Multi-objective Topology Optimization Research Articles

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

Multi-objective topology optimization and numerical investigation of heat sinks based on triply periodic minimal surface lattices

In thermal management applications, such as heat sinks (HSs) for electronic devices, cellular materials have extensively been employed. In recent years, there has been a growing attention towards employing topology optimization for enhancing hydraulic and heat transfer performance of HSs by optimizing their topology. The utilization of triply periodic minimal surface (TPMS) based structures presents distinctive prospects for customizing the design and performance of HSs. However, their potential remains unexplored in the context of customizing additively manufactured porous optimized HSs. Consequently, there is a need for research aimed at examining their coupled hydraulic and thermal performance. Density mapping approaches are used to build a variable density TPMS-based HSs from the output of topology optimization by applying the TPMS level-set equations that relate relative density and the level-set constant. In this work, a relative density mapping methodology is applied to thermo-fluid optimization problem to design a TPMS-based convective cooling system. An in-house MATLAB code was developed to perform a multi-objective topology optimization. After that, uniform and variable density (mapped from topology optimization results) TPMS-based HSs are analyzed using Star-CCM + CFD software to investigate their hydraulic and heat transfer performance. An experimental setup was established, and the numerical results were validated using uniform TPMS-based heat sinks. Results showed that incorporating TPMS with topology optimization has a great potential in thermal management applications as pressure drop across the heat sink was reduced while maintaining the performance.

Research on multi-objective topology optimization of unmanned sightseeing vehicle frame based on Analytic Hierarchy Process

To optimize the frame of a sightseeing vehicle, this paper proposes a multi-objective topology optimization method combining Analytic Hierarchy Process (AHP) and topology optimization. Firstly, the edges of the unmanned sightseeing car are statically analyzed. The rectangular steel frame structure of the original frame is replaced with square plates, the basic model of the unmanned sightseeing car frame is established, and a single-objective topology optimization mathematical model of the frame is established to optimize the topology design of the frame. Then, in order to design a frame structure that meets all the working conditions at the same time, a mathematical model of multi-working condition topology optimization is established, and the weights of each working condition are determined by using AHP, and the multi-working condition topology optimization design of the frame is carried out. Finally, a comparison of the comprehensive performance of the frame before and after optimization shows that the proposed method enables the optimized frame to meet the strength requirements under various working conditions, resulting in a weight reduction of 16.5 kg.

Multi-objective Topology Optimization Design for a Certain Launcher Bracket

To achieve weight reduction and enhance the firing accuracy of a specific type of launch device, the bracket was selected as the optimization subject for multi-objective topology optimization. Single-objective optimization often overlooks other influencing factors. To address the limitations of single-objective optimization, this study adopts the variable density method from the SIMP approach and proposes a multi-objective topology optimization based on compromise programming. This study, through multi-objective topology optimization of the bracket, obtained an optimized topology structure that maximizes static stiffness and the dynamic low-order natural frequencies of the launch device bracket at launch angles of 0°, 53°, and 85°, with an azimuth angle of 0°. Finally, the obtained topology structure was validated using finite element software. The design method presented in this paper not only enhanced the stiffness of the bracket structure for such launch devices and increased the first two natural frequencies of the bracket but also achieved weight reduction. The optimization design process also provides a reference for other mechanical structures.

Multi-objective topology optimization of macro structure and microtubule network structure for self-healing material

Abstract Self-healing materials possess the capability to promptly repair minor damages occurring during service, thereby effectively preventing safety accidents. This paper investigates a multi-objective topology optimization method for the macro structure and microtubule network of self-healing materials around pure epoxy resin materials, aiming to enhance the damage healing capability of the microtubule network while meeting the mechanical performance requirements of the macro structure. By introducing the design variables of macro structure and microtubule network, the corresponding topological description functions are established respectively. And study applies logical operations and post-processing techniques to generate an embedded microtubule network structure description. The objective functions include the flexibility of the macro structure, the along-travel head loss, and the total length of the microtubule network, with material volume serving as a constraint. In order to determine the head loss of the three-dimensional microtubule network structure, a Hardy-Cross method based on flow initialization and loop search is proposed. Multi-objective topology optimization is designed based on moving morphable components algorithm, enumeration method and Pareto principle. Develop iterative termination conditions by assessing the disparity between Pareto solution sets in each generation, thereby ensuring algorithm convergence. The numerical example of the Messerschmitt–Bölkow–Blohm (MBB) beamyields a flexibility of 0.059 without a carrier and 0.0728 with a carrier the macrostructural flexibility without a carrier is 81.0% compared to with a carrier, and the macrostructural profiles and the overall flexibility of the MBB beams with/without a carrier are close to each other. This method serves as a reference for optimizing large-scale self-healing structures.

Multi-objective topology optimization for materials with negative Poisson’s ratio and thermal insulation

Multi-objective topology optimization for materials with negative Poisson’s ratio and thermal insulation

Multi-objective topology optimization design of silicon carbide metal oxide semiconductor field effect transistors power module liquid-cooled heatsink for electric vehicles

Silicon carbide (SiC) metal oxide semiconductor field effect transistors (MOSFETs) is gradually replacing silicon-based insulated gate bipolar transistor (IGBT) as the switching devices in electric vehicle power inverters due to its higher operating temperatures, switching speeds, and frequencyies. However, the high switching frequency of SiC MOSFETs can increase the losses of the power inverter, resulting in an increase in the temperature, which will limit the performance of power inverters. The improvement of power module performance is mainly controlled by optimizing its control methods during operation and improving its cooling system. Currently, the liquid-cooled heatsink used in power modules have disadvantages such as large flow resistance and poor heat dissipation performance. In order to enhance the performance of the heatsink, this study first established a three-dimensional finite element model of SiC MOSFETs power module based on a pin fin heatsink. The accuracy of the model was verified by numerical and experimental methods. Secondly, based on numerical analysis, a multi-objective topology optimization method for the power module liquid-cooled heatsink is proposed. This method takes heat exchange and fluid dissipation energy as the objective function and uses weight factors to adjust the influence of each on the objective functions. Additionally, the temperature distribution of the heatsink is considered to optimize its performance. Finally, the numerical results show that the topology-optimized heatsink exhibits better performance at high coolant volumetric flow rates. When the coolant volumetric flow rate is 14 L/min, the pressure drops of topology-optimized heatsink is reduced by 63.94 % and the junction temperature of the power module is reduced by 0.24 % compared with the pin fin heatsink. This topologically optimized heatsink could be helpful to improve the performance of existing power module heatsinks.

Multi-objective topology optimization simulation study based on motor

Abstract OptiStruct software is applied for structural optimization of the motor structure to solve the problem of resonance in a specific operating frequency range and reduce the motor operating noise. Comparing the experimental and simulated modal frequencies, a modified multi-objective topology optimization model is proposed to ensure the validity of the model, and a new optimization function is constructed to optimize the multi-objective topology of the motor housing. The results show that the geometric reconfiguration of the motor housing concerning the optimized model force transmission path achieves the effectiveness of reducing resonance noise. The multi-objective topology optimization model provides a feasible way to solve the motor-specific frequency resonance and operation noise problems.

Inverse design of nonlinear metasurfaces for sum frequency generation

Abstract Sum frequency generation (SFG) has multiple applications, from optical sources to imaging, where efficient conversion requires either long interaction distances or large field concentrations in a quadratic nonlinear material. Metasurfaces provide an essential avenue to enhanced SFG due to resonance with extreme field enhancements with an integrated ultrathin platform. In this work, we formulate a general theoretical framework for multi-objective topology optimization of nanopatterned metasurfaces that facilitate high-efficiency SFG and simultaneously select the emitted direction and tailor the metasurface polarization response. Based on this framework, we present novel metasurface designs showcasing ultimate flexibility in transforming the outgoing nonlinearly generated light for applications spanning from imaging to polarimetry. For example, one of our metasurfaces produces highly polarized and directional SFG emission with an efficiency of over 0.2 cm2 GW−1 in a 10 nm signal operating bandwidth.

Design of intelligent drill bit embedded structure based on multi-objective topology optimization method

To address the issues of mechanical performance changes, stress concentration, and displacement in the original drill bit structure caused by the design of embedded structures in intelligent drill bits, the optimal topology of the drill bit was calculated using multi-objective topology optimization methods. Optimal values under various load conditions were obtained using single-objective topology optimization methods combined with penalty functions. Based on these optimal values, calculations for the intelligent drill bit embedded structure were performed using a trade-off planning method. Following this, the initially optimized results were redesigned using NURBS modeling methods to create an embedded structure that meets structural performance requirements. The embedded structure meeting these requirements was then tested through orthogonal simulation to verify its mechanical performance under various complex load conditions. The results show that the embedded structure drill bits designed based on multi-objective optimization generally surpass traditional drill bit structures and those optimized using multi-objective methods in terms of maximum Mises stress and maximum deformation, particularly in external and internal petal configurations, demonstrating good performance in enhancing structural strength.

Multi-objective topology optimization method for multi-axis random vibration based on hybrid cellular automata

Considering the lack of effective solutions for multi-axis random vibration topology optimization problems, and recognizing that multi-axis random vibration excitation is the most common loading conditions experienced by structures during their operational life, this paper proposes a multi-objective topology optimization method for multi-axis random vibration. By combining Hybrid Cellular Automata (HCA) and Analytic Hierarchy Process (AHP), this method aims to enhance the vibration resistance of structures and extend their fatigue life during the topology optimization phase. To validate the effectiveness and engineering practicality of this method, two engineering cases were designed: a cantilever beam case and an automotive steering knuckle case. Multi-objective topology optimization were conducted with objectives including mass, stiffness, and vibration intensity metric (root-mean-square stress). The two cases demonstrate that the control group's topology model exhibits weaker resistance to random vibrations and shorter fatigue life. In contrast, the validation group's topology model introduces an additional load path near the excitation point, effectively dissipating the impact of vibration excitation. This enhances the structure's vibration resistance and significantly extends its fatigue life.

Multi-objective topology optimization design of thermal-mechanical coupling structure based on FPTO method

Multi-objective topology optimization design of thermal-mechanical coupling structure based on FPTO method

Vulnerability-driven multi-objective topological optimization of aircraft protections

Enhancing the survivability of platforms is paramount for increasing their safety level and limiting the loss of lives. This is particularly important in the military field, where aircraft vulnerability has been studied for decades through specifically developed frameworks. So far, most of the contributions have focused on improving the accuracy of methods for assessing the vulnerability to ballistic projectiles, mainly by advancing our understanding of the penetration of the threat through the components of the platform. Although state-of-the-art solutions allow conducting accurate assessments, the information provided by such methods has not been fully exploited yet for automatically designing corrective solutions and improving the survivability of platforms. For this reason, this work proposes a vulnerability-driven multi-objective topological optimization algorithm for designing protective surfaces. A genetic algorithm is used to describe the Pareto front delimiting the space of solutions characterized by optimal vulnerability and weight. The number of clusters that constitute the protections proposed by the optimization algorithm is minimized by adopting a spatial filter that penalizes fragmented designs. The framework is demonstrated through a case study involving a portion of a realistic remotely piloted aircraft system impacted by ballistic projectiles.

Multi-Objective Topology Optimization of Conjugate Heat Transfer Using Level Sets and Anisotropic Mesh Adaptation

This study proposes a new computational framework for the multi-objective topology optimization of conjugate heat transfer systems using a continuous adjoint approach. It relies on a monolithic solver for the coupled steady-state Navier–Stokes and heat equations, which combines finite elements stabilized by the variational multi-scale method, level set representations of the fluid–solid interfaces and immersed modeling of heterogeneous materials (fluid–solid) to ensure that the proper amount of heat is exchanged to the ambient fluid by solid objects in arbitrary geometry. At each optimization iteration, anisotropic mesh adaptation is applied in near-wall regions automatically captured by the level set. This considerably cuts the computational effort associated with calling the finite element solver, in comparison to traditional topology optimization algorithms operating on isotropic grids with a comparable refinement level. Given that we operate within the constraint of a specified number of nodes in the mesh, this allows not only to improve the accuracy of interface representation and motion but also to retain the high fidelity of the numerical solutions at the grid points just adjacent to the interface. Finally, the remeshing and resolution steps both run within a highly parallel environment, which makes it possible for the proposed algorithm to tackle large-scale problems in three dimensions with several tens of millions of state degrees of freedom. The developed solver is validated first by minimizing dissipation in a flow splitter device, for which the method delivers relevant optimal designs over a wide range of volume constraints and flow rate distributions over the multiple outlet orifices but yields better accuracy compared to reference data from literature obtained using uniform meshes (in the sense that the layouts are more smooth, and the solutions are better resolved). The scheme is then applied to a two-dimensional heat transfer problem, using bi-objective cost functionals combining flow resistance and thermal recoverable power. A comprehensive parametric study reveals a complex arrangement of optimal solutions on the Pareto front, with multiple branches of symmetric and asymmetric designs, some of them previously unreported. Finally, the algorithmic developments are substantiated with several three-dimensional numerical examples tackled under fixed weights for heat transfer and flow resistance, for which we show that the optimal layouts computed at low Reynolds number, that are intrinsically relevant to a broad range of microfluidic application, can also serve as smooth solutions to high-Reynolds-number engineering problems of practical interest.

Comprehensive examination of topologically optimized thermo-fluid heat sinks

This study investigates the thermal performance of topologically optimized heat sinks. The primary aims are to conduct a comprehensive parametric study, compare thermal outputs with the benchmark model, and validate numerical simulations through experimental testing. Multi-objective topology optimization is formulated based on thermal compliance and power dissipation. Selected optimized models were built and tested. The parametric study revealed promising design variables, leading to numerical convergence with interconnected flow paths. The promising variables were found under weighted thermal compliances (wh) between 0.3 and 0.9 and targeted liquid fractions (θFV) between 0.5 and 0.8. Additionally, at low operating pressures, for example, at 0.01 kPa, the temperature difference between optimized and benchmark models could be as much as 30 °C. Nonetheless, the temperature difference between both models became smaller at higher operating pressures. Furthermore, the comparison of temperature measurements, pressure drops, and thermal imaging showed reasonable agreement between experimental and numerical results. Additionally, the effect of design variables on thermal performance was confirmed through experiments. The heat sink with higher wh exhibited a lower temperature than that of the model with lower wh. In summary, this research highlights the crucial role of design variables in achieving a balance between temperature and pressure drop.

Multi-objective topology optimization of porous microstructure in die-bonding layer of a semiconductor

Multi-objective topology optimization of porous microstructure in die-bonding layer of a semiconductor

Multi-Objective Topology Optimization Method for Hybrid-Type Motors Combining Combinatorial Optimization and Local Search

Multi-Objective Topology Optimization Method for Hybrid-Type Motors Combining Combinatorial Optimization and Local Search

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

Multi-objective structure optimization and performance analysis of catalytic micro-reactor channel designed by an improved topology optimization model

Previous micro-reactor channel studies mainly focus on the limited design space or structure layout, rarely exploits design forms in which the procedural topology structure evolves freely. Therefore, a multi-objective topology optimization model are proposed for the inverse free evolution of micro-reactor channels, which can synergistically balance the effects among three objectives of reaction rate, flow loss and heat transfer to achieve optimal comprehensive performance. The topology optimization problem is formulated based on the material density-based design variable. The fluid dynamics response of design variables at each optimization iteration is updated by solving multi-physics governing equations, objective functions and variable constraints. Adjoint-based sensitivity analysis and GCMMA algorithm are used to obtain the gradient information of objective functions and update design variables, respectively. Additionally, the strict volume constraints and proposed pseudo-design-domain concept are introduced into the multi-objective function. In numerical examples, the influence of different Re conditions and different multi-objective weight-ratios on optimal designs is investigated, and their regular evolution mechanisms and the trade-off between performance optimization and structure evolution are analyzed. Then, the optimization principles for topology structure and performance parameters under the control of multi-objective functions are revealed. Finally, the comprehensive performance of micro-reactors under topology optimization method is compared with that of traditional micro-reactors to demonstrate the effectiveness of the improved method and reveal the physical mechanisms of multi-objective performance enhancement. The comparison results show that topology optimization designs can achieve 86.1% growth in reaction rate and 47.1% reduction in flow loss, and comprehensive performance coefficients have also been significantly optimized.

Topology optimization of wheel spoke under fatigue tests considering the rotation characteristics of automobile wheels

The topology structure of wheel spoke has a great impact on the safety and lightweight of automobile wheels. However, the rotation process of the wheels is difficult to be reflected in the design and optimization. In this paper, the topology optimization of wheel spoke under fatigue tests considering the rotation characteristics is studied. The bending fatigue test and radial fatigue test are first introduced and the corresponding computation models are presented to calculate the mechanical performances of the wheel hub. The relationship between the internal stress and the number of the wheel spokes is established, and the mechanical performances with different number of wheel spokes are analyzed to guide the selection to the number. Then, the rotation characteristics of the wheel hub are simplified as static loads at different directions or positions according to the configuration of the wheel spokes. A comprehensive evaluation function which includes the test and load levels is defined by the compromise programming method to simulate the stress during the rotation process. Two levels of topology optimization methods are determined. Next, a mathematical model of multi-objective topology optimization for the wheel spoke is established based on the Solid Isotropic Material with Penalization, and a new wheel hub is obtained. Finally, the mechanical performances are compared with the original wheel hub. The obtained results show that the stiffness and strength of the wheel hub are improved under two test conditions, while the weight is reduced by 2.75%.