Topology Optimization Analysis Research Articles

Topology optimization analysis of a frame-core tube structure using a cable-bracing-self-balanced inerter system

Topology optimization analysis of a frame-core tube structure using a cable-bracing-self-balanced inerter system

Structural Optimization of an Unmanned Ground Vehicle as Part of a Robotic Grazing System Design

Unmanned ground vehicles (UGVs) have gained increased attention in different fields of application; therefore, their optimization requires special attention. Lowering the mass of a UGV is especially important to increase its autonomy, agility, and payload capacity and to reduce dynamic forces. This contribution deals with optimizing a UGV unit prototype that, when connected with similar units, forms a moving electric fence for animal grazing. Together, these units form a robotic system that is intended to solve the critical problem of lack of human capacity in herding and grazing. This approach employs topology optimization (TO) and finite element analysis (FEA) to lower the mass of a UGV unit and validate the design of its structural components. To our knowledge, no optimization of this type of UGV has been reported in the literature. Here, we present the results of a case study in which a set of four load cases served as a basis for the optimization of the UGV frame. Response surface analysis (RSA) was used to identify the worst load cases, while substructuring was used to allow for more detailed meshing of the frame portion that was subjected to TO. Thereby, we demonstrate that the prototype of the UGV unit can be built using standard parts and that TO and FEA can be efficiently used to optimize the load-carrying structure of such a specific vehicle.

Topology optimization and bionic analysis of heat sink fin configuration based on additive manufacturing technology

Fins are extensively employed in heat sinks for high heat flux components. In this study, three distinct objective functions, namely temperature gradient minimization (TO-I type fin), average temperature minimization (TO-II type fin), and entransy dissipation minimization (TO-III type fin), are established for topology optimization design of the heat sink fin structure to effectively minimize the temperature of the heat source. By conducting a comparative analysis of the configuration features and thermal performance of optimized fins with different objective functions, it is evident that the TO-I type fin exhibits superior thermal performance. When the fin volume fraction φ is 0.3, the heat source center temperature of TO-I type fin is 2.67 K and 4.55 K lower than that of TO-II type fin and TO-III type fin, respectively. Meanwhile, the bionic analysis of the optimized fins under different objective functions using fractal theory reveals that the fractal dimension of the TO-I type fin is 1.4038, which is the closest to the average fractal dimension of many kinds of leaf veins in nature (D¯f= 1.3762), which indicates that the optimized fins have the bionic characteristics most similar to those of the leaf blade. Finally, the three topology optimization fins were fabricated using boundary-filtering optimization 3D printing technology. Comparative tests verified the advantage of minimizing the temperature gradient as the objective function of topology optimization and demonstrated its potential for thermal performance and lightweighting applications, especially under high heat source operating conditions.

Broadband topology optimization of three-dimensional structural-acoustic interaction with reduced order isogeometric FEM/BEM

This paper presents a model order reduction method to accelerate broadband topology optimization of structural-acoustic interaction systems by coupling Finite Element Methods and Boundary Element Methods. The finite element method is used for simulating thin-shell vibration and the boundary element method for exterior acoustic fields. Moreover, the finite element and boundary element methods are implemented in the context of isogeometric analysis, whereby the geometric accuracy and high order continuity of Kirchhoff-Love shells can be guaranteed and meantime no meshing is necessary. The topology optimization method takes continuous material interpolation functions in the density and bulk modulus, and adopts adjoint variable methods for sensitivity analysis. The reduced order model is constructed based on second-order Arnoldi algorithm combined with Taylor's expansions which eliminate the frequency dependence of the system matrices. Numerical results show that the proposed algorithm can significantly improve the efficiency of broadband topology optimization analysis.

Finite Elements Analysis and Topology Optimization of Parking Brake Lever and Ratchet

Topology optimization is known as one of the basic categories of structural optimization. Topology optimization is received increasing attention in many engineering disciplines. Topology optimization contributes to minimizing emissions and environmental effects by increasing material utilization efficiency and manufacturing sustainability. The mechanical parking brake is still used in many vehicles. This study aims to contribute to the reduction in vehicle weight by applying topology optimization. In addition, it also purposes to promote sustainability in manufacturing by reducing material usage and energy consumption. A CAD model was created by considering the existing mechanism element dimensions. The parking brake lever mechanism component was evaluated using topology optimization and finite element analysis methods. Static analyses were performed using a finite element analysis program. The results of this analysis were used as input data for topology optimization. In the topology optimization, the response constraint mass was increased by 5 increments from 50% to 95%. As a result, the maximum equivalent (von Mises) stress for the parking brake lever is 230,29 MPa, and for the ratchet is 11,559 MPa. The maximum total deformation value for the brake lever is 0,95853 mm and for the ratchet is 0,0079482 mm. The parking brake lever mass decreased by 18,48% from 0.27751 kg to 0.22622 kg. The ratchet mass decreased from 0.095042 kg to 0.061911 kg by 34.85%.

Design of Reinforced Ribs for Spaceborne Parabolic Cylindrical Reflector Antenna Based on Topology Optimization and Parametric Analysis

The normal operation of spaceborne parabolic cylindrical reflector antennas under various operating conditions relies on maintaining the root mean square (RMS) of the reflector surface’s deformation within reasonable limits. In engineering practice, the designing of reinforced ribs is the primary way to control the RMS of the reflector surface. However, the layout and dimensions of reinforced ribs for many existing designs rely on the experience of the designer and lack a theoretical foundation. This leads to suboptimal layouts and dimensions in many designs, deviating from the optimal design. To address these concerns, this study proposes a comprehensive design approach that combines both topology optimization and parametric analysis. Optimization and parametric analysis were conducted for a large-sized spaceborne composite parabolic cylindrical reflector antenna. The layout and dimensions of the reinforced ribs were reconstructed based on the optimization results and parametric analysis. This study also obtained the influence of the height and thickness of the reinforced ribs on the RMS of the reflector surface. Subsequently, utilizing antenna temperature field simulations as thermal excitation inputs, finite element thermal distortion analyses were conducted for the reflector surfaces without reinforced ribs, with the original reinforced ribs designed based on empirical methods, and with optimized reinforced ribs. In comparison to the original design of the reinforced ribs, the optimized design, without an increase in the volume of the reinforced ribs, reduced the RMS of the reflector surface from 0.6025 mm to 0.5561 mm, resulting in an optimization ratio of 7.7%. Moreover, when compared to the reflector surface without reinforced ribs, the optimized design achieved a 17.9% reduction in RMS.

Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem

Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem

Structure Design Improvement and Stiffness Reinforcement of a Machine Tool through Topology Optimization Based on Machining Characteristics

Machining characteristics were applied to topology optimization for machine tool structure design improvement in this study, and the goals of lightweight and high rigidity of the structure were achieved. Firstly, an ultrasonic-assisted grinding experiment was carried out on zirconia to investigate the surface roughness, surface morphology, grinding vibration, and forces. Then, the topology optimization analysis was conducted for structure design improvement, in which the magnitude of the grinding vibration was utilized as the reference for selecting the topology subsystems and the grinding force was used as the boundary conditions of the static analysis in the topology optimization. Hence, columns, bases, and saddles were redesigned for structure stiffness improvement, and the variations in the effective stress, natural frequency, weight, and stiffness of the whole machine tool were compared accordingly. The results showed that the deduced topological shape (model) can make the natural frequency and stiffness of the whole machine tool tend to be stable and convergent with a weight retention rate more than 75% as the design constraint. The subsystem structures with larger effective stress distributions were designated for stiffness improvement in the design. At the same time, the topological shape (model) was also employed in the design for weight reduction, focusing on minimizing redundant materials within the structure. In contrast to the consistency of the modal shapes before and after topological analysis, the sequential number of the modal mode of the machine tool model after topological analysis was advanced by two modes relative to those of the original situation, which means the original machine tool may be out of its inherently resonant frequency range. Also, the natural frequencies corresponding to each mode had an increasing tendency, and the maximum increase was 110.28%. Furthermore, the stiffness of the machine tool also increased significantly, with a maximum of 355.97%, leading to minor changes of the machine tool’s weight. These results confirm that the topology optimization based on machining characteristics proposed in this study for structure redesign improvement and stiffness enhancement is effective and feasible.

Parametric topology optimization design and analysis of additively manufactured joints in spatial grid structures

This paper presents a complete computer-aided workflow for the parametric topology optimization (TO) design, numerical analysis and additive manufacturing (AM) of steel joints in spatial grid structures. A fully parametric TO design framework for steel joints in spatial grid structure was developed based on the Grasshopper platform. The joint models were parametrically established based on subdivision surface technology and further topology optimized through the bi-directional evolutionary structural optimization (BESO) algorithm with the support of cloud computing server. The structural performance of the optimized joints was thoroughly investigated via the parametric finite element analysis. Variables of loading conditions and TO parameters (target volume and filter radius) that affect the compliance, maximum displacement, maximum stress and stress distribution were taken into account. Analysis showed that the target volume governed the joint structural behaviour while the filter radius affected the geometric details of optimized joint. The practicability of proposed workflow was demonstrated through a parametric optimization design framework of a double-layer spatial grid structure with hundreds of steel joints. A typical optimized joint made of 316L stainless steel was additively manufactured using selective laser melting. This workflow is highly automatic and featured by high design flexibility and integration degree as well as good transplanted ability.

Topology optimization and numerical analysis of cold plates for concentrating photovoltaic thermal management

Continuous advances in concentrating photovoltaic (CPV) panel efficiency are increasingly affected by cell temperature. Improving PV panel cooling performance is critical. This application optimizes the internal flow channel structure of PV panel cooling systems using topology optimization techniques like multi-objective and multi-stage optimization with penalty factors. Three-dimensional CFD simulation is used to compare the heat transfer performance of topology optimized channel cooling configuration and traditional straight channel cooling configuration for photovoltaic panel systems. Effects of inlet flow rates, concentration ratios, and other parameters on cooling performance are investigated. Results show the topology optimized flow channel configuration has better cooling than the straight channel. At different concentration ratios, the solar cell temperature reduces 13.85%–23.45%. The optimized application also has lower inlet and outlet pressure drops for the same operating conditions, requiring less external power. Compared to the straight channel, the topology optimized flow channel increases net PV system output power 3.00%–19.37% at different concentration ratios. Applying topology optimization provides new ideas for optimizing PV cooling system designs.

Design and Fabrication of a Lightweight and Wearable Semirigid Robotic Knee Chain Exoskeleton

Abstract With the population of people affected by lower limb disability and physical impairments continuing to grow, engineers in response have begun to develop exoskeletons designed to assist and rehabilitate those in need. While there have been great strides and advancements in the development of exoskeletons, many of them are still too cumbersome, heavy, and expensive for most people. The project described in this paper aims to design and manufacture a wearable robotic knee exoskeleton that helps solve some of the drawbacks that exoskeletons have today. The exoskeleton is designed with lightweight and durable three-dimensional (3D)-printed PETG, TPU, and PLA components combined with soft, flexible, and wearable materials to achieve improved human–robot interaction while providing support when bending and extending the knee joint. The three main assemblies designed in this project were a 3D-printed semirigid knee chain, a 3D-printed flexible shin brace, and a motor actuator assembly mounted on a carbon fiber back plate. The semirigid knee chain is actuated using a Bowden cable which allows the heavy motor to be relocated onto the user's back. solidworks topology optimization and finite element analysis (FEA) were used to reduce weight while keeping the overall strength of the chain and ensuring the safety factor of 2. The exoskeleton was observed to be able to withstand applied torques of up to 29 N·m during the walking functionality test. This exoskeleton is also designed to be integrated into a larger hip exoskeleton system.

Fatigue analysis and optimization design of key components of synthesizing equipment for artificial diamond based on a method of information exchange system.

In this article, a method of information exchange system (MIES) has been proposed to optimize the structure of the hinge sleeve of cubic (HSC), a key component of synthetic diamond. The MIES method integrates static analysis, topology optimization, and fatigue failure analysis. By using this method, the lightweight design of the structure was ensured while meeting the fatigue life requirements. The weight of the optimized model was reduced from 5729.9 kg to 4593.4 kg, and the fatigue life was 1.127E+05, which meets the serviceability requirements. The steps of the method are as follows: First, the model of HSC was established. According to the loading conditions, the basic material data and boundary conditions were set, and the stresses and strains of the HSC were calculated. The optimized region was obtained by topological analysis of the HSC structure using the variable density method. The fatigue life of the model was then calculated by combining the stress life method and the average stress correction method. Simulations were performed using the above method to obtain the six nodes of maximum stress in the HSC. These nodes were used as control points for the structural optimization design. The HSC model was optimized by optimizing the structure in the region of the control variable points. Computational analysis of the optimized HSC model was carried out using the information exchange system. After repeated optimization of the structure of the HSC model, a model with a lightweight design was obtained. The ANSYS simulation results showed that the final mass of the HSC model was reduced by 19.83%. Stress and life were within the design requirements. The information exchange system has better computational performance, feasibility, and reliability compared to traditional theoretical methods.

STO-DAMV: Sequential topology optimization and dynamical accelerated mean value for reliability-based topology optimization of continuous structures

In deterministic topology optimization (TO), due to not taking into account the uncertainties of the structural system, explicitly, resulting optimal layouts may conclude in low reliable levels or unreliable optimum design conditions. The objective of reliability-based topology optimization (RBTO) is to integrate the reliability concept into topology optimization, finding the optimized structures priori by the designer through a mathematical framework guaranteeing that the least reliability level is achieved. In the present investigation under a constant volume fraction, the bisection algorithm is implemented for approximating the optimal feature of the structure in the TO framework by applying the moving iso-surface threshold (MIST) topology optimization approach. The results from the previous step are employed to consider uncertainties by a reliability analysis algorithm. A reliability analytical method based on dynamical accelerated formulation is combined with the TO-based bisection algorithm as a novel sequential topology optimization and reliability analysis (STORA) for RBTO. The descent condition is guaranteed in the dynamical accelerated mean value method to search the most probable point which is applied in TO for finding optimum layouts of continuous structure problems. A dynamical step factor in the reliability loop of the STORA and the MIST integration are applied to find the optimum layouts in the optimization loop. Illustrative examples are presented for validation and to maintain the capability of the proposed sequential topology optimization and dynamical accelerated mean value (STO-DAMV). Based on the results, it is demonstrated that the application of reliability analysis with the integration of bisection in topology optimization can produce a robust reliability analysis with stable results in RBTO which facilitates a more reliable design than that acquired by TO. It is also concluded that, under identical accuracy, STO-DAMV for STORA is improved in view of computational robustness.

TOPOLOGY OPTIMIZATION DESIGN AND MECHANICAL ANALYSIS OF A PERSONALIZED LUMBAR FUSION DEVICE

Objective: To reduce the shielding effect caused by the large elastic modulus of metal fusion devices after osteotomy for the treatment of scoliosis. Methods: A personalized fusion device was designed using reverse engineering techniques, three-dimensional modeling, topology optimization, and finite element analysis. A finite element model of the lumbar spine after orthopedic surgery was established from an actual case. A fusion device was implanted into the lumbar spine before and after the optimized design for simulation calculations, respectively. The similarities and differences in the mechanical properties of the different fusion devices and vertebrae were compared. Based on the topological optimization of the mechanical properties of the fusion system, a lightweight fusion device was designed and the stress-shielding effect on the lumbar vertebrae was improved. Results: The topologically optimized fusion device described in the current case was 60% lighter while maintaining the strength of the fusion. After optimization, the average strain of the fusion was increased by up to 200% and the stiffness was significantly decreased. The average equivalent stress of cancellous bone was increased by up to 9.55% for the PEEK fusion device. In contrast, the topologically optimized fusion can increase the average equivalent stress of cortical bone by 5.63% and reduce the stress-masking effect of vertebrae. Conclusion: Topologically optimized titanium alloy fusion devices can significantly reduce the mass of the implant as well as reduce fusion stiffness. Additionally, a topology-optimized titanium alloy fusion device can effectively improve the stress-shielding effect of cortical bone.

Force Characteristics and Mechanical Topology Optimization of Hydraulic Machine Structures: Statics and Dynamics

In this paper, the design requirements of the hydraulic testing machine are based on the actual force conditions. Static and dynamic performance analyses of the stressed components of the hydraulic machine are carried out and the mechanical topology is optimized. Combining the static and dynamic objective functions of the structure, a fast variable density topology method is proposed, thus improving the optimization efficiency. After setting the positions of the optimized and non-optimized regions. It can be found that the optimized mechanical performance is more superior as the number of iterations increases. The results show that the stress in the strut is 175.75 MPa and the maximum stress in the upper beam structure is 43.708 MPa. The first sixth order frequency is much higher than the operating frequency of 3 Hz. The final results of the mechanical topology optimization analysis show. The optimized structure of the upper, middle and lower crossbeams resulted in a mass reduction of 38%, 36% and 5.57%. The maximum stresses in the upper and middle crossbeams were reduced by 10.33%, 8.3% and 51.8%, respectively. The deformation was reduced by 6.14% at the fastest time; the inherent frequency of the first 3 orders was increased to achieve light weight. The overall mechanical properties became better after optimization, and the dynamic and static stability of the frame was improved. Translated with www.DeepL.com/Translator (free version)

Development of an innovative test machine for tyre, wheel and suspension systems for automotive and industrial vehicles

Reliability and efficiency of automotive and industrial vehicles are strongly affected by the behaviour of the components involved in the interaction with the ground. For this reason, components like tyres, wheels and suspension systems are physically tested, for performance and durability assessment. Anyway, standard test machines are generally designed for testing only one specific component.The aim of this work is the design of an innovative test machine, able to perform different kinds of tests, for tyre, wheel and suspension system components, on a unique bench. The machine is a flat track type, better fit than traditional drum types in simulating real tyre-to-ground contact conditions. The core of the machine is a Gough-Stewart platform, where the flat track is fixed, which is moved by six hydraulic actuators to reproduce multiple work configurations, for extended time periods or numerous test block repetitions. After the preliminary design phase, the machine components were subjected to topology optimization and modal analysis by FEM, to reduce weights and avoid any issues related to the expected working frequencies. Given the quality of the results achieved, currently, the software design for closed-loop control configuration is under development, for the machine prototype next construction.

Simulation of random fields on random domains

This paper focuses on the simulation of random fields on random domains. This is an important class of problems in fields such as topology optimization and multiphase material analysis. However, there is still a lack of effective methods to simulate this kind of random fields. To this end, we extend the classical Karhunen–Loève expansion (KLE) to this class of problems, and we denote this extension as stochastic Karhunen–Loève expansion (SKLE). We present three numerical algorithms for solving the stochastic integral equations arising in the SKLE. The first algorithm is an extension of the classical Monte Carlo simulation (MCS), which is used to solve the stochastic integral equation on each sampled domain. However, such approach demands remeshing each sampled domain and solving the corresponding integral equation, which can become computationally very demanding. In the second algorithm, a domain transformation is used to map the random domain into a reference domain, and only one mesh for the reference domain is required. In this way, remeshing different sample realizations of the random domain is avoided and much computational effort is thus saved. MCS is then adopted to solve the corresponding stochastic integral equation. Further, to avoid the computational effort of MCS, the third algorithm proposed in this contribution involves a reduced-order method to solve the stochastic integral equation efficiently. In this third algorithm, stochastic eigenvectors are represented as a sum of products of unknown random variables and deterministic vectors, where the deterministic vectors are efficiently computed by solving deterministic eigenvalue problems. The random variables and stochastic eigenvalues that appear in this third algorithm are calculated by a reduced-order stochastic eigenvalue problem constructed by the obtained deterministic vectors. Based on the obtained stochastic eigenvectors, the target random field is then simulated and reformulated as a classical KLE-like representation. Finally, three numerical examples are presented to demonstrate the performance of the proposed methods.

A designer’s challenge: Unraveling the architected structure of deep sea sponges for lattice mechanical metamaterials

Biomimetic and Bioinspired designs have been investigated due to the advances in modeling, mechanics and experimental characterization of structural features of living organisms. To accomplish bioinspiration for fields such as robotics, adhesives and smart materials, it is required to comprehend how Nature accomplished enhanced mechanical behavior. Among the plethora of complex organisms spanning at different lengthscales, the deep sea sponge Euplectella Aspergillum has been of particular interest due to its lattice structure that can be the framework to design mechanical metamaterials. However, despite its intriguing morphology, constraints in the fabrication and modeling of scalable and nonuniform materials has hindered the study of its mechanical performance and how to harness it. Moreover, a comprehensive FEA model that encompasses the whole spectrum of its constitutive and structural performance has not been reported. In this study, it is aimed to characterize and model the mechanical behavior of this sponge from a structural standpoint. Utilizing various experimental techniques, an FEA mechanical model is developed to study the nonlinear buckling analysis of the sponge’s lattice structure and its resilience to failure. Finally, through topology optimization and sensitivity analysis, a new mechanical metamaterial is proposed. Our results elucidate how mechanical characterization and FEA modeling can be employed for a deeper understanding of Nature’s tailored hierarchy and the design of metamaterials.

OPS-ITO: Development of Isogeometric Analysis and Topology Optimization in OpenSEES for Free-Form Structural Design

Unlike the current design routine manually defining geometries for computational analyses, a future-oriented computer-aided design tool can generate a structural model through automated model optimization and iterative analyses. The topology optimization technique uses elemental density variables to formulate a computationally varying model based on analysis results, while an isogeometric analysis could facilitate the automatic iteration without adapting the mesh scheme at each step. This paper aims to bring these capabilities in the open-source simulation platform OpenSEES. The IGAQuad and IGABrick elements using NURBS based shape functions and geometric description are developed in this widely-used finite element modelling framework, which are then ported to a density-based topology optimization module. The modelling capabilities of the IGA elements have been verified using classic problems. The model optimization processes for loaded structural members are demonstrated using 2D and 3D cases, in which the eventually obtained geometric models are fundamentally different from the original boxy shapes but of less material cost and comparable structural performance. Although the development in this paper remains limited, the open-source and modular code infrastructure of OpenSees could facilitate continuous development on the basis of the topology optimization and isogeometric analysis in this paper, aiming for a computational tool to synergize the free form structural design and the advanced construction technologies.

An Efficient Decoupled Reliability-Based Topology Optimization Method Based on a Performance Shift Strategy

AbstractIn this paper, a new efficient reliability-based topology optimization (RBTO) method is proposed for structures, in which the double-loop optimization is equivalently decoupled into a sequential process based on a performance shift strategy. First, a volume minimization RBTO formulation is built for structures considering displacement or compliance reliability constraints. Second, an efficient decoupling scheme is proposed to turn the double-loop RBTO into a series of deterministic topology optimization and reliability analysis. For the reliability analysis, the reliability probability is calculated based on the probability distribution function of the performance function, and the probability distribution function can be solved by the maximum entropy method based on the raw moments calculated by the multiplicative dimension reduction method. A performance shift strategy is then applied to build an equivalence between probabilistic constraint and deterministic constraint to formulate the deterministic topology optimization. Thirdly, the adjoint variable method is applied to obtain the sensitivity information for topological design variables, and a gradient-based optimization algorithm is used to update the design variables. Finally, four typical numerical examples are used to verify the advantage of the proposed method. Compared with the traditional sequential optimization and reliability assessment (SORA) method, the proposed RBTO method results in a design with a 5.4% smaller volume value to reach the same reliability index requirement for the cantilever beam, and the function calls are 354 times less than that of the SORA method.