An Adaptive Feature-Driven Method for Structural Topology Optimization

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

This paper presents a zeroth-order (non-gradient based) methodology for topology optimization of continuum structures. The solid and void elements in the design domain are represented by binary design variables. As in the SIMP method, design variables are assumed to represent the non-dimensional density of the individual finite elements and their contribution to structural stiffness in the model. The optimization procedure begins by specifying a desired volume fraction over a discretized domain and associated boundary conditions. Based on a randomized distribution of solid and void elements, a finite element analysis is performed to identify the strain energy of individual elements. While keeping the volume fraction fixed, the solid elements with low strain energy are converted into void elements whereas the void elements with high strain energy are converted into solid elements. The strain energy threshold for element exchange is specified at the beginning and can be adjusted in the course of optimization. Through subsequent repetition of analysis and exchange steps, the optimal topology corresponding to minimum compliance emerges with no gray elements to filter out. The general characteristics of the Element Exchange Method are demonstrated through solutions of several benchmark problems.

This chapter introduces the improvement and application of swarm algorithm named Group Search Optimizer (GSO) in civil structure optimization design. GSO is a new and robust stochastic searching optimizer, as it is based on PS (produce and scrounger) model and the animal scanning mechanisms. An improved group search optimizer named IGSO was presented based on harmony search mechanism and GSO. The implementation of IGSO for different optimal purposes is presented in detail, including the application of IGSO to truss structure shape optimal design, to truss structure dynamic optimal design, to truss structure topology optimization design. Different truss structures are used to test the GSO and IGSO in structural shape optimization, dynamic optimization and topology optimization.

Structural topology optimization.- On basic properties of Michell's structures.- Validation of numerical method by analytical benchmarks and verification of exact solutions by numerical methods.- Introduction to shape and topology optimization.- Homogenization method for shape and topology optimization.- Level set method for shape and topology optimization.- Compliance minimization of two-material elastic structures.- Some notes on topology optimization of vibrating continuum structures.- Topology optimization of vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps.- On optimum shape design and periodicity of band-gape beam structures.- Topological design for minimum dynamic compliance of continuum structures subjected to forced vibration.- Topological design for minimum sound emission from bi-material structures subjected to forced vibration.- Discrete material optimization of vibrating laminated composite plates for minimum sound emission.- Optimization of diffusive transport problems.- Fluid topology optimization: stokes and Navier-stokes models.- Topology optimization of coupled multi-physics problems.- Topology optimization based on the extended finite element method.- Topology optimization of meso- and nano-scale problems.- Topology optimization under uncertainty.- A brief review of numerical methods of structural topology optimization.- The free material design in planar elasticity.

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

The upper arm plays an important role in an industrial robot. In order to reduce the requirements of the driving system, a topology optimization is carried out based on the SIMP method. Additional analysis including static and dynamic finite element analyses are performed before and after the optimization. The results shows that the optimization has reduced the mass down to 44.4 % of the original arm while the displacement are not larger and first frequency are not lower than the unoptimized arm, respectively.

In this chapter, a topology optimization algorithm based on the topological derivative concept combined with a level-set domain representation method is presented. The model problem is governed by the elasticity system into two spatial dimensions. The topological asymptotic expansion of a tracking-type shape functional, associated with the nucleation of a small circular inclusion endowed with different material property from the background, is rigorously derived. Finally, the obtained theoretical result is used as a steepest-descent direction in the optimization process, which is applied in the context of compliance structural topology optimization and topology design of compliant mechanisms.

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 effective utilization of materials and the optimization of structural performance have become important research topics. In this context, the technique of topological optimization emerges as a potent approach to refine the geometrical configuration and structural layout under specified limitations, with the goal of attaining superior functionality. The present study predominantly centers on the utilization of topological optimization, which is enhanced by the modification of feasible regions in the realm of single-phase materials. Firstly, a topology optimization model for single-phase materials is established, aiming to minimize compliance under the constraint of structural volume. A sub-model of this model is proposed based on the feasible region adjustment scheme. Subsequently, leveraging the moving asymptote method for approximating the expansion of the objective function, we derive an approximation of the second-order derivative of the objective function. This derivative is then subjected to a convexity treatment to ensure the robustness of the optimization process. By integrating the primary derivative of the objective function, a quadratic Taylor series approximation for the objective function is formulated. The issue is addressed by employing a smooth dual-solution approach. Ultimately, a series of validation cases are showcased to demonstrate the effectiveness of the method. This method not only effectively improves material utilization and structural performance but also provides a new optimization approach for engineering design.

The main goal of the present research is to propose an integrated methodology to address the fatigue performance of topology optimized components, produced by additive manufacturing. The main steps of the component design will be presented, specially the methods and parameters applied to the topology optimization and the post-smoothing process. The SIMP method was applied in order to obtain a lighter component and a suitable stiffness for the desired application. In addition, since residual stresses are intrinsic to every metallic additive manufacturing process, the influence of those stresses will be also analyzed. The Laser Powder Bed Fusion was numerically simulated aiming at evaluating the residual stresses the workpiece during the manufacturing process and to investigate how they could influence the fatigue behavior of the optimized component. The effect of the built orientation of the workpiece on the residual stresses at some selected potential critical points are evaluated. The final design solution presented a stiffness/volume ratio nearly 6 times higher when compared to the initial geometry. By choosing the built orientation, it is possible impact favorably in the fatigue life of the component.

The object investigated in this work is a design method for the supporting structure of vehicle rudders, which are the crucial components in flight control system. As a practical application of topology optimization for additive manufacture, the design process was presented in this article. To obtain the optimal material distribution, topology optimization based on SIMP method was applied, with compliance minimization as the optimization objective. A numerical optimization model was built and calculated in Inspire, and the result in an equivalent load scheme of 30 percent point load and 70 percent uniform pressure was adopted to be the initial geometry for the subsequent design. Concentrating on realizing the optimized geometry, this design took a series of technical constrains for additive manufacture and mass requirements into consideration. Notably, the FEM simulation for the supporting structure is necessary, which consist of stress analysis and mode analysis. And the technical feasibility was verified in its practical manufacturing process. Finally, by the experiment about dynamic characteristic, it is verified that the lightweight rudder designed in this work can satisfy all the requirements for flight control.

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.

Topology optimization (TO) aims at defining the ideal layout of structures in order to minimize the use of material within a given design space. Such goal is pursued by applying an optimization strategy, where the possible solutions are the feasible geometries, and the functional to minimize is the mass structure. Obtaining high performance in terms of mass reduction depends on many factors. The most well-known and widespread topological optimization approaches can be divided into two main categories: microscopic and macroscopic. In microscopic approaches, such as SIMP and BESO, the feasible domain available for the solid material is divided in a finite number of discrete elements (FEM). The density of the material of each element represents the design variables, which may vary with continuity in SIMP method (density approach) or being binary in BESO Method (evolutionary approach). In macroscopic approaches, such as Level Set, the parameters describing the evolution of the boundaries of the solid domain of the structure are the design variables. Again, a discretization of the design domain is required, even if the implementation of this strategy in the optimization algorithm doesn’t intrinsically need the decomposition in a finite number of elements.

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