topology optimization of multi-material piezoelectric actuators and energy harvesters. These codes provide the extensions of the previously published 2D topology optimization codes for piezoelectric actuators and energy harvesters (Struct Multidisc Optim 63 (2), 983–1014) with two major contributions: (1) ex...

Sound is an essential sensing element for many organisms in nature, and multiple species have evolved organic structures that create complex acoustic scattering and dispersion phenomena to emit and perceive sound unambiguously. To date, it has not proven possible to design artificial scattering structures that rival the performance of those found i...

Preemptive identification of potential failure under loading of engineering structures is a critical challenge. Our study presents an innovative approach to built-in pre-failure indicators within multiscale structural designs utilizing the design freedom of topology optimization. The indicators are engineered to visibly signal load conditions appro...

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for some inverse problems, the benefit for topology optimization has been limited -- where the focus of investigati...

Fourier’s law dictates that heat flows from warm to cold. Nevertheless, devices can be tailored to cloak obstacles or even reverse the heat flow. Mathematical transformation yields closed-form equations for graded, highly anisotropic thermal metamaterial distributions needed for obtaining such functionalities. For simple geometries, devices can be...

Three-dimensionally sculpted dielectric nanostructures supporting material(air) confined optical modes with single-emitter mode volumes three(four) orders of magnitude below the diffraction limit, $V_{\textbf{r}_0} \approx 0.0004 \left[\lambda/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 0.00003 \left[\lambda/2\right]^3\right)$, are discovered us...

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e. components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are modeled using a fully coupled non-linear thermo-mechanical finite element framework. To obtain the intricate...

This work presents an 808-line Matlab educational code for combined multi-scale topology optimisation and phasor-based dehomogenisation titled deHomTop808. The multi-scale formulation utilises homogenisation of optimal microstructures to facilitate efficient coarse-scale optimisation. Dehomogenisation allows for a high-resolution single-scale recon...

Topology optimization can be employed to manipulate transient thermal behavior for heat transfer devices. As a gradient-based approach, transient topology optimization faces challenges with the CPU cost of the associated forward and backward time-stepping procedure. This study introduces a harmonic analysis-based substitute optimization method to a...

We experimentally demonstrate an InP nanocavity with a mode volume of 0.26 (λ/2n)³. This is an order of magnitude smaller than the mode volumes previously demonstrated in photonic crystal point-defect cavities realized in III-V materials and four times smaller than what is often referred to as the diffraction-limited volume, Vλ= (λ/2n)³. The nanoca...

A multi-material active structure is a mechanical system made of passive and active materials with the ability to alter its configuration, form, or properties in response to changes in the environment. Active structures have been investigated to design lightweight structures and structures with the ability to “smartly” alter their shapes and/or int...

This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem...

The quality factor of resonator is described by a dilution factor defined as the ratio of tension to linear strain energies. We implement topology optimization of resonators with the dilution factor as an objective. The finite element model combines mesh refinement and a mixed formulation to accurately model the boundary effects in eigenmode.

Classical gradient-based density topology optimization is adapted for method-of-moments numerical modeling to design a conductor-based system attaining the minimal antenna Q-factor evaluated via an energy stored operator. Standard topology optimization features are discussed, e.g., interpolation scheme and density and projection filtering. The perf...

Thermo-optical phase shifters (TOPSs) have emerged as an important building block in silicon photonics platforms due to their ability to dynamically control the optical phase of light. To enable wide-scale adoption in practical applications, it is paramount that TOPSs are optimized for low power consumption, low optical loss, small footprint, small...

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. T...

This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem...

Structures and materials with programmable mechanical responses are desirable for many applications. Great advancement has been achieved and led to the discovery of metastructures/metamaterials with unconventional programmed properties. While most established studies focus on two-dimensional (2D) or pseudo-three-dimensional systems, certain complex...

Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for additive manufacturing, infill is often neglected as a component of the optimized structure. In this paper, b...

Recently, metamaterials, sandwich panels, and a combination of both have shown potential for creating lightweight, load-bearing structures with good noise and vibration suppression properties. However, designing these structures is difficult due to the complex vibroacoustic innate physics and the need to balance conflicting requirements. Structural...

We introduce a strategy preventing the occurrence of spurious modes in the spectrum computed by linearized buckling analysis in the context of topology optimization. Spurious buckling modes may appear in low density regions, a well‐known and largely discussed phenomenon. However, localized modes may also appear in solid areas, where stress concentr...

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. T...

This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are evaluated by the means of a source-doublet panel method for the aerodynamic response and linear elastic finit...

Additive manufacturing (AM) processes have proven to be a perfect match for topology optimization (TO), as they are able to realize sophisticated geometries in a unique layer-by-layer manner. From a manufacturing viewpoint, however, there is a significant likelihood of process-related defects within complex geometrical features designed by TO. This...

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bendsøe and Kikuchi from 1988, which lately has been revived due to advances in manufacturing methods like additive manufacturing. Orthotropic microstruc...

Classical gradient-based density topology optimization is adapted for method-of-moments numerical modeling to design a conductor-based system attaining the minimal antenna Q-factor evaluated via an energy stored operator. Standard topology optimization features are discussed, e.g., the interpolation scheme and density and projection filtering. The...

Mechanical structures are often simultaneously subjected to thermal and mechanical loading, both of which can lead to buckling failure. Developing efficient structural forms with better capacity for stability is important to keep structures safe. This study aims to optimize structural buckling capacity by using a density-based topology optimization...

The rates of optical processes, such as two-photon absorption and spontaneous photon emission, are strongly dependent on the environment in which they take place, easily varying by orders of magnitude between different settings. Using topology optimization, we design a set of compact wavelength-sized devices, to study the effect of optimizing geome...

Stretch‐dominated truss and plate microstructures are contenders in the quest for realizing architected materials with extreme stiffness and strength. In the low volume fraction limit, closed‐cell isotropic plate microstructures meet theoretical upper bounds on stiffness but have low buckling strength, whereas open‐cell truss microstructures have h...

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact o...

Topology optimization has developed tremendously and new approaches, algorithms and applications are appearing on a daily basis. However, how to fairly evaluate and compare new concepts and ideas to existing ones is an open question due to the broadness of modelling approaches, geometry parameterizations and physical applications. Ideally, the comm...

Nanotechnology enables in principle a precise mapping from design to device but relied so far on human intuition and simple optimizations. In nanophotonics, a central question is how to make devices in which the light-matter interaction strength is limited only by materials and nanofabrication. Here, we integrate measured fabrication constraints in...

Much work has been done in multiscale topology optimization for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which lately has been revived due to advances in manufacturing methods like additive manufacturing. Orthotropic microstructures local...

This paper addresses the concept of predetermined breaking points in topology optimization. The aim is to propose and investigate a novel formulation to design optimized topologies in which one can control where failure will occur first in case of overload; in addition, the optimized topology must withstand the design load after the damaged part is...

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation...

This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations....

This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are evaluated by the means of a source-doublet panel method for the aerodynamic response and linear elastic finit...

This work presents an extension of the highly efficient de-homogenization method for obtaining high-resolution, near-optimal 2D topologies optimized for minimum compliance subjected to multiple load cases. We perform a homogenization-based topology optimization based on stiffness optimal Rank-N microstructure parameterizations to obtain stiffness o...

Recently, a systematic approach for the design of lattice materials with extreme buckling strength has led to optimized hierarchical lattice materials with unprecedented load carrying capacity. This is obtained at the cost of a small decrease in linear stiffness. However, the superior buckling resistance of such optimized hierarchical lattice mater...

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation...

Buckling strength estimation of architected materials has mainly been restricted to load cases oriented along symmetry axes. However, realistic load scenarios usually exhibit more general stress distributions. This study employs local member analyses to estimate the buckling strength surface of stretch-dominated lattice structures. As an integral p...

We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order homogenization approach, which replaces the discrete truss by an effective continuum description to be treated...

The existence of a single topologically protected edge state in the first bulk bandgap for acoustic/elastic valley Hall insulators (VHIs) with zigzag interface configurations (ZICs) is well known. However, in this work, we show that an ultra-broadband edge-state pair in this bandgap can be created using the inverse design by topology optimization....

This work proposes an approach for structural Topology Optimization enforcing geometrical features on optimized designs using a predefined library of geometrical patterns. The approach applies a density-based Topology Optimization subject to a geometrical constraint guiding the design toward shapes matching the geometrical features found in the pre...

This paper proposes a novel topology optimization procedure for designing structures with infill-supported enclosed voids for additive manufacturing (AM). In such structures, the open and enclosed regions are separately treated, where the open regions are the standard voids but the enclosed ones are filled by porous materials. The applied porous in...

We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order homogenization approach, which replaces the discrete truss by an effective continuum description to be treated...

Significance Creating structures to realize function-oriented mechanical responses is desired for many applications. Yet, the use of a single material phase and heuristics-based designs may fail to attain specific target behaviors. Here, through a deterministic algorithmic procedure, multiple materials with dissimilar properties are intelligently s...

In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods. Homogenization can represent microstructures at length scales decoupled from the resolution of the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 la...

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogeniza...

In this work, a topology optimization approach is developed for additive manufacturing (AM) of 2D and 3D self-supporting structures. Three important issues, i.e., overhang angle control, avoidance of the so-called V-shaped areas and minimum length scale control are addressed. 2D solid polygon and 3D polyhedron features are introduced as basic desig...

The dynamics of engineering structures are of great importance for topology optimization problems in both academia and industry. However, for design problems where broadband frequency responses are required, the computational burden becomes enormous, especially for large-scale applications. To remedy this numerical bottleneck, using the Reduced-Ord...

Ever since the publication of the 99-line topology optimization MATLAB code (top99) by Sigmund in 2001, educational articles have emerged as a popular category of contributions within the structural and multidisciplinary optimization (SMO) community. The number of educational papers in the field of SMO has been growing rapidly in recent years. Some...

This paper presents a novel strategy for structural topology optimization considering damage. In engineering practice, structures are typically designed to have a certain load‐bearing capacity, with a minimal material volume or cost. We aim to optimize the topology of a structure to have a minimal weight while guaranteeing a predefined load capacit...

Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute a promising platform for various quantum technologies and foundational research. Traditionally, the improvement of the resonator’s performance through nanomechanical structural engineering has been driven by human intuition and insight. Such an approach is ineffic...

This work proposes a systematic topology optimization approach for simultaneously designing the morphing functionality and actuation in three-dimensional wing structures. The actuation was modeled by a linear-strain-based expansion in the actuation material. A three-phase material model was employed to represent structural and actuating materials a...

This paper revisits the optimal thickness profile problem of a single cooling fin using a one-dimensional heat conduction equation with a convection boundary condition. Firstly, in contrast to previous works, we apply an approach using optimality conditions based on requiring stationarity of the Lagrangian functional of the optimisation problem. Th...

Mechanical metamaterials that achieve ultimate anisotropic stiffness are highly desired in engineering practice. Particularly, the plate microstructures (PM) that are comprised of 6 sets of flat plates have been proved to attain any extreme stiffness in theory. In this paper, we solve two remaining issues for design of optimal PMs. On one hand, we...

In this study, we develop a design methodology with a basis in gradient-based topology optimization and a geometrical reduced-order thermal/hydraulic model for actively cooled microvascular composite panels. The proposed method is computationally very efficient owing to the suggested simplifications while preserving the required accuracy. The analy...

Sigmund’s 2001 educational paper with a self-contained 99-line MATLAB code had far-reaching impact to teaching and research of topology optimization. This brief note aims to close the gaps on self-contained content desirable for classroom teaching. The goal is to add clarity to the theoretical foundation, and to enable students’ learning of the com...

Optical nanocavities confine and store light, which is essential to increase the interaction between photons and electrons in semiconductor devices, enabling, e.g., lasers and emerging quantum technologies. While temporal confinement has improved by orders of magnitude over the past decades, spatial confinement inside dielectrics was until recently...

Variable thickness sheet and homogenization-based topology optimization often result in spread-out, non-well-defined solutions that are difficult to interpret or de-homogenize to sensible final designs. By extensive numerical investigations, we demonstrate that such solutions are due to non-uniqueness of solutions or at least very flat minima. Much...

This work proposes a systematic topology optimization approach to simultaneously design the morphing functionality and actuation in three-dimensional wing structures. The actuation is assumed to be a linear strain-based expansion in the actuation material and a three-phase material model is employed to represent structural and actuating materials,...

Stress‐constrained topology optimization requires techniques for handling thousands to millions of stress constraints. This work presents a comprehensive numerical study comparing local and global stress constraint strategies in topology optimization. Four local and four global solution strategies are presented and investigated. The local strategie...

In this article, we demonstrate the state-of-the-art of multi-scale topology optimization for 3D structural design. Many structures designed for additive manufacturing consist of a solid shell surrounding repeated microstructures, so-called infill material. We demonstrate the performance of different types of infill microstructures, such as isotrop...

Buckling strength estimation of architected materials has mainly been restricted to load cases oriented along symmetry axes. However, realistic load scenarios normally exhibit more general stress distributions. In this paper we propose a simple yet accurate method to estimate the buckling strength of stretch-dominated lattice structures based on in...

This paper corrects an error in the software provided with J. Opt. Soc. Am. B 38, 510 (2021)JOBPDE0740-322410.1364/JOSAB.405955.

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogeniza...

We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a...

In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. A...

Metamaterial mechanisms are structures composed of periodic cells that possess special mechanism responses. This paper proposes a topology optimization method based on a variable linking scheme for the design of metamaterial mechanisms. A robust formulation is included to improve the manufacturing reliability of the designs and prevent de-facto hin...

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented...

This paper presents a class of 3D single-scale isotropic materials with tunable stiffness and buckling strength obtained via topology optimization and subsequent shape optimization. Compared to stiffness-optimal closed-cell plate material, the material class reduces the Young’s modulus to a range from 79% to 58%, but improves the uniaxial buckling...