Topology Optimization Research Articles

Shape optimization for high efficiency metasurfaces: theory and implementation

Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction often imposes performance limitations. On the other extreme, inverse design based on topology optimization leverages non-local coupling to achieve high efficiency, but leads to complex and difficult to fabricate structures. In this paper, we demonstrate numerically and experimentally a shape optimization method that enables high efficiency metasurfaces while providing direct control of the structure complexity through a Fourier decomposition of the surface gradient. The proposed method provides a path towards manufacturability of inverse-designed high efficiency metasurfaces.

Voroto: multiscale topology optimization of voronoi structures using surrogate neural networks

Voroto: multiscale topology optimization of voronoi structures using surrogate neural networks

Stress and Strain Analysis for a Topological Optimized Beam

This paper presents a study of a beam manufactured using fused deposition modeling (FDM) which was topologically optimized and subjected to 3-point bending. In this paper polylactic acid (PLA) was used as a material in order to obtain the beams. Topology optimization is a method widely used in the additive manufacturing (AM) field, that uses algorithmic models to optimize the material layout within some parametric restrictions, like conditions, constraints, or sets of loads and it maximizes the performance and capability of the design by extracting material from different zones that are insignificant in terms of carrying loads to reduce the weight of the model. In the first step, the stress and strain state of the simple beam was numerically and analytically calculated, likewise, the experimental test of the beam subjected to 3-point bending was achieved. After the calculus for the simple beam, the next phase aims at the topological optimization process of the beam subjected to 3-point bending. For all the numerical investigations a calibrated material determined experimentally was used. Following calculations and experimental tests, a final version of the beam topologically optimized was reached, with a minimization of the cost regarding the mass of the beam and the material required for its reproduction.

Coupling light into a guided Bloch surface wave using an inversely designed nanophotonic cavity

Controlling the propagation of light in the form of surface modes on miniaturized platforms is crucial for multiple applications. For dielectric multilayers that sustain Bloch surface waves at their interface to an isotropic dielectric medium, a conventional approach to manipulate them exploits shallow surface topographies fabricated on top of the truncated stack. However, such structures typically exhibit low index contrasts, making it challenging to confine, steer, and guide the Bloch surface waves. Here, we theoretically and experimentally demonstrate a device for a Bloch surface wave platform that resonantly couples light from a cavity to a straight waveguide. The structure is designed using topology optimization in a 2D geometry under the effective index approximation. In particular, the cavity–waveguide coupling efficiency of the radiation emitted by an individual source in the cavity center is optimized. The cavity is experimentally found to exhibit a narrow resonant peak that can be tuned by scaling the structure. The waveguide is shown to guide only light that resonates in the cavity. Fully three-dimensional simulations of the entire device validate the experimental observations.

Inverse design of polaritonic devices

Polaritons, arising from the strong coupling between excitons and photons within microcavities, hold promise for optoelectronic and all-optical devices. They have found applications in various domains, including low-threshold lasers and quantum information processing. To realize complex functionalities, non-intuitive designs for polaritonic devices are required. In this contribution, we use finite-difference time-domain simulations of the dissipative Gross–Pitaevskii equation, written in a differentiable manner, and combine it with an adjoint formulation. Such a method allows us to use topology optimization to engineer the potential landscape experienced by polariton condensates to tailor its characteristics on demand. The potential directly translates to a blueprint for a functional device, and various fabrication and optical control techniques can experimentally realize it. We inverse-design a selection of polaritonic devices, i.e., a structure that spatially shapes the polaritons into a flat-top distribution, a metalens that focuses a polariton, and a nonlinearly activated isolator. The functionalities are preserved when employing realistic fabrication constraints such as minimum feature size and discretization of the potential. Our results demonstrate the utility of inverse design techniques for polaritonic devices, providing a stepping stone toward future research in optimizing systems with complex light–matter interactions.

Hybrid topology optimization combining simulated annealing for designing unpolarized high-efficiency freeform metasurface in-coupler for augmented reality waveguide

High-efficiency in-couplers with unpolarized responses are crucial for the performance of waveguide augmented reality displays. Freeform quasi-3D metasurfaces (FQ3DM), which integrate freeform metasurfaces with multilayer films, is one possible solution to achieve this. However, the performance of FQ3DM is limited by the lack of inverse design algorithms capable of optimizing its overall structure. In this work, we proposed a hybrid topology optimization combining simulated annealing (HTO-SA) algorithm that alternates between topology optimization and simulated annealing to find the global optimum for both the shape and thickness of FQ3DM. With the HTO-SA algorithm, we designed an unpolarized high-efficiency in-coupler that achieves an average efficiency of 90% across a 20° field-of-view for both transverse electric and transverse magnetic polarization. We envision that our proposed approach can be generalized to the design of high-performance diffractive optical devices.

Multidisciplinary Optimization of Gyroid Topologies for a Cold Plate Heat Exchanger Design

Abstract The strive to reduce the environmental impact of aviation has led to electrification and increasing demand for powerful on-board power electronic systems. These high-performance electrical components are bound to produce significant amounts of low-quality heat waste that, if not dissipated properly, will lead to malfunctioning and even permanent damage. For this reason, high-performance heat exchangers (HX) represent a key enabler for future advances in aircraft systems electrification and are vital to meet net zero goals and reduce the aviation's carbon footprint. For a given volume of the exchanger, the heat flow rate can be increased by adopting more sophisticated fluid domains. However, excessive geometrical complexity will lead to an increase in pressure losses, often resulting in inhomogeneous temperature distributions. In this paper, a novel optimization procedure is employed to maximize the efficiency of a high-performance heat exchanger, while minimizing overall pressure loss and temperature gradients. The optimization is performed with full three-dimensional high-fidelity computational flow simulations. The geometry of the fluid domain is constituted by triply periodic minimal surfaces (TPMS), with a parametrization based on thickness and aspect ratios, done by using the ntopology suite. To assess the performance gain, the topology-optimized design is compared against the datum case and a conventional serpentine design.

Tailoring coil geometry for achieving uniform heating through coil shape topology optimization for induction heating-based metal wire additive manufacturing

Tailoring coil geometry for achieving uniform heating through coil shape topology optimization for induction heating-based metal wire additive manufacturing

PCM-BESO: a reformative multi-constraints topology optimization method using point cloud modeling oriented to additive manufacturing

PCM-BESO: a reformative multi-constraints topology optimization method using point cloud modeling oriented to additive manufacturing

Differential evolution-based topology optimization using Karhunen-Loève expansion

Topology optimization is a widely adopted structural optimization approach that aims to maximize desired performance based on mathematical and physical principles. Gradient-based methods are common for obtaining optimal configurations; however, they struggle with problems involving numerous local optima and non-differentiable problems, which prevent the derivation of design sensitivity. To address these issues, this study explores the application of the Success History-Based Differential Evolution with Linear Population Size Reduction and Semi-Parameter Adaptation, which is regarded as LSHADE-SPA algorithm, known for its strong search capabilities. Nevertheless, its computational cost makes it impractical for topology optimization, especially as the number of design variables increases. To overcome this challenge, a novel structure representation method utilizing the Karhunen-Loève (KL) expansion is constructed. Applying truncated KL expansion instead of conventional density methods to represent structural configurations reduces the number of design variables. This article introduces a differential evolution-based topology optimization method utilizing truncated KL expansion and validates its effectiveness through applications in various structural and fluid problems. The method is particularly suited to highly nonlinear problems, such as negative Poisson's ratio structures and micro-mixer designs. The findings here indicate that differential evolution with truncated KL expansion can serve as an efficient and robust topology optimization method, proving particularly effective for solving optimization problems that are challenging for conventional gradient-based approaches. Notably, the proposed methodology not only delivers superior results but also alleviates computational burdens, thereby advancing the prospects of topology optimization in various engineering applications.

Recent Advances in electrode optimization of electrochemical energy devices using Topology Optimization

Abstract Topology optimization (TO) has emerged as a prominent trend in recent years, driven by its ability to explore optimized material distributions from scratch. Recently, there has been a significant shift in the application of TO, in optimizing systems involving complex electrochemical reactions, particularly electrode porous structures. This paper aims to examine the utilization of TO in enhancing electrodes across various electrochemical devices. It encompasses a broad spectrum of applications, including the optimization of porous electrodes through the density-based method and interfaces between electrodes and electrolytes through the level-set method. The paper will delve into the challenges and opportunities associated with employing TO in electrode design for electrochemical devices. These challenges involve addressing computational complexity, the absence of theoretical foundations for optimized structures, and the fabrication of complex structures for practical real-world applications. Additionally, beyond TO, the paper will spotlight other notable techniques in the structural design of porous electrodes using mathematical optimization. By offering insights into state-of-the-art research and developments in TO's application to electrode design, this paper provides researchers with valuable resources to navigate the evolving landscape of electrode design for electrochemical energy devices.

Enhancing sports mouthguards with PLA + and PC: stress reduction, energy absorption, and topology optimization.

The objective of this paper was to compare the effectiveness of different materials for mouthguards in preventing oral and maxillofacial injuries during sports activities. The present study compares the stress-reduction and energy absorption capabilities of two other fused filament materials - poly(lactic-acid plus) (PLA+) and polycarbonate (PC), with Ethylene-vinyl acetate (EVA), which is the most commonly used material for mouthguard fabrication. Two human skulls were modelled, and a boxing glove simulated punches along the x, y, and z-axes with 5mm displacement with 1 kN force. Firstly, the maximum principal stress curve in the skull was compared for forces along the three perpendicular directions. Furthermore, the present study examines materials energy absorption properties, including their specific energy absorption characteristics and initial peak von Mises stresses. Additionally, a topology optimization approach is used to create an alternative design for a mouthguard to improve specific energy absorption. The model without a mouthguard showed the highest stress concentration of 32.298MPa in the teeth, followed by the EVA material, which resulted in a maximum principal stress of 28.525MPa. Fused filament 3D materials, such as PLA + and PC, on the other hand, showed better mechanical effectiveness in both lower jaw dislocation and lower maximum principal stress by 30.82% and 51.25% in the mandibular and maxillary teeth. Though EVA comparatively shows better specific energy absorption capability at 2.24kJ/kg post-optimization than PLA + and PC, the peak principal stress experienced in the mandibular region was comparatively higher. The topology optimization, however, improved the energy-absorbing capabilities of PLA + by 4.5 times, reaching 1.37kJ/kg and PC from 0.165kJ/kg to 0.38kJ/kg. This study demonstrates that PLA + and PC have better stress reduction capabilities than EVA and could be promising materials for the fabrication of mouthguards in sports activities. This study highlights the importance of topology optimization in dental materials science and engineering to develop safer and more effective mouthguard designs.

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory.

The finite-volume theory has shown to be numerically efficient and stable for topology optimization of continuum elastic structures. The significant features of this numerical technique are the local satisfaction of equilibrium equations and the employment of compatibility conditions along edges in a surface-averaged sense. These are essential properties to adequately mitigate some numerical instabilities in the gradient version of topology optimization algorithms, such as checkerboard, mesh dependence, and local minima issues. Several computational tools have been proposed for topology optimization employing analysis domains discretized with essential features for finite-element approaches. However, this is the first contribution to offer a platform to generate optimized topologies by employing a Matlab code based on the finite-volume theory for compliance minimization problems. The Top2DFVT provides a platform to perform 2D topology optimization of structures in Matlab, from domain initialization for structured meshes to data post-processing. This contribution represents a significant advancement over earlier publications on topology optimization based on the finite-volume theory, which needed more efficient computational tools. Moreover, the Top2DFVT algorithm incorporates SIMP and RAMP material interpolation schemes alongside sensitivity and density filtering techniques, culminating in a notably enhanced optimization tool. The application of this algorithm to various illustrative cases confirms its efficacy and underscores its potential for advancing the field of structural optimization.

Multiqubit quantum state preparation enabled by topology optimization

Using topology optimization, we inverse-design nanophotonic cavities enabling the preparation of pure states of pairs and triples of quantum emitters. Our devices involve moderate values of the dielectric constant, operate under continuous laser driving, and yield fidelities to the target (Bell and W) states approaching unity for distant qubits (several natural wavelengths apart). In the fidelity optimization procedure, our algorithm generates entanglement by maximizing the dissipative coupling between the emitters, which allows the formation of multipartite pure steady states in the driven-dissipative dynamics of the system. Our findings open the way toward the efficient and fast preparation of multiqubit quantum states with engineered features, with potential applications for nonclassical light generation, and quantum sensing and metrology.

Digital dynamic modeling and topology optimized design of shell face mills

This paper presents digital modeling of shell face mills in milling cylinder heads. The cutter's structural dynamics and its mode shapes are predicted using a Finite Element system. The geometries of the cutter body and inserts are imported from their Computer Aided Design (CAD) models. The insert edge is discretized into small segments to model its varying normal rake and inclination angles, which affect the cutting mechanics. The cutter is dynamically assembled with the target machine tool spindle using the receptance coupling method. A general dynamic cutting force model, which considers the varying edge geometry and inserts’ run-outs, is developed and used to predict cutting forces and chatter stability diagrams. The proposed model is experimentally verified to demonstrate the feasibility of the systematic application of physics-based digital design and analysis of tools for the mass machining of specific parts. The cutter body shape is optimized to increase the stiffness of the bending mode shape that caused chatter via topology optimization, which led to five-fold increase in the absolute stable depth of cut.

A Harmonic Response Topology Optimization Method Based on Hybrid Cellular Automata

Abstract Hybrid cellular automaton (HCA) method is a topology optimization method with high convergence efficiency. Harmonic response topology optimization problem has been widely researched and common frequency-domain methods have been applied to solve this problem. Despite this, little work has so far been undertaken to utilize HCA method to improve the calculation efficiency of harmonic response topology optimization. In this paper we present a methodology which applies HCA method to solve harmonic response topology optimization problem. Mode displacement method (MDM), mode acceleration method (MAM) and full method (FM) are common frequency-domain methods which are respectively utilized as harmonic response analysis methods in this study. The examples under rotating loads demonstrate that the feasibility of this methodology at one specific frequency excitation and multiple frequencies excitation. This paper presents and implements a high convergence efficiency method for harmonic response topology optimization, this method can converge in 20–30 iterations. This method can extend the application range of HCA method and improve the optimization efficiency of harmonic response topology optimization.

Isogeometric proportional topology optimization (IGA-PTO) for multi-material problems

This study addresses the multi-material optimization problem by the effective and robust isogeometric proportional topology optimization (IGA-PTO) approach. Non-uniform rational B-spline basis functions are used for descriptions of geometry, displacement field, and density fields of material phases. The alternating active-phase algorithm is employed to convert the optimization problem with multiple constraints into a series of sub-problems of single constraint. Several examples are exhibited, and intensive comparisons with the gradient-based optimality criteria (OC) algorithm are presented to highlight the superior performance of the proposed PTO algorithm. Finally, the optimized topologies are prototyped using 3D printing technology to evidence the manufacturing feasibility.

Investigation of scalable chiral metamaterial beams for combined stiffness and supplemental energy dissipation

Abstract Metamaterials have gained important interest in the research community attributable to advances in additive manufacturing enabling their fabrication at reasonable costs. The vast majority of their applications and demonstrations are at micro- and nano-scales, and challenges remained regarding the larger scale applications. In this paper, we are interested by the scalability of metamaterials, targeting structural engineering applications. To do so, we explore mechanisms capable of providing both bending stiffness and high-performance energy dissipation. Our study includes beams constructed with chiral topologies of different structural hierarchy orders, and we also explore three new topologies that we termed chiral friction, chiral-rectangular and chiral-hexagonal design to engineer the beams and the use of friction rods with tunable post-stress that inserted longitudinally through the beams to provide enhanced friction. The mechanical performance of the metamaterial beams is characterized through a series three-point bending tests. Of interest is to evaluate the bending stiffness, shape recoverability, and energy dissipation capabilities. We find that the chiral-hexagonal topology equipped with a non-stressed friction rod exhibit excellent energy dissipation capabilities, showing an improved loss factor by 11.9 times compared to the control beam using 68% of its materials density. Moreover, the use of the post-stress mechanism shows that it is possible to augment both its shape recovery and bending stiffness up to 99.3% and 47.1%, respectively. Overall, our investigation shows that it is possible to engineer scalable metamaterial beams targeting structural engineering applications, and that the use of topology optimization and strategically designed post-tensioning mechanism can allow tuning of mechanical performance.

Three-dimensional coupled vibration failure analysis and structural optimization of the crankshaft of the diesel engine used in the shale gas fracturing truck

The crankshaft is the key component of the shale gas fracturing truck's diesel engine. Mass imbalance due to errors in the manufacturing process and other damage caused by long periods of operation can cause vibration for the crankshaft vibration problem. The static analysis is carried out based on the ignition condition of the second cylinder. The modal analysis of the crankshaft is then carried out. The modal analysis showed that resonance could cause significant deformation of the crankshaft. Consequently, harmonic response analysis, stochastic vibration analysis, and topology optimization were carried out on the crankshaft. The results show that the modes of each order of the crankshaft of the fracturing truck diesel engine are diverse. The modal amplitude is large. Fatigue damage is easily generated. After optimization, the mass of the crankshaft is reduced, the first natural frequency is increased, and the crankshaft is far away from the resonance interval while avoiding resonance failure. This document provides theoretical guidance for the design, optimization, research, and development of crankshafts.

Nonlinear vibration analysis of sandwich plates with inverse-designed 3D auxetic core by deep generative model

Building on a deep generative model (DGM), this paper introduces an innovative sandwich plate structure featuring an inverse-designed auxetic 3D lattice core and conducts a detailed investigation of its nonlinear vibration characteristics and effective Poisson's ratios under various parameter settings. By incorporating a conditional estimator and quality loss evaluation functions, the enhanced conditional generative adversarial networks are capable of designing 3D truss auxetic topologies that achieve customized negative Poisson's ratios without reliance on subjective experience. Additionally, lattice specimens are created using 3D metal printing, and the mechanical properties of these DGM-based 3D auxetic structures are validated through vibration experiments and finite element models. These structures exhibit significantly superior natural frequencies compared to those obtained through conventional topology optimization methods reported in existing literature. The study also explores the impact of different functionally graded configurations, temperature variations, boundary conditions, and dimensional parameters on the natural frequency, nonlinear vibration response, and effective Poisson's ratio of the inverse designed auxetic sandwich plates.