Structure Topology Optimization Design Research Articles

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

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.

Multi-scale collaborative prediction of optimal configuration for carbon fiber woven composites based on deep learning neural networks

Since carbon fiber woven composite panels contain complex fiber bundle structures, the aim of this paper is to investigate the factors influencing the macro-equivalent properties and topological flexibility of composite panels resulting from variations in fiber bundle configuration. Firstly, the structural topology optimization design of carbon fiber composite plates was achieved using a multi-scale modeling approach with the variable density method. Nonlinear relationships between carbon fiber bundle configuration parameters and macroscopic equivalent properties, as well as macroscale topological flexibility, were determined using deep learning methods, respectively. The maximum error in the predicted values of the deep learning network model does not exceed 0.5% when compared with the results of the finite element calculations. In addition, utilizing deep learning networks to predict macro-equivalent properties of composites can significantly decrease computational time. The impact of varying the number of filaments in fiber bundles and the spacing of the fiber bundles on the flexibility of the topology was determined using a deep learning network. The optimal topological flexibility, along with its corresponding fiber bundle spacing and number of fiber bundle filaments, are globally searched within the design domain using an adaptive genetic algorithm. The study in this paper can provide a reference for designing fiber bundle configurations of composites for practical applications.

Topology Optimization Design and Mechanical Properties of 3D-Printed Solid-Lattice Hybrid Structures with Variable-Density or Iso-Density

Topology Optimization Design and Mechanical Properties of 3D-Printed Solid-Lattice Hybrid Structures with Variable-Density or Iso-Density

Topology optimization design of recoverable bistable structures for energy absorption with embedded shape memory alloys

In this work, multistable mechanical metamaterials with recoverable capabilities are designed for high energy absorption and resistance to repetitive impacts. Based on the known curved beam with energy dissipation characteristics, the shape memory alloys (SMAs) curved beam is added and optimized to achieve recoverability of the bi-layer beam structure. To simultaneously achieve bistable characteristics and recoverability in the designed metamaterial, the optimization model is formulated to maximize the energy absorption capacity of the structure while constraining the peak and valley forces. To solve this complex and highly nonlinear topological optimization problem with stringent constraints, the topological design of the SMAs layer is represented using a limited number of design variables along with the material-field series expansion strategy, and the optimization problem is subsequently solved using a non-gradient-based optimization algorithm. Finite element simulation results demonstrated that the optimized design possesses a substantial capacity for energy absorption. Additionally, the design structure can recover to its initial state from buckling induced by the initial load by regulating the external temperature. Different multistable metamaterials, including those designed to prevent repetitive impacts, have been further developed based on the designed recoverable high-energy-absorbing bistable unit cells, utilizing combinations of varying energy absorption capacities.

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.

A level set reliability-based topology optimization (LS-RBTO) method considering sensitivity mapping and multi-source interval uncertainties

With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, structural design methods are facing more and more factors to be considered. It is necessary to develop advanced design technology. In this paper, a sensitivity mapping technique is proposed to improve the effect of topology optimization based on a gradient optimization algorithm. The applicability of this technology is analyzed. In addition, considering the influence of multi-source uncertainties in the whole life cycle of the structure, a reliability-based topology optimization strategy based on the level set method is proposed. The sensitivity of displacement constraint and reliability constraint with pseudo time is derived. Numerical examples and Monte Carlo verification results fully illustrate the applicability, effectiveness, and efficiency of the proposed method. This method has been successfully applied to the topology optimization design of the rocket skid structure.

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.

Topology Optimization Design of Resonant Structures Based on Antiresonance Eigenfrequency Matching Informed by Harmonic Analysis

Abstract In this article, we present a design methodology for resonant structures exhibiting particular dynamic responses by combining an eigenfrequency matching approach and a harmonic analysis-informed eigenmode identification strategy. This systematic design methodology, based on topology optimization, introduces a novel computationally efficient approach for 3D dynamic problems requiring antiresonances at specific target frequencies subject to specific harmonic loads. The optimization’s objective function minimizes the error between target antiresonance frequencies and the actual structure’s antiresonance eigenfrequencies, while the harmonic analysis-informed identification strategy compares harmonic displacement responses against eigenvectors using a modal assurance criterion, therefore ensuring an accurate recognition and selection of appropriate antiresonance eigenmodes used during the optimization process. At the same time, this method effectively prevents well-known problems in topology optimization of eigenfrequencies such as localized eigenmodes in low-density regions, eigenmodes switching order, and repeated eigenfrequencies. Additionally, our proposed localized eigenmode identification approach completely removes the spurious eigenmodes from the optimization problem by analyzing the eigenvectors’ response in low-density regions compared to high-density regions. The topology optimization problem is formulated with a density-based parametrization and solved with a gradient-based sequential linear programming method, including material interpolation models and topological filters. Two case studies demonstrate that the proposed design methodology successfully generates antiresonances at the desired target frequency subject to different harmonic loads, design domain dimensions, mesh discretization, or material properties.

Structural Optimization of the Lower Door of the Main Landing Gear of an Aircraft

In this paper, the topology optimization algorithm is used to optimize the main structure of the main landing gear lower door of an aircraft by combining the structural strength, structural stiffness, and processing technology [1-2]. Considering the balance of structural weight, structural strength, and material distribution, the structural topology optimization design result with reasonable structure, good manufacturability, and moderate weight is finally obtained.

Dynamic topology optimization of continuum structures considering moving mass excitations

The structures excited by the moving mass are widely existed in nature and engineering. The dynamic loads are related to time and space and greatly affect structural performances. However, the moving mass problems have not been considered in the topology optimization design of continuum structures. Therefore, this paper proposes a novel dynamic topology optimization method to design the continuum structures considering moving mass excitations. Firstly, the finite element formulation is established to solve the dynamic responses for the moving mass excitations by using the HHT-α method. Secondly, in the density-based framework, the dynamic topology optimization problem is formulated to minimize the mean strain energy constrained with the total volume, whose interpolation scheme is the rational approximation of material properties. Thirdly, the sensitivities of the optimization problem are derived by using the adjoint variable method in the discretize-then-differentiate scheme. Finally, numerical examples demonstrate the effectiveness of the proposed method and the influence of the moving mass excitations on the topological structures.

Topology Optimization of Strength-Safe Continuum Structures Considering Random Damage

Spacecraft in the aerospace field and military equipment in the military field are at risk of being impacted by external objects, which can cause local damage to the structure. The randomness of local damage is a new challenge for structural design, and it is essential to take random damage into account in the conceptual design phase for the purpose of improving structure’s resistance to external shocks. In this article, a random damaged structure is assumed to have damages of the same size and shape at random locations, and the random damage is considered as multiple damage conditions of the structure. In order to improve the randomness and comprehensiveness of the multiple damage conditions, the stacking strategy is used to generate the distribution of the damage area. Following this strategy, the topology optimization design of the random damaged structure, which is to minimize the weight of the structure with a constraint on the stress of the structure under multiple damage conditions, is formulated based on the independent continuous mapping (ICM) method. The dual sequence quadratic programming (DSQP) algorithm combined with the stress globalization method is adopted to solve the optimization problem. The numerical examples demonstrate the effectiveness and applicability of the proposed method in the topology optimization of strength-safe continuum structures.

Topology optimization design of dual-channel metasurface structure with controllable amplitude of retroreflection and mirror reflection

For oblique incident electromagnetic waves, the generation of double reflection channels including retroreflection channel is of great significance in improving target recognition performance and navigation performance. In double channel reflection, controlling the ratio of retroreflection to specular reflection is the key to realizing reflection power distribution. In order to realize the control of the proportion of the reflected power in each channel, a topology optimization method for designing the reflective metasurface microstructure with dual channel is proposed in this paper. The implementation mechanism is investigated, physical model of metasurface with dual reflection channel including retroreflection channel is established, and the topology optimization model of metasurface microstructure with specific power ratio of the retroreflection to specular reflection is established. As a numerical example, a dual channel metasurface reflector with a 1∶1 ratio of retroreflection power to specular reflection power is designed for a 10 GHz plane wave in the TE mode with a pitch angle of –30°. The designed metasurface exhibits strong directionality in the retroreflective direction, and the reflection amplitudes in both directions are similar. The retroreflective metasurface with the maximum retroreflection ratio is designed. The retroreflection ratio of the designed metasurface is 0.093. There is no specular reflection or other singular reflection, and the strong reflection on the metasurface is concentrated at –30°. The ratio of the main beam power to the total reflection power is 0.900. The simulated and experimental results verify the feasibility of the proposed method.

基于BESO的产品结构拓扑优化设计方法研究

基于BESO的产品结构拓扑优化设计方法研究

Topology Optimization Design of Micro-Channel Heat Sink by Considering the Coupling of Fluid-Solid and Heat Transfer

To investigate the effect of the target weight coefficient on the structure design of the micro-channel heat sink, an innovative method for the topology optimization design of micro-channel structures with different bifurcation angles is adopted. In this study, the improved interpolation function, density filtering, and hyperbolic tangent projection methods are adopted to obtain a clear topological structure of the micro-channel heat sink. The heat transfer of the micro-channel heat sink under different bifurcation angles is compared. At the same time, the influence of the two different objective functions, heat transfer, and flow energy consumption, is analyzed in the topology optimization of micro-channel heat sinks. The results show that when the bifurcation angle is 135°, both the heat transfer and the average outlet temperature of the micro-channel heat sink obtain the maximum value, and the heat transfer effect is the best. With the increase of the heat transfer weighting coefficient, the distribution of solid heat sources in the main channel increases, and the refinement of the branch channels also increases. On the other hand, although the heat transfer effect of the micro-channel heat sink is the best, the corresponding flow energy consumption is larger.

Research on multi-condition topology optimization design of stainless steel spot welding vehicle considering weight coefficient

A multi-condition topology optimization research method with weight coefficients is proposed to optimize the topological optimization of solder joints of stainless steel spot welding vehicle. Based on the SIMP variable density method, the compromise planning method, the orthogonal experiment design method, the gray correlation method, the entropy weight method and the analytic hierarchy process are used to introduce the weight coefficients, and objective function of the multi-objective topology optimization of the welding points of the stainless steel spot welding vehicle is established. This method realizes the topology optimization of the stainless steel spot welding vehicle model with the goal of flexibility the minimizing of multiple working conditions. It is concluded that the entropy weight method is more suitable for determining the weight coefficient analysis of objective function of multi-condition topology optimization. The average variation value of the flexibility under the three working conditions is the largest, and the number of solder joints is reduced by 17.8% after optimization. The proposed multi-condition topology optimization research method can be applied to the topology optimization design of railway vehicle structure.

Multiphysics Field Topology Optimization Design of Main Support Structure of High-Temperature Superconducting Magnets

The high-temperature superconducting magnet (HTS) is one of the core technologies of a superconducting maglev. The effects of multiphysics fields including electromagnetic, mechanical, and thermal should be taken into consideration in design. Traditional design methods rely on the initial configuration and the engineer's experience and only consider the design for the heat conduction performance or the structure strength, which often significantly increases the weight. To solve the above problems, based on COMSOL Multiphysics software, the mathematical model of topology optimization of the main support was established with electromagnetic force and thermal stress as the input loads. The objective functions were assigned to total strain energy and heat leakage, combined with stress value and volume fraction constraint conditions. The solid isotropic material with penalization (SIMP) method was used to carry out the topological analysis of multiphysics. Finally, the innovative structure of main support is obtained. Through finite element analysis of multiphysics fields, the heat leakage, the max Von-Mises stress, and weight were taken as evaluation indexes to compare the optimal structure performance. The results show that the method adopted in this paper can reduce the heat leakage by 61.7% while reducing the weight of the main support by 85%, and the max Von-Mises stress does not exceed the yield limit of the material. The work of this paper provides a theoretical foundation for the engineering design of the heat conduction structure of a HTS magnet.

Additional Cover

The cover image is based on the Research Article Topology optimization design of multi-material quasi-periodic cellular structures for thermoelastic responses by Guowei Liang et al., https://doi.org/10.1002/nme.7012.

Topology optimization design of the main structure of 6-DOF manipulator based on the variable density method

In order to solve the problems of too large mass, too complex structure and poor flexibility of the 6-DOF manipulator, the topological optimization theory based on variable density method is applied to the 6-DOF manipulator, the topology optimization of the main structural components of the manipulator is carried out with the help of the finite element software ANSYS, and the optimized structure is simplified according to the density distribution of the units and the requirements of manufacturability, the results are compared and analysed by static mechanics. It shows that the whole mass of the 6-DOF manipulator is reduced by 47.23% without changing the original mechanical properties after topological optimization, and the optimized model can meet the requirements of manufacturability, the optimization effect is significant, which can be used as a reference for the structure optimization of the 6-DOF manipulator.

Topology optimization design of three-dimensional multi-material and multi-body structure based on irregular cellular hybrid cellular automata method

In recent years, Hybrid Cellular Automata Method (HCAM) has been successfully applied to solve structural topology optimization problems. However, there was no report on HCAM research of three-dimensional composite structure composed of multiple materials and multiple bodies. Therefore, in this paper, three-dimensional non-cube cells of irregular size (such as tetrahedral cells with adaptive changes inside length) and Finite Element Method (FEM) are introduced to extend HCAM, which is better and more flexibly to fit complex geometric shapes. Furthermore, a better structure configuration of multi-material and multi-body structure is obtained. The typical example study showed that the proposed topology optimization method could effectively remove the redundant materials of multi-material and multi-body structure, and the optimized structure configuration could still meet the requirements of the original condition after geometric reconstructed. Thus it provided a reference for the intelligent design of other products.