Multi-objective topology optimization and structural analysis of periodic spaceframe structures

Free-mounted cooling plate multi-objective topology optimization method towards precision machine tool heat dissipation: An experimental and numerical study

This paper addresses single and multiobjective topology optimization of truss-like structures using genetic algorithms (GA's). In order to improve the performance of the GA's (despite the presence of binary topology variables) a novel approach based on kinematic stability repair (KSR) is proposed. The methodology consists of two parts, namely the creation of a number of kinematically stable individuals in the initial population (IP) and a chromosome repair procedure. The proposed method is developed for both 2D and 3D structures and is shown to produce (in the single-objective case) results which are better than, or equal to, those found in the literature, while significantly increasing the rate of convergence of the algorithm. In the multiobjective case, the proposed modifications produce superior results compared to the unmodified GA. Finally the algorithm is successfully applied to a cantilevered 3D structure.

Aiming at the multiobjective topology optimization design of the structure, this paper proposes a method to establish the comprehensive objective function based on the normalized subobjective of the compromise programming method and to determine the weight coefficient of the subobjective of the comprehensive objective function by the analytic hierarchy process (AHP). By using statistical analysis and modal analysis, the static and dynamic characteristics of the gear can be obtained. The single objective topology optimization is used to reduce the compliance of the gear and elevate the low-order natural frequency, and the frequency weighting method is used to suppress the oscillation phenomenon in the frequency-single-objective optimization. AHP was used to determine the weight coefficient of each subtarget. The compromise programming method is used for multiobjective topology optimization, and the gear design is improved according to the optimization results. By analyzing the improved gear structure, the weight of the optimized gear is reduced by 25.3%. The overall stiffness performance and strength performance are enhanced, and the natural frequencies of each order are improved to different degrees.

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 method for multi-axis random vibration based on hybrid cellular automata

This letter presents an application of multiobjective topology optimization to ultrawideband (UWB) antenna design. The design of UWB antennas is very challenging because it involves multiple design goals including miniaturization, a wide impedance bandwidth, uniform gain variation, and enhanced time-domain pulse preservation. Although topology optimization has been a popular approach for UWB antenna design, a multiobjective version that systematically copes with all the design details is critically lacking, and the early attempts have not been very successful. In this letter, we propose a Pareto-based technique for multiobjective topology optimization, showing that the proposed methodology facilitates the development of a UWB antenna with compact size, a wide bandwidth, uniform gain variation, and high fidelity factors. The optimized UWB antenna occupies a small area of $15 \times 15~\hbox{mm}^2$ , showing excellent impedance matching and stable broadside gains throughout 3.1–10.6 GHz. In addition, the variation of group delay drops dramatically from 0.94 to 0.40 ns, and the fidelity factor is enhanced from around 0.80 to 0.92. The simulated and measured results are exhibited, confirming the validity of multiobjective topology optimization.

The performance of the cage can directly affect the service life of the bearing. This paper presents a cage topology optimization method for improving the heat dissipation and structural stiffness. Firstly, a multi-objective structural topology optimization model is established based on the SIMP method and MMA algorithm, the effects of force and thermal load are considered comprehensively. Secondly, considering the centrifugal force and frictional heat, under the conditions of a given volume constraint, the bearing cage topology optimization model is carried out with heat dissipation weakness and compliance as the optimization objectives. Using iterative calculations based on the MMA algorithm and boundary smoothing processing, the structure with the optimal material layout is obtained. Finally, compared with the initial structures, the maximum temperature reduces about 27% and the maximum stress reduces about 14.8%. The results show that topology optimization can provide a reference for the design of bearing cages, which can improve the structural performance while reducing weight.

The mathematical model of thermomechanical coupling multi-objective topology optimization for anisotropic structures was established using the element-free Galerkin (EFG) method, and the weighted function of compliance and heat dissipation was defined as the objective function. The proposed model and procedure were verified by the topological results based on the finite element method. The multi-objective EFG optimal topological structures have clearer boundary profiles even without using the sensitivity filtering technique. The effects of the weight coefficient, thermal conductivity factor, Poisson's ratio factor, off-angle and volume fraction on the multi-objective EFG optimal topological structure and multi-objective function were evaluated in detail, and reasonable ranges of the above parameters were recommended to improve the heat dissipation and mechanical performance. The multi-objective optimal results of the anisotropic structure were 3D printed and compared with the isotropic material, and their temperature, displacement and stress were improved, which reflects the advantages of orthotropic structures.

Computational multiobjective topology optimization of silicon anode structures for lithium-ion batteries

This work presents a method to develop computational models for topology optimization of linear elastic structures, when we have more than one objective function, each of them with different individual optimal solution.The method is developed for multi-objective optimization problems. Its purpose is to evolve an evenly distributed group of solutions to determinate the optimum Pareto set for the given problem.The algorithm evaluates a set of solutions (population) sorting it by considering domination properties and using a definition of filter to retain Pareto solutions.To reduce computational effort, it is introduced, in the initial population, optimal solutions of each of the single-objective problems.The computational model is applied and tested in two numerical applications.

This article deals with the comparative performance of some established multi-objective evolutionary algorithms (MOEAs) for structural topology optimization. Four multi-objective problems, having design objectives like structural compliance, natural frequency and mass, and subjected to constraints on stress, etc., are posed for performance testing. The MOEAs include Pareto archive evolution strategy (PAES), population-based incremental learning (PBIL), non-dominated sorting genetic algorithm (NSGA), strength Pareto evolutionary algorithm (SPEA), and multi-objective particle swarm optimization (MPSO). The various MOEAs are implemented to solve the problems. The ground element filtering (GEF) technique is used to suppress checkerboard patterns on topologies. The results obtained from the various optimizers are illustrated and compared. It is shown that PBIL is far superior to the others. The optimal topologies from using PBIL can be compared with those obtained by employing the classical gradient-based approach. It can be considered as a powerful tool for structural topological design.

This paper presents a multi-objective topology optimization method for the temperature field considering the material nonlinearities. Although a large number of papers have studied the topology optimizations of the heat transfer problems, none of them considered the influence of the material nonlinearity properties. In this paper, the material nonlinearity is considered. Based on the nonlinear assumption, the mathematical model of the corresponding topology optimization is presented first. Then, the sensitivities of the objectives and the constraints respect to the design variables are derived. And the optimization routines are discussed. After establishing the theories and solving scheme, a software is developed by MATLAB for the topology design of the nonlinear heat transfer. Several nonlinear numerical examples are presented. And the corresponding optimal results generated under the linear assuming are also collected for comparisons. Furthermore, this paper also simply discusses the preventing approaches of instabilities and the implementation methods of some other unusual engineering constraints. These true engineering considerations are very helpful for the real industry design experiences.

Aiming at the problems such as low computational efficiency and long process in dynamic topology optimization, combined with bi-directional evolutional structure optimization, the dynamic optimization problem is transformed into the static optimization problem in multiple load cases. Newmark method is used to analyze the structure dynamics load. The topology optimization model based on equivalent static load is established. On the basis of the equivalent static load, multi-objective dynamics evolutionary structure optimization is studied. And the mathematical model of the dynamic stiffness and natural frequency about the multi-objective optimization is established. The mathematical formula of the sensitivity is deduced. Then a complete optimization iterative process is given. The numerical example illustrates that it is feasible to solve the multi-objective dynamic topology optimization with equivalent static loads. Modal tracking technique is introduced to the multi-objective dynamic topology optimization. The numerical example shows that modal tracking technology can track the required modal in the optimization process.

Multi-objective topology optimization and thermal performance of liquid-cooled microchannel heat sinks with pin fins

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.