Topology Optimization Research Articles

Reliability-based topology optimization of imperfect structures considering uncertainty of load position

In this paper, a novel optimization technique is implemented to explore the effects of considering uncertain load positions. Therefore, the integration of reliability-based design into structural topology optimization, while considering imperfect geometrically nonlinear analysis, is proposed. By comparing the results obtained from perfect and imperfect geometrically and materially nonlinear analyses, this study examines the impact of nonlinearity on probabilistic and deterministic analyses. Concerning probabilistic analysis, the originality of this research lies in its incorporation of the position of the applied load as a stochastic variable. This distinctive approach complements the consideration of other relevant parameters, including volume fraction, material properties, and geometrical imperfections, with the overarching goal of capturing the variability arising from real-world conditions. For the assessment of uncertainties, normal distribution is assumed for all these parameters. Normal distributions are chosen due to their advantages in terms of simplicity, ease of implementation, and computational efficiency. These characteristics are particularly beneficial when dealing with complex optimization algorithms and extensive analyses, as is the case in our research. The proposed algorithm is validated according to the results of benchmark problems. Structural examples like cantilever beam, pinned-shell, and L-shaped beam problems are further explored within the context of imperfect geometrically nonlinear reliability-based topology optimization, with specific regard to the probabilistic aspect of the location of the externally applied loads. Moreover, the results of the suggested approach suggest that the inclusion of a probabilistic design strategy has influenced topology optimization. The reliability index acts as a controlling constraint for the resulting optimized configurations, including the mean stress values associated with the resulting topologies.

Research on design method of lattice turbine disk based on topology optimization

Abstract As a typical structure of an aero-engine, turbine disk has been used in high-temperature and high-speed environments for a long time, and its mass accounts for a large proportion. Therefore, its lightweight design is urgent. With the development of an aero-engine towards a high thrust-to-weight ratio, the turbine speed continues to increase, and the single-stage load continues to increase, which makes the design of the turbine disk face more problems and challenges. The uniform material turbine disk structure has made it difficult to meet its comprehensive performance requirements. To address this issue, this paper proposes a lattice turbine disk design idea, changing the uniform organization pursued by traditional design and achieving optimal performance through the integration of design innovation and manufacturing process innovation. This paper takes the turbine disk as the research object to establish a lattice turbine disk design method. By using the topology optimization method based on progressive optimization, the cell configuration can be obtained. After that, combined with the structural characteristics of the turbine disk, the design of the dot matrix auxiliary plate disk is realized. Finally, taking a turbine disk as an example, this paper carried out the optimization design of the turbine disk and obtained the lattice disk with better performance, which verified the feasibility of the method.

Enhancing the cooling performance of thermocouples: a power-constrained topology optimization procedure

Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form pk=pσ>pα=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_k=p_{\\sigma }>p_{\\alpha }=1$$\\end{document} for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

Uniform multiple laminates interpolation model and design method for double–double laminates based on multi-material topology optimization

Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed to describe the certainty of the stacking direction in multi-layer composite structures, inspired by the interpolation model in multi-material topology optimization. Specifically, the stiffness matrices of all alternative angle combinations of laminates are interpolated to form virtual laminates. The UMLI model eliminates the need for adding interlayer constraints during the optimization process. Then, the optimization problem is defined to minimize the compliance of the composite structures and is solved using the gradient-based optimization algorithm. Finally, the proposed method is applied to the design of the composite stiffened panel, the composite Unmanned Aerial Vehicle (UAV) wing, and the rear fuselage. The results demonstrate that the UMLI model and proposed optimization method have considerable potential in the angle optimization design of multi-layer structures.

Multiscale topology optimization for designing locally resonant acoustic metamaterials with specified low-frequency bandgaps

Locally resonant acoustic metamaterials (LRAMs) have significant potential to isolate low-frequency vibrations and noise, whereas designing them with specified bandgaps is challenging. Compared to the monoscale method, the multiscale method can design microstructures that form equivalent materials to act as scatterers, coatings, and matrices. This may aid in obtaining LRAMs that are sometimes difficult to achieve with the monoscale method. Therefore, a multiscale topology optimization method is presented to design LRAMs with bandgaps that meet specified frequency constraints. Since bandgap optimizations are complicated, many local minimum solutions may exist when using sensitivity-based methods. To mitigate this issue, a macro-parameter optimization stage using a genetic algorithm (GA) is added between the macro and micro optimizations in this top-down multiscale framework. As a result, the method comprises three optimization stages: macro-bandgap optimization, macro-parameter optimization, and micro-optimization. Since the macrostructures consist of multiple microstructures and the microstructures consist of multiple materials, a parameterized level-set-based multi-material topology method is adopted to obtain topologies on both scales. The effectiveness of the proposed method is demonstrated through numerical examples of two optimization problems. The first is to obtain LRAMs with the maximum bandgap width while ensuring their bandgaps encompass specified frequency ranges. The other is to obtain LRAMs with specified bandgaps. Successfully obtained LRAMs with specified bandgaps demonstrate the application prospects of this method in designing structures and devices to address issues related to vibrations and noise.

Topology optimization framework of multiple-phase materials with stress and dynamic constraints under self-weight loads

Topology optimization framework of multiple-phase materials with stress and dynamic constraints under self-weight loads

Reliability-based structural-thermal topology optimization of lightweight metal foam skeleton microstructure using the fully analytical adjoint method

Reliability-based structural-thermal topology optimization of lightweight metal foam skeleton microstructure using the fully analytical adjoint method

Topology optimization of multi-material structures subjected to dynamic loads

Traditional designs for multi-material structures are mostly based on static loads. However, engineering structures are often subjected to dynamic loads. This paper firstly and systematically conducts an in-depth study on the topological design of multi-material structures under dynamic loads. In this method, the definition of design variable adopts the ordered solid isotropic material with penalization (ordered-SIMP) method to normalize the design variable, without introducing any additional variables, the HHT-α method is employed to solve the dynamic optimization problem. To address the dynamic optimization problems with constraints on mass and cost, a convex optimization method based on the concept of sensitivity separation is used to update the design variables, and search for the structural topologies. Finally, this paper provides some numerical examples with respect to time-varying, material parameters, load amplitude, load direction and multiple loads, to discuss in depth the topological and numerical results of these examples.

Multiscale fail-safe topology optimization for lattice structures

Multiscale fail-safe topology optimization for lattice structures

Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices

Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices

Topology optimization of link mechanisms for comprehensive synthesis of component arrangement and structure using micropolar elasticity model

This paper proposes a method for topology optimization of link mechanisms with multiple outputs, using a multi-material micropolar elasticity model. This approach allows for comprehensive optimization of both the arrangement and structure of the link mechanism components. By utilizing a continuum model that incorporates micropolar elasticity, we can specify bending stiffness independently from tensile stiffness, resulting in deformation characteristics that approximate a link mechanism. The optimization problem of designing link mechanisms for multiple outputs is reformulated as a boundary value problem within this model framework. The design goal is to synthesize a link mechanism that not only follows a desired path but also possesses the required degrees of freedom. To achieve this, the objective function is defined by the displacement error under external force and the strain energy in the links. The multi-material micropolar elasticity model is then optimized through a gradient-based optimization method, focusing on this objective function. The effectiveness and applicability of our methodology are demonstrated through several numerical case studies.

A New Two-Phase Design Process for a Compliant Mechanism Gripper

The structural design of the components with high accuracy and controllable motion is the focus of precision industries. As a result, researchers found that components created via compliant mechanisms were much preferable. Monolithic structures known as compliant mechanisms allow motion to be achieved without the need of traditional joints. The compliant mechanisms make it easier to build microscale devices because they do not have hard junctions. In this study, a novel two-phase design methodology for compliant mechanism forceps is proposed. In order to eliminate high-stress areas, forceps are often constructed as a distributed compliant mechanism. To offer a distributed planar design, topological optimization is introduced with new approach. Design domain introduced with pattern of holes restricts the single point contact formation and large area formation which yield distributed compliant mechanism. The parametrization technique is implemented to convert the conceptual design to working design. The design of compliant forceps is assessed using finite element analysis (FEA) based on structural considerations. Finally, a handle-equipped microgripper prototype has been developed. Experimental verification demonstrates the gripper's performance and variation is less than 3% with numerical results. Integerated force sensor measure the gripping force and compared the reaction force estimated through FEA.

Compliant Mechanism Synthesis Using Nonlinear Elastic Topology Optimization With Variable Boundary Conditions

ABSTRACTIn topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization's effectiveness for many mechanism design problems. We remove this limitation by developing a method which automatically determines optimal positioning of a prescribed input displacement and a set of supports simultaneously with an optimal material layout. Using nonlinear elastic physics, we synthesize a variety of compliant mechanisms with large output displacements, snap‐through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using manually designed boundary conditions used in previous studies, the mechanisms presented in this paper see performance increases ranging from 47% to 380%. The results show that nonlinear mechanism responses may be particularly sensitive to boundary condition locations and that effective placements can be difficult to find without an automated method.

Innovative design and process simulation of aviation bracket based on topology optimization and additive manufacturing

Abstract In this paper, topology optimization(TO) and laser powder bed fusion (LPBF) technology were combined to explore the key technology of parts integration design and manufacturing oriented to performance, structure and manufacturing process. With the help of topology optimization(TO), the lightweight design of the aviation bracket achieved the weight loss goal of 87.69% in this work. The thermophysical properties of TC4 were calculated by thermodynamic calculation, and the temperatue interval of Laser Powder Bed Fusion for TC4 is 1800 ℃- 3000 ℃ was determined . Additionally, the LPBF macro-scale simulation was carried out. The results showed that the maximum temperature in the printing process is lower than 2500℃, and the maximum displacement is 4.87 mm, which only appears in the non-design space. Finally, the safety factor and maximum displacement of aviation bracket are 1.3 and 0.8 mm, and the maximum Mises stress is 654 MPa, all of which meet the design requirements.

Development of a Design Procedure Combining Topological Optimization and a Multibody Environment: Application to a Tram Motor Bogie Frame

Nowadays, it is essential to find increasingly rapid and efficient design strategies. This approach becomes crucial in the railway industry, where components must be verified according to multiple reference standards, both structurally and dynamically. In this context, the present research activity aims to develop a fast and effective desin procedure based on European reference standards. The goal was to develop the geometry of a motor bogie frame for a tram vehicle, integrating three fundamental tools for development: finite element simulations and topological structural optimization, a Write Computer Aided Design (CAD) environment, and a multibody environment. Their integration could enhance design accuracy, streamline the traditional design workflow, and support innovation. The optimization process involved the introduction of complex technological constraints, directing the geometry toward production by casting. A tool was developed to automate running dynamics simulations and the output of results for immediate verification of the entire vehicle performance. Finally, the new geometry was tested both structurally and dynamically. The mass was reduced by approximately 7% while ensuring satisfactory mechanical performance. The maximum value of stress was reduced by about 16%. The dynamic performance showed negligible variation, confirming the encouraging outcomes to make this procedure increasingly effective and reliable.

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.