Topology Optimization Approach Research Articles

An improved proportional topology optimization method combining a polarized material interpolation scheme and Heaviside threshold function

An improved proportional topology optimization (IPTO) method is proposed in this work. The main improvement of this method is that the conventional solid isotropic material with penalization (SIMP)-based material interpolation scheme is replaced by a polarized material interpolation scheme, and the Heaviside threshold function is adopted based on the original proportional topology optimization (PTO) method. By using this approach, the minimum compliance problem can be solved without requiring the numerical derivation of the sensitivity function. To verify the feasibility and effectiveness of the proposed method, two-dimensional (2D) and three-dimensional (3D) cantilevers and L-bracket beams are used as examples. The 2D results obtained by the IPTO method are compared with those obtained by the PTO and SIMP methods. Numerical examples demonstrate that IPTO can acquire better objective function values and more ideal topology structures compared to PTO and SIMP. Furthermore, IPTO offers significant advantages over PTO and SIMP in terms of convergence speed and the ability to suppress intermediate density elements. Additionally, this method enables topology optimization design under multiple working conditions. Therefore, it provides an effective approach for structural topology optimization in research and engineering applications. With appropriate adjustment, this method can also be applied to composite material design and heat conduction design.

One-shot procedures for efficient minimum compliance topology optimization

In this paper, a one-shot approach for minimum compliance topology optimization is investigated. In the convex case of variable thickness sheet optimization, an optimality criteria scheme with a single step of an iterative state solver converges to the same solutions as an accurate procedure. This remarkable behavior is explained by the crucial role of the geometric multigrid preconditioner that generates accurate design sensitivities on a coarse scale. When applied to SIMP-based topology optimization, a one-shot procedure yields designs with the same primary load-transferring features as an accurate procedure. The difference is in the absence and presence of thin features that have a relatively minor impact on the objective. Several practical remedies are suggested that can close the small performance gaps between the one-shot procedure and an accurate one. The solution scheme is directly applicable to large-scale problems executed on parallel computers, allowing for significant computational savings.

Phase-field method combined with optimality criteria approach for topology optimization

This paper introduces a novel topology optimization framework by combining the phase-field method and optimality criteria approach. This novel approach allows for the automatical addition of holes in the initial shape, a capability that is not achievable with the conventional phase-field model based on boundary changes for topology optimization. The distribution of the material is changed according to the sensitivity of the optimality criteria approach to nucleate holes. After the nucleation of the new holes, they are utilized for topology optimization using the phase-field method. To demonstrate the accuracy and effectiveness of the proposed approach, we conduct several numerical examples based on the two-dimensional minimum compliance problem. The obtained numerical results show the proposed method's fast convergence compared to the conventional phase-field method.

Evolutionary topology optimization approach to design multiphase soundproof systems with poroelastic media

SummaryWith the constant development of cities, noise sources have become increasingly present inside and outside living environments. Consequently, soundproof systems comprised of porous materials have been widely adopted as filling fabric of closed‐space structures, such as in the components of buildings, airplanes or automobiles. However, in many situations, simply filling spaces may not be the most effective approach. In that scenario, this work introduces a multiphase acoustic topology optimization methodology to design closed‐space structures for sound attenuation. Based on the Bi‐directional Evolutionary Structural Optimization (BESO) algorithm, the proposed approach combines Biot's poroelasticity equations, expressed in the mixed /p form, and the Unified Multiphase (UMP) technique to fully describe the multiphysics involved in the acoustic, poroelastic and elastic model relations. An objective function contemplating different combinations of structural, viscous and thermal dissipated powers is maximized over multiple frequencies. Volume constraints in each material phase and a novel material interpolation scheme are also considered. The resultant topologies present enhanced dissipated power levels and manufacturability, even when compared with various baseline configurations of similar volume fractions.

Coupling of bond-based peridynamics and continuous density-based topology optimization methods for effective design of three-dimensional structures with discontinuities

This study proposes continuous density-based three-dimensional topology optimization (TO) approaches developed by coupling the peridynamic theory (PD) with optimality criteria (OC) and proportional approach (PROP). These frameworks, abbreviated as PD-OC-TO and PD-PROP-TO, can be practically utilized to enhance the fracture toughness of the structures during the optimization process by taking critical regions into account as pre-defined cracks. Breaking the non-local interactions (bonds) between relevant PD particles enables us to readily model cracks. Utilizing this advantage, we solve several benchmark optimization problems including different numbers, positions, and alignments of the cracks. The major differences between the proposed methods are examined by comparing optimum topologies for various cracked scenarios. Moreover, the mechanical behaviour of the optimized structures is investigated under dynamic loads to prove the significant improvements achieved by the present approach in the final designs. The results of dynamic analyses reveal the viability of both PD-TO methods for increasing the fracture toughness of the structure in the optimization stage. Overall, the proposed approach is confirmed as a superior design and optimization tool for future engineering structures.Graphical abstract

Converting pixel‐type topology optimization results to MMC‐representation based on sparse optimization and its applications

AbstractHow to realize the switching between various topology optimization approaches such as SIMP and moving morphable component (MMC) method, is a crucial challenge in the field of structural design. In this article, a robust conversion framework is proposed to convert a pixel‐type topology optimization result to MMC representation. Based on the sparse optimization approach, the framework enables the determination of the minimum number of components with a specified shape error. This method provides an efficient bridge for these two types of geometric descriptions, and promotes the free switching between the topology optimization frameworks with pixel‐based and MMC‐based design domains. The proposed procedure contains a pre‐processing of resolution improvement, symmetry axis extraction with sparse optimization, and variational shape approximation. Two practical applications are demonstrated using the proposed framework. First, it can be applied to the intermediate results of SIMP, to achieve faster optimization convergence. Furthermore, a stress‐based shape optimization approach can be applied to the obtained MMCs, and novel progressive continuity constraints are also introduced to maintain boundary continuity. Several examples demonstrate advantages of the proposed framework.

A dynamic topology optimization design method based on multiple domain variable parameters

Topology optimization has been extensively studied for obtaining desired functional performances of a structure within a predefined design domain. However, existing topology optimization approaches mainly focus on the static structure. Additionally, a structure is generally consisted of multiple materials and its loading state is quite complicated in practical applications, which are seldom considered simultaneously during design optimization. In this paper, a dynamic topology optimization design method based on multiple domain variable parameters is proposed to solve these issues. First, a structure is divided into multiple domains, and an optimal topology model of discrete structure is proposed. Then, the constraints are relaxed and a per-element variable is introduced to process the design variables continuously. To eliminate the undesirable checkerboard patterns, a filtering method is proposed and an approach of projection is presented for determining the volume of the projected structure according to the practical design requirements. After that, a dynamic continuous optimization model is put forward for solving the optimal solution of the complex structure under various working conditions. Finally, the effectiveness and efficiency of the proposed method are validated by constructing a topology optimized link of the press.

Multi-objective optimization for designing porous scaffolds with controllable mechanics and permeability: A case study on triply periodic minimal surface scaffolds

Design of tissue scaffolds in terms of multiple objectives such as mechanical and biological performances simultaneously remains challenging. In this paper, we present the development of a topology optimization approach that enables to design porous scaffolds with consideration of both mechanical and fluid properties simultaneously. The relationship between structural parameters, mechanical and mass transport properties was investigated, and then the scaffolds were optimized under the constraint of given pore size, porosity and specific surface area. Case studies on the optimized design of triply periodic minimal surface (TPMS) scaffolds were performed to illustrate the effective of our approach. Simulation and experimental results demonstrated that the proposed optimization approach fully decouples the mechanical and mass transport properties, specifically, under given porosities, the elastic modulus and permeability of optimized scaffolds ranged from 1.33 GPa to 16.7 GPa and 0.07 × 10−8 m2 to 1.62 × 10−8 m2, respectively. Three types of optimized gradient scaffolds were designed and they all exhibited significant functional gradients and high adjustability. The proposed approach decouples synergy and enables individual customization of multi-physics properties, providing practical guidance for gradient scaffolds with desired performance.

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal C 1 continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.

Plastic-limit probabilistic structural topology optimization of steel beams

This work presents a novel geometrically nonlinear analysis with imperfections reliability-based topology optimization (RBTO) approach, considering the volume fraction and geometric imperfections as random variables due to their crucial connections to the manufacturability of web openings in steel I-beams. The objective is achieved by controlling the plastic behavior through limit analysis, which imposes a limit on the plastic ultimate load multipliers. The suggested method is developed by imposing constraints related to the available material volume. The bi-directional evolutionary structural optimization (BESO) method is utilized to fulfill the objectives of this paper. The adequacy of the proposed technique is demonstrated by comparing the results of the algorithm with benchmark steel beams that have conventional web openings. Based on the numerical examples, it appears that the selected technique has the potential to increase the load capacity of steel beams while utilizing the same quantity of material within the design domain. Moreover, the improved beams also exhibit better performance in terms of stress levels. The results of this research suggest that the proposed technique enhances the load capacity of steel beams while maintaining the same quantity of material and improving their performance in terms of stress levels.

Deformation control method for active shape morphing lattice structure using topology optimization approach

This study introduces an active shape-morphing lattice structure along with a method for controlling its deformation. A shape memory alloys (SMA) based smart lattice unit cell is proposed, this smart lattice unit cell is capable of accomplishing three distinct types of basic deformations by activating various SMA actuators through heating. By assembling these smart lattice unit cells, an entire structure can be constructed, which can undergo various modes of deformation through the activation of different actuators. To assess the deformation effects, a 3D printed active shape morphing lattice structure model is employed. Furthermore, a deformation control method for active shape morphing lattice structure using topology optimization approach is established. The optimization model takes into account both energy consumption and structural deformation errors. To illustrate the application of this approach, a numerical example involving an airfoil structure with bending deformation is presented. The desired deformation is attained with minimal energy consumption and only a 1% margin of error in deformation.

Designing MEMS accelerometer for enhanced sensitivity and reduced cross-sensitivity in landslide monitoring

MEMS accelerometers capable of detecting weak motions are required in measuring landslide movements. The sensor’s sensitivity and its independent readings of various acceleration modes are crucial factors in the design of these sensors. In addition, it is highly desired to fabricate these sensors with low-cost and flexible manufacturing technologies such as surface micromachining. This paper presents an advanced topology optimization approach to design the suspended structure for the maximum level of sensitivity and for a low cross-sensitivity in the reading of principal and lateral modes, while it is manufacturable with a low-cost surface micromachining process. The effect of inertial forces as a variable loading condition and mode switch prevention is applied using a meta-heuristic topology optimization method with simulated annealing. Considering the unique results of this topology optimization, PolyMUMPs surface micromachining is employed to manufacture the developed sensor. The fabricated sensor is subjected to measurement and subsequent comparison with analogous designs from the literature. The outcomes reveal a sensitivity of 0.3pF/g and cross-axis sensitivity of 0.048%, signifying a noteworthy advancement for surface micromachined accelerometers. Notably, this design, coupled with the devised topology optimization methodology, holds the potential for adoption by sensor manufacturers for diverse commercial applications.

Topology optimization of multi-material active structures to reduce energy consumption and carbon footprint

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 internal forces. Recently, the potential of active structures to reduce environmental impact, i.e., reduce energy consumption and greenhouse gas (GHG) emissions, has been investigated. It has been verified that, compared to passive structures, active structures can not only use less material but also consume less energy and cause less GHG emissions during their service life, and thus have a significant potential to be applied as environment-friendly mechanical structures. This study aims to develop a general topology optimization (TO) approach to design novel multi-material active structural systems to reduce environmental impact. The approach is based on the density-based TO scheme. Passive and active materials are considered in the TO process and are required to be optimally distributed according to the optimization objective and constraints. The energy consumption or GHG emissions caused by the structure during its service life are treated as the objective function to be minimized under multiple displacement requirements. Typical examples are carried out to verify the developed approach. Results show that the topology optimized active structures may not only achieve significant weight savings but also less energy consumption and GHG emissions compared to equivalent topology optimized passive structures, which indicates that the developed approach has the potential to be applied to design novel structural systems with lighter weight, larger span, and with less environmental impact compared to conventional passive structural systems.

Explicit Topology Optimization of Voronoi Foams.

Topology optimization can maximally leverage the high DOFs and mechanical potentiality of porous foams but faces challenges in adapting to free-form outer shapes, maintaining full connectivity between adjacent foam cells, and achieving high simulation accuracy. Utilizing the concept of Voronoi tessellation may help overcome the challenges owing to its distinguished properties on highly flexible topology, natural edge connectivity, and easy shape conforming. However, a variational optimization of the so-called Voronoi foams has not yet been fully explored. In addressing the issue, a concept of explicit topology optimization of open-cell Voronoi foams is proposed that can efficiently and reliably guide the foam's topology and geometry variations under critical physical and geometric requirements. Taking the site (or seed) positions and beam radii as the DOFs, we explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a highly efficient local finite difference method to estimate the derivatives. During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The foam's mechanical property is also computed with a much-improved efficiency by an order of magnitude, in comparison with benchmark FEM, via a new material-aware numerical coarsening method on its highly heterogeneous density field counterpart. We show the improved performance of our Voronoi foam in comparison with classical topology optimization approaches and demonstrate its advantages in various settings.

Effects of inlet and outlet configurations on the topological optimization design of cooling plates for lithium-ion batteries

Topology optimization is a critical tool for enhancing the cooling efficiency and temperature uniformity of cooling plates, particularly in the context of designing thermal management systems for electric vehicle battery packs. This research employs a topology optimization approach centered on outlet enthalpy as the objective function to create a variety of cooling plates with different inlet and outlet configurations. Through an extensive numerical analysis, a comparative study is conducted among several configurations, including one inlet and one outlet (OP), two inlets and one outlet (TP), two inlets and two outlets (TTP), and four inlets and two outlets (FTP). Under 75 Pa conditions, FTP(y8) shows maximum temperature reductions of 0.42 %, 0.14 %, and 0.04 % compared to OP, TP(b), and TTP, respectively. The temperature difference also decreases by 38.55 %, 20.00 %, and 10.20 % in the respective comparisons. Additionally, as the pressure increases from 25 Pa to 75 Pa, the heat transfer coefficient of FTP(y8) experiences a notable 1.36-fold increase. Moreover, at 75 Pa, the performance evaluation criterion (PEC) value of FTP(y8) even exceeds twice the baseline. Under a 3C discharge rate, FTP(y8) excels with a maximum temperature of 304.49 K, reducing temperature differences and exhibiting superior cooling performance.

Stereolithography 3D Printing As a Versatile Tool to Manufacture Porous Electrodes for Redox Flow Batteries

Redox flow batteries show potential for large-scale energy storage; yet their current costs limit widespread implementation. As the porous electrode microstructure defines the available surface area for electrochemical reactions, electrolyte transport, and fluid pressure drop [1], enhancing the electrode performance is a promising strategy to increase power density and thus reduce system costs. Conventional fibrous porous electrodes are repurposed from fuel cell gas diffusion electrodes and have not been tailored to sustain the requirements of liquid-phase electrochemistry. Therefore, new manufacturing techniques offering high control over the electrode microstructure and resulting properties need to be developed [2]. In this context, 3D printing techniques are uniquely suited to manufacture controlled and deterministic architectures, enabling the tuning of electrochemical performance and hydraulic resistance [3].In this work, we employ stereolithography 3D printing using a commercial desktop printer, followed by carbonization, to manufacture model grid structures and investigate their potential as redox flow battery electrodes. We use microscopy, tomography, spectroscopy, fluid dynamics, and electrochemical diagnostics, to evaluate the thermal behavior, manufacturing fidelity, and fluid and mass transport performance of ordered lattice structures in non-aqueous redox flow cells. We find that the flow field geometry (flow through versus interdigitated), printing orientation with respect to the printing platform, and pillar geometry (Figure 1a) influence the flow cell performance. The printing orientation impacts the surface roughness and resin spreading, which determines the electrode morphology, influencing the internal surface area, shrinking direction after carbonization, and thus the charge transfer, mass transfer, and hydraulic resistances. Moreover, mass transfer rates within the electrode are increased by altering the pillar shape to a helical or triangular design, or by using an interdigitated flow field design, providing directions to improve electrolyte mixing through the electrode. Although the commercial electrodes feature a greater internal surface area and therefore a better electrochemical performance, the area-normalized mass transfer coefficients and pressure drop can be reduced by utilizing 3D printed electrodes (Figure 1b-c). Going forward, 3D printing technologies that enable finer features combined with carbonization at elevated temperatures can be used to manufacture multi-scale electrode structures simultaneously providing excellent electrochemical performance and low hydraulic resistance. We anticipate that combining 3D printing with emerging computational topology optimization approaches could enable the bottom-up design of advanced electrode materials for electrochemical devices [4]. Acknowledgments The authors gratefully acknowledge the Dutch Research Council (NWO) through the Talent Research Program Veni (17324) and the 4TU.HTM grant for financial support.

Topology-optimized freeform broadband optical metagrating for high-efficiency large-angle deflection

A metagrating made of periodic arrays of subwavelength inclusions has great capability for efficient manipulation of the impinging wavefront at subwavelength scale. However, it suffers from a significant practical issue in that the diffraction efficiency declines rapidly along with the increase of deflection angle, especially for broadband application scenarios. Here, we comprehensively investigated different topology optimization approaches to design the broadband optical metagrating for high-efficiency large-angle deflection, including single-wavelength optimization (SO), max-min optimization (MO), and average optimization (AO). It is demonstrated that the AO approach is more appropriate to optimize the broadband high-efficiency metagrating. Specifically, a freeform metagrating of up to about a 70° deflection angle at a central wavelength of 10.6 µm with diffraction efficiency exceeding 80% over a broad bandwidth of 4.36 µm in the infrared range is demonstrated based on the AO approach. It is also shown that, for all three optimization approaches, the quasi-catenary metagrating optimized from initial catenary structures has the evident advantage on bandwidth compared to that optimized from initial discrete structures. Our results provide insights into the inverse design of metagratings and may find potential applications in broadband achromatic metalenses and other broadband meta-devices.

Dynamic Topology Optimization of Constrained Layer Damping Structure Considering Non-Uniform Blast Load

The non-uniform distributed pressure of impact wave is usually simplified into concentrated or uniform load equivalently in the optimization design of constrained layer damping structure. However, for the thin-walled structure, it becomes necessary to regard the load as a non-uniform distribution. In this paper, a topology optimization approach is proposed considering the blast load with non-uniform distribution, aiming to unveil its impact on optimization layouts and dynamic responses. Initially, the smoothed particle hydrodynamics (SPH) algorithm is used to obtain the blast pressure what are extracted and integrated into the optimization model. Subsequently, the relative density is regarded as design variable. The construction of material penalty model and the topology optimization model are based on polynomial interpolation scheme (PIS). The sensitivity of objective function is deduced employing an improved adjoint variable method (AVM) to fit the load forms, and the Newmark-[Formula: see text] method is used to calculate the dynamic response. The optimization criterion (OC) is adopted to update the design variables. Finally, two numerical examples are used to exhibit the validity and accuracy of the presented methodology. The findings indicate that the distributed form, spread velocity, excited position and excited amplitude of the blast load all exert a notable influence on optimization results and dynamic response. These results underscore the valuable engineering application of this research and introduce a fresh perspective to the challenge of topology optimization under the blast case.

A WaveGAN Approach for mmWave-Based FANET Topology Optimization.

The integration of dynamic Flying Ad hoc Networks (FANETs) and millimeter Wave (mmWave) technology can offer a promising solution for numerous data-intensive applications, as it enables the establishment of a robust flying infrastructure with significant data transmission capabilities. However, to enable effective mmWave communication within this dynamic network, it is essential to precisely align the steerable antennas mounted on Unmanned Aerial Vehicles (UAVs) with their corresponding peer units. Therefore, it is important to design a novel approach that can quickly determine an optimized alignment and network topology. In this paper, we propose a Generative Adversarial Network (GAN)-based approach, called WaveGAN, for FANET topology optimization aiming to maximize the network throughput by selecting the communication paths with the best channel conditions. The proposed approach consists of a WaveGAN model followed by a beam search. The former learns how to generate optimized network topologies from a supervised dataset, while the latter adjusts the generated topologies to meet the structure requirements of the mmWave-based FANET. The simulation results show that the proposed approach is able to quickly find FANET topologies with a very small optimality gap for different network sizes.

Topology optimization of extruded beams modeled with the XFEM for maximizing their natural frequencies

In this paper, an efficient topology optimization approach is developed for maximizing the fundamental natural frequency of extruded beams. Mass fraction and static compliance bounds are defined using inequality-type constraints in the optimization problem. An XFEM approach, previously proposed by the authors for analyzing beam elements, is extended herein to compute the natural frequencies of the beam. The method allows for 3D modeling of beams with a significant reduction in the number of degrees of freedom and therefore also yields efficient optimization procedure. This reduction is made possible by incorporating global enrichment functions in the longitudinal direction, which enables a significant reduction in the number of elements in that direction without loss of accuracy. A nonlinear optimization problem is formulated using continuous density-based design variables that represent the material distribution in the beam’s cross-section. The optimization problem is then solved using a gradient-based approach with analytical sensitivities. The well-known Solid Isotropic Material with Penalization (SIMP) method is used to acquire discrete solutions. We study the optimal design of short and long beams. It is shown that for short beams, localized vibration modes appear within the cross-section, leading to a significant distortion deformation mode of the cross-section. The optimized design of the long beam shows global deformation modes with an increase of 15% in the fundamental frequency compared with a non-optimized design consisting of a hollow rectangular cross-section with the same mass.