Multi-objective Topology Optimization Research Articles

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.

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 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 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 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%.

Multi-objective topology optimization for thermo-elastic systems based on periodic constraints

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance.

Soft Robotic Joints With Anisotropic Stiffness by Multiobjective Topology Optimization

Soft Robotic Joints With Anisotropic Stiffness by Multiobjective Topology Optimization

Multi-objective topology optimization of heat transfer surface using level-set method and adaptive mesh refinement in OpenFOAM

The present study proposes a new efficient and robust algorithm for multi-objectives topology optimization of heat transfer surfaces to achieve heat transfer enhancement with a less pressure drop penalty based on a continuous adjoint approach. It is achieved with a customized OpenFOAM solver, which is based on a volume penalization method for solving a steady and laminar flow around iso-thermal solid objects with arbitrary geometries. The fluid-solid interface is captured by a level-set function combined with a newly proposed robust reinitialization scheme ensuring that the interface diffusion is always kept within a single local grid spacing. Adaptive mesh refinement is applied in near-wall regions automatically detected by the level-set function to keep high resolution locally, thereby reduces the overall computational cost for the forward and adjoint analyses. The developed solver is first validated in a drag reduction problem of a flow around a two-dimensional cylinder at the Reynolds numbers of 10 and 40 by comparing reference data. Then, the proposed scheme is extended to heat transfer problems in a two-dimensional flow at the Prandtl number of 0.7 and 6.9. Finally, three-dimensional topology optimization for multi-objective problems is considered for cost functionals with different weights for the total drag and heat transfer. Among various solutions obtained on the Pareto front, 4.0% of heat transfer enhancement with 12.6% drag reduction is achieved at the Reynolds number of 10 and the Prandtl number of 6.9. Moreover, the optimization of a staggered pin-fin array demonstrates that the optimal shapes and arrangement of the fins strongly depend on the number of rows from the inlet. Specifically, the pin-fins in the first and third rows extended in the upstream direction further enhance heat transfer, while the fins in the second row vanish to reduce pressure loss.

Multi-objective Topology Optimization of Sandwich Lattice Structures for Vibration Suppression: Numerical and Experimental Investigations

Multi-objective Topology Optimization of Sandwich Lattice Structures for Vibration Suppression: Numerical and Experimental Investigations

Augmented Lagrangian approach for multi-objective topology optimization of energy storage flywheels with local stress constraints

Augmented Lagrangian approach for multi-objective topology optimization of energy storage flywheels with local stress constraints

Structure Improvement and Optimization of Gantry Milling System for Complex Boring and Milling Machining Center

To enhance the efficiency and machining precision of the TX1600G complex boring and milling machining center, a study was conducted on the structure of its gantry milling system. This study aimed to mitigate the influence of factors such as structural quality, natural frequency, and stiffness. The approach employed for this investigation involved mechanism topology optimization. To initiate this process, a finite element model of the gantry milling system structure was established. Subsequently, an objective function, comprising strain energy and modal eigenvalues, was synthesized. This objective function was optimized through multi-objective topology optimization, taking into account certain mass fraction constraints and considering various factors, including processing technology. The ultimate goal of this optimization was to create a gantry milling structure that exhibited high levels of dynamic and static stiffness, a superior natural frequency, and reduced mass. To validate the effectiveness of these topology optimization results, a comparison was made between the new and previous structures. The findings of this study serve as a valuable reference for optimizing the structure of other components within the machining center.

Topology and Size Optimized Design and Laser Welding of the U-Frame for Free-Space Laser Communication Telescopes

The success of laser communications heavily relies on the stiffness, dynamic properties, static performance, and manufacturability of the U-frame. The U-frame is a fundamental element in satellite-to-ground laser communication telescopes. However, there is currently a lack of research on the optimal design of U-frames, leading to a significant gap between ideal construction and practical manufacturability. To address these concerns, this study proposes a comprehensive approach that combines multi-objective topology optimization and multi-start size optimization techniques. This approach considers the multidisciplinary constraints imposed by mechanical, control, and optical systems. The objective is to achieve both the conceptual and detailed design of a novel U-frame, while also ensuring thorough consideration of the structure’s manufacturability during the optimization process. The prototype of the optimized U-frame was successfully fabricated using laser welding processes. The tensile test conducted on the prototype supported the idea that laser welding can enhance the micro-grain size of the joint, leading to improved overall mechanical properties. In particular, the joint strength achieved through laser welding was found to be 1.5 times greater than that achieved through TIG (Tungsten Inert Gas) welding. Additionally, the results obtained from the free vibration experiment closely aligned with the simulation, confirming the feasibility of manufacturing the optimized structure. The optimized structure demonstrated an improvement of 7.13% in dynamic performance and 29.61% in static performance compared to the first-generation structure. Additionally, there was a reduction of 29.89% in mass without affecting the remaining performance aspects. The successful fabrication of the prototype validates the feasibility of the proposed welding process and highlights the superiority of the new U-frame.

Lightweight design method of orthotropic steel bridge deck with U-ribs based on multi-objective optimization

This paper proposed a lightweight design method for orthotropic steel bridge deck U-ribs. Firstly, the U-rib is analyzed in static structural properties. An analytic hierarchy model was constructed to maximize the stiffness for multi-objective topology optimization. Secondly, a parametric reconfiguration model of the topologically optimized U-rib was established. Finally, static tests are carried out and the performance of the 3D printing scale model was tested. The test results show that the method is effective. Weight of the original model with U-rib is 99.8 kg, and the weight of its optimized model is 76.8 kg. The method achieved a weight reduction of 23% for the U-ribs, and the stiffness still met the permitted conditions. The orthotropic steel bridge deck composed of the optimized U-ribs effectively reduced the weight by 150 kg on the basis of basically unchanged stiffness. The method provides an important reference for the lightweight transformation of assembled bridge structures.

Multi-objective topology optimization design of truss structures based on evidence theory under limited information

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.