Topology Optimization Design Research Articles

A general parametric finite element modeling and stress response analysis methods for pipeline system using the nonconforming solid element

In the dynamic topology optimization design of pipeline system, parametric finite element modeling (PFEM) is needed to improve the model reconstruction efficiency. Taking a typical spatial single pipeline as the research object, this paper innovatively presents a PFEM method of pipeline system based on the newly constructed nonconforming solid (Solid-NC) element. The stiffness and mass matrices of the spatial 8-node Solid-NC element with second-order boundary accuracy are obtained by introducing the node-free displacement items and statics condensation method. The PFEM method of the pipeline body is proposed by selecting the straight-line segment lengths as the pipeline shape control parameters. The PFEM method of the pipeline is described in detail, including the node coordinate solutions of straight-line and curved arc segments based on the direction vector method and vector decomposition method, respectively, and the simulation of the clamp mechanical properties considering the actual pre-tightening state of the clamp. Furthermore, the modal analysis is carried out, the node stress response solution is solved based on the stress smoothing method, and the effectiveness of the PFEM method is verified through experiment. Finally, the mesh quality and model reconstruction efficiency of the PFEM method is analyzed, the results show that the developed PFEM method has higher mesh quality and fast model reconstruction speed, and the model reconstruction time is shortened by 544.5 times at most compared with ANSYS software.

Optimized topology design of finned ducts for internal flow thermal performance by discrete variable eigenvalue-related optimization

Optimized topology design of finned ducts for internal flow thermal performance by discrete variable eigenvalue-related optimization

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.

Topology Optimization Design of Typical Functional Structural Parts

Topology optimization is a commonly used lightweight design method that involves reducing the weight ofstructural parts while retaining their function. It is widely used in the lightweight design of auto parts. In this paper, thetopology optimization of a typical structural part was analyzed by using the relative density method. Calculations indicatedthat the strength of the structural part could be maintained under 70% mass reduction. The results of the analysis showedthat this method helps improve the structure of parts.

A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method

In recent years, the research and development of high-speed trains has advanced rapidly. The main development trends of high-speed trains are higher speeds, lower energy consumption, higher safety, and better environmental protection. The realization of a lightweight high-speed car body is one of the key features in the development trend of high-speed trains. Firstly, the basic dimensions of the car body’s geometric model are determined according to the external dimensions of the body of a CRH EMU, and the specific topology optimization design domain is selected to establish the finite element analysis model; secondly, the strength and modal analyses of the topology optimization design domain are carried out to check the accuracy of the design domain and provide a comparative analysis for subsequent design. Then, the variables, constraints, and objective functions of the topology optimization design are determined to establish the mathematical model of topology optimization, and the design domain is calculated for topology optimization under single and multiple conditions, respectively. Finally, based on the topology optimization calculation results, truss-type reconstruction modeling is carried out for the car body’s side walls, roof, underframe, end walls, and other parts. Compared with the conventional EMU body structure, the weight of the reconstructed body structure is reduced by about 18%. The results of the finite element analysis of the reconstructed car-body structure prove the reliability and safety of the structure, indicating that the reconstructed car-body scheme meets the corresponding performance indicators.

A dynamic topology optimization design method based on multiple domain variable parameters

Topology optimization has been extensively studied for obtaining desired functional performances of a structure within a predefined design domain. However, existing topology optimization approaches mainly focus on the static structure. Additionally, a structure is generally consisted of multiple materials and its loading state is quite complicated in practical applications, which are seldom considered simultaneously during design optimization. In this paper, a dynamic topology optimization design method based on multiple domain variable parameters is proposed to solve these issues. First, a structure is divided into multiple domains, and an optimal topology model of discrete structure is proposed. Then, the constraints are relaxed and a per-element variable is introduced to process the design variables continuously. To eliminate the undesirable checkerboard patterns, a filtering method is proposed and an approach of projection is presented for determining the volume of the projected structure according to the practical design requirements. After that, a dynamic continuous optimization model is put forward for solving the optimal solution of the complex structure under various working conditions. Finally, the effectiveness and efficiency of the proposed method are validated by constructing a topology optimized link of the press.

Passive mitigation of low-frequency vibration modes in lightweight structures based on a new generation of acoustic black holes

Topology optimization and generative design are methods used to lighten structures under specific loads. The resulting lightweight components are usually softer in the directions perpendicular to the applied efforts, such as in the case of cranes. This results in the possible excitation of structural modes at very low frequencies, which can lead to premature aging of lightweight structures. In this paper, we present a new design of acoustic black hole (ABH), able to mitigate vibration modes in a test 3D-printed lightweight structure, from 20 Hz upwards. The novel ABH weights less than 10 grams and can be readily screwed on the structure. Its design is based on that of a classic ABH, with additional winglets and/or rods, to increase the vibrating mass without significantly changing the stiffness of the ABH. This results in a strongly reduced ABH cut-on frequency. The winglets and/or rods also result in a greatly increased contact area between the ABH and the viscoelastic dissipative material, with positive effects on the ABH damping efficiency. The new ABHs could successfully be used, first to damp the fundamental vibration mode of aluminum cylinders, and then to reduce the amplitude of the first three structural modes of the test lightweight structure. The new ABH manages to damp modes at frequencies several times lower than the ones found in the literature, which are promising results.

Stress-constrained topology optimization for multi-material thermo-hyperelastic compliant mechanisms based on inverse motion

A stress-constrained topology optimization design for the multi-material thermo-hyperelastic compliant mechanism is investigated in this article, using inverse motion analysis. Through the inverse motion analysis approach, precise control over the geometry of the deformed structure is achieved. A topology optimization model is established for the multi-material thermal hyperelastic compliant mechanism, incorporating constraints on volume, cost and stress, while maximizing displacement as the objective function. Filtering is implemented using an improved partial differential equation, and the stress problem is addressed using the ϵ-relaxation method and the p-norm aggregation function. The sensitivity analysis of the displacement objective function and the stress constraint is conducted. Considering the multi-material thermally actuated actuator as an example, the influence of the stress constraint on the topology optimization design is studied. The results indicate that inverse motion analysis allows for effective control of the output end position of the deformed compliant mechanism.

Topological optimization design for support structure under multiple loading conditions

In view of the lightweight and high stiffness requirements of a certain type of spacecraft support, combined with the special performance and environment of the support, topology optimization technology is introduced into the optimal design of the support structure in the space field. The topology optimization and design of the support are carried out with the stiffness as the objective function and the quality as the constraint condition, and the design of "space hugging configuration" is proposed, and the simulation verification and experimental verification are carried out. Firstly, different load conditions of the support were analyzed and studied. Secondly, the initial model was established based on the relative position relationship between the support and the mounting surface of the loaded equipment. Finally, a design method of the support structure was established based on the combination of topology optimization under multi-load conditions and size optimization considering the influence of strength. The stiffness and strength of the optimized structure were checked under multiple load conditions, and the fundamental frequency was 2.05 times of the index requirement. The maximum response stress is lower than the yield limit of the material used, which meets the strength requirement. Finally, the vibration test is carried out to verify the support. After the test is completed, the position accuracy of the support interface meets the requirements of the index. The obtained bracket has high structural stability, meets the high performance requirements of the load equipment, verifies the feasibility of the topology optimization method, and provides an effective method for the design of lightweight high-stiffness structures.

Mechanical metamaterial design with the customized low-frequency bandgap and negative Poisson's ratio via topology optimization

The precise control of both the mechanical deformation and wave propagation characteristics of metamaterial through design holds significant importance and presents a challenging task. This paper proposes a novel two-stage topological optimization design method for customizing both negative Poisson's ratio and locally resonant bandgap in the mechanical metamaterial. In the optimized model, the negative Poisson’s ratio structure is firstly obtained by optimizing the material distribution within the matrix region, then the metamaterial with the customized negative Poisson’s ratio and bandgap range is obtained through the second stage optimization. In the analysis of the metamaterial unit cell, the topology-dependent Poisson’s ratio is calculated based on the equivalent elastic matrix obtained through the homogenization method. The range of bandgap is estimated using the effective mass analytical model of the spring-mass system. Thus, the range of bandgap is determined by only a few geometric parameters instead of topological structure under given assumptions. The customized bandgap ranges can be extended by introducing more resonators into the unit cell and combining different unit cells into an assembled structure. Numerical examples are provided to demonstrate the efficacy of the proposed method.

Bionic topology optimization design and multi-objective optimization of guide arm

Lightweight design is universally recognized as a critical criterion for many engineering problems. In addition to the well-developed topology optimization (TO) method, structural bionics is also considered an effective approach to developing innovative structure designs with lightweight. In the process of natural evolution, bamboo has developed a unique hollow structure with ingenious mechanical properties. Inspired by these characteristics, this paper selected bamboo as a bionic prototype to carry out bionic structure optimization of guide arm. First, the initial guide arm was modeled and simulated for its mechanical behavior. Secondly, similarity analysis between bamboo and guide arm was performed from three aspects, and the parametric bionic guide arm model was established step by step. Then, the key parameters affecting the performance of the bionic guide arm were verified by the parameter sensitivity analysis method. The multi-objective optimization was carried out with the minimum of the total mass and the maximum deformation of guide arm as the optimization objectives. The optimal solution of Pareto solution set was determined by multi-objective decision methods of the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and Gray Relational Analysis (GRA). Finally, finite element (FE) method was used to make a comparison between the initial model and the optimal bionic model in terms of mechanical performance. According to the results, under the premise of the mass of the optimized bionic model decreased by 17.44%, the maximum deformation was decreased by 9.24%, the equivalent stress was decreased by 17.33%, and the first-order frequency was increased by 22.92%. Comparison results showed that the proposed bionic model provided the best lightweight solution for guide arm. This study reveals that structural bionics provides a new solution for the lightweight design of guide arm and similar beam structural components.

Grouping-Based Optimal Design of Collector System Topology for a Large-Scale Offshore Wind Farm by Improved Simulated Annealing

Grouping-Based Optimal Design of Collector System Topology for a Large-Scale Offshore Wind Farm by Improved Simulated Annealing

The Current Design for Additive Manufacturing Research Frontier

Design for additive manufacturing (DFAM) seeks to develop designs that take advantage of the unique capabilities of additive manufacturing (AM) processes to maximize benefits. In this paper, several issues at the frontier of DFAM research are highlighted. First, the need is described to include as-manufactured mechanical and other physical properties, such as topology and shape optimization and generative design, during computational design. AM processes rarely produce parts with homogeneous composition and isotropic properties, so design methods and tools should not assume them. Second, the topic of designing for the AM process chain is important since AM-fabricated parts typically need postprocessing operations, such as support removal, finish machining, heat treatments, etc. DFAM methods need to incorporate the entire process chain, not just the AM process, which is explored with an example from metal powder bed fusion. Third, potentially, the largest benefit of AM can be realized by radically rethinking product architectures. Examples of an electric motorcycle and an assistive exosuit illustrate the ideas and potential benefits. Finally, some thoughts on design for 4D printing are offered, specifically for 3D printed morphing and deployable systems that utilize the shape memory effect.

Topology optimization for additive manufacturing of CFRP structures

Combining design optimization and additive manufacturing (AM) enables the full exploitation of the potential for heightening the performance of carbon fiber reinforced plastic (CFRP) structures. This study simultaneously conducts topology optimization and fiber path design by employing the radial basis function (RBF) based level set function (LSF). Fiber paths are determined instinctively for the inherent advantages of the LSF, and fiber orientations are parameterized accordingly. Manufacturing drawbacks such as gaps and overlaps can be avoided by introducing a fast-marching method. To verify the effectiveness of the optimization method, three groups of optimized and empirical designs are fabricated by the AM technique, respectively, and the experimental tests are further carried out. Finite element (FE) models are also reconstructed based on the printing schemes, and then the FE simulation is validated by the experimental tests. With the proposed optimization method, stiffnesses for all three groups of the optimal samples are significantly improved compared with the empirical counterparts. The FE modeling technique is capable of reproducing the experimental results. This study paves a new way to develop an integrated framework of optimization, additive manufacturing, experimentation, and validation to deliver high-performance CFRP structures.

Topology optimization design of microstructures with zero Poisson's ratio

Mechanical metamaterials are materials that possess unconventional mechanical properties that are not found in homogeneous materials, achieved through specific artificial microstructures. Topology optimization is an effective design method for such materials. In this paper, a topology optimization-based method for designing zero Poisson's ratio mechanical metamaterials is proposed. Firstly, a zero Poisson's ratio topology optimization objective function is constructed based on the energy homogenization method, and the optimal microstructure topology configuration and elastic coefficient matrix under different initial topologies and volume fractions are obtained through the boundary density evolution topology optimization method. To improve the saw tooth effect of the boundaries, the node density level set method is used to smooth the boundaries of the microstructure. Then, in finite element simulation analysis, it is demonstrated that the proposed method can effectively design microstructures with zero Poisson's ratio properties. It is also shown that microstructures with expected stiffness and zero Poisson's ratio properties can be obtained by changing the volume fraction and selecting materials with different stiffnesses. Finally, the unit cell is periodically arranged to form a multi-lattice metamaterial, and its zero Poisson's ratio mechanical performance in both X and Y directions is verified.

Topology Optimization Design and Dynamic Performance Analysis of Inerter-Spring-Damper Suspension Based on Power-Driven-Damper Control Strategy

In this paper, the problem of broadband vibration suppression of power-driven-damper vehicle “inerter-spring-damper” (ISD) suspension is studied. The suspension can effectively inherit the low-frequency vibration suppression effect of ISD suspension and the high-frequency vibration suppression effect of the power-driven-damper control strategy. Based on the structural method, this paper proposes four suspensions with different structures. The optimal structure and parameters are obtained by using pigeon-inspired optimization. The results show that, based on the optimal structure, the Root-Mean-Square (RMS) of body acceleration and the RMS of suspension working space are reduced by 23.1% and 6.6%, respectively, compared to the traditional passive suspension. The influence of the damping coefficient on the dynamic performance of the power-driven-damper vehicle ISD suspension is further studied. The vibration suppression characteristics of the proposed suspension are simulated and analyzed in both the time domain and frequency domain. It is shown that the power-driven-damper vehicle ISD suspension can effectively reduce vibrations across a wide frequency range and significantly improve body acceleration and suspension working space, thereby enhancing the ride comfort.

Effects of inlet and outlet configurations on the topological optimization design of cooling plates for lithium-ion batteries

Topology optimization is a critical tool for enhancing the cooling efficiency and temperature uniformity of cooling plates, particularly in the context of designing thermal management systems for electric vehicle battery packs. This research employs a topology optimization approach centered on outlet enthalpy as the objective function to create a variety of cooling plates with different inlet and outlet configurations. Through an extensive numerical analysis, a comparative study is conducted among several configurations, including one inlet and one outlet (OP), two inlets and one outlet (TP), two inlets and two outlets (TTP), and four inlets and two outlets (FTP). Under 75 Pa conditions, FTP(y8) shows maximum temperature reductions of 0.42 %, 0.14 %, and 0.04 % compared to OP, TP(b), and TTP, respectively. The temperature difference also decreases by 38.55 %, 20.00 %, and 10.20 % in the respective comparisons. Additionally, as the pressure increases from 25 Pa to 75 Pa, the heat transfer coefficient of FTP(y8) experiences a notable 1.36-fold increase. Moreover, at 75 Pa, the performance evaluation criterion (PEC) value of FTP(y8) even exceeds twice the baseline. Under a 3C discharge rate, FTP(y8) excels with a maximum temperature of 304.49 K, reducing temperature differences and exhibiting superior cooling performance.

An improved integrated framework based nodal density variable and Voronoi polygon for FE-based topology optimization

In this paper, an improved integrated framework is developed to deal with the numerical instability problems in FE-based topology optimization design methods. The proposed method mainly consists of two coupled computational layers: the upper layer for material geometric description, and the lower layer for structural analysis and sensitivity calculation. In the upper layer, the design domain is discretized by Delaunay triangulation, and a smooth and continuous material density description is obtained by interpolating the densities at nodes of Delaunay triangulation with Shepard interpolants. In the lower layer, the dual Voronoi polygon for Delaunay triangulation is used to generate the finite element mesh, and the virtual element method is applied to handle Voronoi polygon for structural response. Following this framework, the separate description of density distribution avoids the problem of geometric description relying on FE mesh in some existing work. Meanwhile, the use of Voronoi polygon provides more accurate finite element discretization of constantly changing material distributions. Typical numerical examples for the minimum compliance optimization problem reveal that the proposed method can eliminate checkerboards and mesh-dependencies effectively, and get approximate discrete 0/1 solutions without any filter. The simulation results demonstrate the efficiency and robustness of the proposed formulation and numerical techniques.

MNEARO: A meta swarm intelligence optimization algorithm for engineering applications

Artificial rabbits (AR) optimization is a newly proposed swarm intelligence algorithm. The idea of AR optimization (ARO) is inspired by the nature behaviors of the AR including the detour foraging, the random hiding and the energy shrink. Although ARO has better performance than many classical natural heuristic algorithms, it still has some disadvantages such as lacking the diversity of the population and easy to trap in the local optimal. To mitigate the influence of the above defects, this paper respectively introduces the mutation strategy, the prey identification strategy and the elite opposition-based learning strategy into the original algorithm, and proposes a new meta swarm intelligence optimization algorithm termed MNEARO. Firstly, the mutation strategy is introduced into the two natural behaviors of ARO to expand its exploration range in the solution space and increase the probability of finding the global optimal. Secondly, replacing the captured individuals with the predators that take better action trajectories to achieve the population evolution. Another candidate population is generated by the prey identification strategy, thus improving the population diversity and dynamics of ARO. Finally, the elite opposition-based learning strategy improves the exploitation ability of ARO and the overall quality of the population by selecting some individuals with the better fitness values as the elites and using the greedy selection before the end of each iteration. A series of performance tests are conducted on the CEC2020 test set in four dimensions and the CEC2022 test set in the highest dimension respectively to verify that the proposed MNEARO has better convergence and robustness. In addition, the practicality of MNEARO is further highlighted through five mechanical optimization designs, two truss topology optimization designs and the vehicle cruise control system. The experimental results show that the proposed MNEARO has a strong competitiveness in solving complex optimization problems with different dimensions.

Machine learning powered sketch aided design via topology optimization

Structural topology optimization is an important design tool in the conceptual design phase of a product. However, the current topology optimization design is mostly driven strictly based on mathematical and mechanical models. Although the innovative design can be automated, it mostly lacks effective manual experience guidance. To improve the efficiency of computer-aided structural design models, this work proposes a sketch-guided topology optimization approach based on machine learning. Using neural network-based style transfer techniques, computer-digitized/hand-drawn sketches are explicitly incorporated into topology optimization in the form of constraint functions. The obtained optimization results not only satisfy the requirements of optimal mechanical properties, but also fully demonstrate the design intention and requirements of designers. Numerical examples show that the proposed approach can effectively compensate for the lack of manual experience guidance for topology optimization.