Ole Sigmund

Ole Sigmund
Technical University of Denmark | DTU · Department of Mechanical Engineering

About

434
Publications
190,677
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39,810
Citations
Introduction
Ole Sigmund currently works at the Department of Mechanical Engineering, Technical University of Denmark. Ole does research in Computing in Mathematics, Natural Science, Engineering and Medicine, Mechanical Engineering and Materials Engineering. His speciality is Topology Optimization
Additional affiliations
January 1995 - present
Technical University of Denmark
Position
  • Professor

Publications

Publications (434)
Article
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...
Preprint
Full-text available
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...
Article
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...
Preprint
Full-text available
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...
Article
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....
Article
Full-text available
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Conference Paper
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...
Article
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...
Article
Full-text available
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...
Article
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Preprint
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,...
Article
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...
Article
Full-text available
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...
Article
This paper corrects an error in the software provided with J. Opt. Soc. Am. B38, 510 (2021)JOBPDE0740-322410.1364/JOSAB.405955.
Preprint
Full-text available
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...
Preprint
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...
Article
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...
Preprint
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Preprint
Full-text available
Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute the ideal systems for applications ranging from high-precision sensing such as magnetic resonance force microscopy, to quantum transduction between disparate quantum systems. Traditionally, the improvement of the resonator's performance - often quantified by its Q...
Article
Full-text available
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations a...
Article
This work presents a high performance computing framework for ultra large scale, shell-element based topology optimization. The shell elements are formulated using a linear elastic, small strain assumption and are of the solid type, meaning that each quadrilateral shell element is extruded and assigned 24 degrees of freedom. The resulting linear sy...
Article
Full-text available
Multi-scale structures, as found in nature (e.g., bone and bamboo), hold the promise of achieving superior performance while being intrinsically lightweight, robust, and multi-functional. Recent years have seen a rapid development in topology optimization approaches for designing multi-scale structures, but the field actually dates back to the semi...
Article
We systematically design composite structures using multi-material topology optimization to achieve tunable elastic responses under finite deformations. We formulate an inverse problem where the errors between the actual (numerical) and the prescribed force–displacement curves are minimized. The framework harnesses multiple hyperelastic materials w...
Article
Full-text available
Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in property-space by carefully designed metamaterials. Development of mechanical metamaterials has gone from open truss lattic...
Preprint
We present a 250 line Matlab code for topol-ogy 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...
Preprint
Available at https://arxiv.org/abs/2012.04310 : This Brief Note revisits the optimal shape problem of a single cooling fin using a one-dimensional heat conduction equation with convection boundary conditions. Firstly, in contrast to previous works, we apply an approach using optimality conditions based on requiring stationarity of the Lagrangian fu...
Preprint
Full-text available
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%, and improves the uniaxial buckling...
Article
Topology optimization (TopOpt) methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient- and non-gradient-based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions, and satisf...
Article
We provide a compact 200 line MATLAB code demonstrating how topology optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as examples. The physics model is solved using the finite element method, and the code utilizes MATLAB’s fmincon algorit...
Preprint
Full-text available
Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in property-space by carefully designed metamaterials. Development of mechanical metamaterials has gone from open truss lattic...
Article
Full-text available
Homogenization-based topology optimization has been shown to be effective but does not directly create mechanical structures. Instead, the method gives a multi-scale description of the optimized design, e.g., lamination thicknesses and directions. To obtain a realizable single-scale design, one can perform a subsequent de-homogenization step. This...
Preprint
Full-text available
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...
Article
Full-text available
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluids. A single design variable is used to describe the physical fields. The solid interface and...
Article
It is challenging to remove the supports in an enclosed void of an additively manufactured structure, while it is much easier in open regions. This paper presents a novel approach to control the minimal overhang angle only in enclosed voids in order to improve the manufacturability of AM structures with as little performance loss as possible. First...
Article
Full-text available
This paper presents an interactive hybrid topology optimization method that (1) employs density for topology optimization and (2) in a seamless fashion uses a Deformable Simplicial Complex for shape optimization. Omitting hole insertions during the shape optimization allows us to utilize adaptive mesh coarsening, which reduces the mesh size with up...
Article
In topology optimization, the treatment of stress constraints for very large scale problems (more than 100 million elements and more than 600 million stress constraints) has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the stress constraints. This paper prese...
Article
Compact and efficient Matlab implementations of compliance topology optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from 3 ⋅ 104 to 4.8 ⋅ 105 elements, the 2D version, named top99neo, shows speedups from 2.55 to 5.5 times compared to the well-known top88 code of Andreassen...
Preprint
Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions and satisfaction of m...
Preprint
We provide a compact 200 line MATLAB code demonstrating how Topology Optimization as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as examples. The physics model is solved using the finite element method and the code utilizes MATLABs fmincon algorithm to solve...
Preprint
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations a...
Article
COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only. Various scatterers such as rough surfaces or nanostructures are typically used to enhance the low efficiency of Raman spectroscopy (surface-enhanced Raman scattering). In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterer...
Preprint
Full-text available
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluid flows. A single design variable is used to describe the physical fields. The solid interface...
Preprint
In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the stress constraints. This paper presents a three-dimensional design methodology that alleviates this shortcoming us...
Article
We consider a non‐smooth convex variational problem appearing as a formal limit of compliance minimization in the vanishing volume ratio limit. The problem has a classical basis pursuit form, and several successful algorithms have been utilized to solve problems of this class in other application contexts. We discuss the well‐posedness and regulari...
Article
Full-text available
This study systematically investigates stiffness and buckling response of finite structures consisting of repeated unit cells of a reference truss lattice microstructure and a topology optimized microstructure with enhanced buckling strength. Structural stability is evaluated using linear buckling, nonlinear pre-buckling, and post-buckling analyses...
Article
This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal multi-scale designs on a very fine mesh (de-homogenization). By performing homogenization-based topology opti...
Article
This paper proposes and investigates two formulations to topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity. The first formulation extends the maximum output displacement robust approach with stress constraints to incorporate the effects of geometric nonlinear behavior...
Article
Full-text available
Girder design for suspension bridges has remained largely unchanged for the past 60 years. However, for future super-long bridges, aiming at record-breaking spans beyond 3 km, the girder weight is a limiting factor. Here we report on a design concept, inspired by computational morphogenesis procedures, demonstrating possible weight savings in exces...
Article
Since its introduction by Bendsøe and Kikuchi in (1988) , topology optimization has developed from a purely academic discipline to the preferred tool for light-weighting structures in automotive, aerospace and other weight conscious industries. Topology optimization solves mechanical and multiphysics design problems allowing the ultimate design fre...
Article
Finding periodic microstructures with optimal elastic properties is usually tackled by a highly resolved, regular finite element model and solid isotropic material penalization. This procedure not only has many advantages, but also requires a comparably high computational effort and challenges in representing stresses accurately. Therefore, an isog...
Article
Panel methods are frequently applied to aerodynamic shape optimization problems due to their fast turnaround time and ability to model arbitrary geometries. Despite being advantageous for design optimization, we have found that panel methods can predict nonphysical results for unconventional geometries. This paper presents robust methods to solve o...
Preprint
Compact and efficient Matlab implementations of compliance Topology Optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from 3·10 4 to 4.8 · 10 5 elements, the 2D version, named top99neo, shows speedups from 2.55 to 5.5 times compared to the well-known top88 code (Andreassen et...
Article
Quality factor (Q) and frequency-quality factor (Qf) of prestressed membrane resonators are enhanced by topology optimization. The optimization targets the fundamental mode which is more easily identified in physical experiments compared to high-order modes embedded in possibly dense frequency ranges. Both intrinsic and extrinsic losses are conside...
Article
We show that topology optimization (TO) of metallic resonators can lead to ∼102 × improvement in surface-enhanced Raman scattering (SERS) efficiency compared to traditional resonant structures such as bowtie antennas. TO inverse design leads to surprising structures very different from conventional designs, which simultaneously optimize focusing of...
Article
Upconversion of sub-band-gap photons constitutes a promising way for improving the efficiency of silicon-based solar cells beyond the Shockley-Queisser limit. 1500 nm to 980 nm upconversion by trivalent erbium ions is well-suited for this purpose, but the small absorption cross section hinders real-world applications. We employ tailored gold nanost...