Search

There are many methods for solving the topology optimization problem of single-material. It is a great challenge how to utilize existing methods or make appropriate improvements to solve multi-material topology optimization problems. In this paper, a multiple solid isotropic material with penalization model (SIMP) of variable density method is proposed to solve the problem of multi-material topology optimization. All candidate materials, including void material, are arranged in descending order of elastic modulus. The material conversion scheme of multiple SIMP is based on the elastic modulus of the candidate material after interpolation. The iterative criterion of multi-material topology optimization is derived from the Kuhn-Tucker condition using the guide-weight method. The innovation of this paper is to transform the multi-material topology optimization problem into multiple SIMP of the variable density method. Three examples show that it is effective and moderate to use the proposed method to solve the problem of multi-material topology optimization. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) is an effective approach to designing novel and efficient heat transfer devices. However, the TO of conjugate heat transfer has been essentially limited to laminar flow conditions only. The present study proposes a framework for TO involving turbulent conjugate heat transfer based on the variable density method. Different from the commonly used and oversimplified Darcy model, this approach is based on the more accurate and widely accepted k-ε model to optimize turbulent flow channels. We add penalty terms to the Navier–Stokes equation, turbulent kinetic energy equation, and turbulent energy dissipation equation, and use interpolation models for the thermal properties of materials. A multi-objective optimization function, aiming to minimize the pressure drop and the average temperature, is set up to balance the thermal and hydraulic performance. A case study is conducted to compare various optimization methods in the turbulent regime, and the results show that the present method has substantially higher optimization effectiveness while remaining computationally inexpensive. [ABSTRACT FROM AUTHOR]

In order to improve the zero-pressure driving performance of the inserts supporting run-flat tire and solve the problems of heavy weight and large moment of inertia, the topology optimization theory based on variable density method was used to optimize the inserts structure of run-flat tire. The mechanical model of zero-pressure driving and the contact finite element model between insert, tire and ground was established. Further, stiffness, strength and modal characteristics of the inserts structure under zero-pressure driving condition before and after optimization were compared and simulated. The results show that under the maximum load of the tire, the optimized inserts structure can reduce the weight by 19.4 % with the requirements of the stiffness and strength, and the load bearing performance of the inserts structure is optimized, and the accuracy of the design is improved. On the premise of satisfying the design requirements of the tire dynamic characteristics, the natural frequency of each order for the optimized inserts structure is reduced. The static load characteristics of the tires under zero-pressure conditions before and after optimization were verified based on the tire load characteristics test bench. The research results provide a reference for the design and optimization of the inserts supporting run-flat tire. [ABSTRACT FROM AUTHOR]

Compliant amplification mechanisms amplify input displacement in the desired output direction. However, owing to structural design, parasitic motion can easily be produced in an unexpected direction. The parasitic motion has a negative effect on the motion accuracy of the mechanism. To solve this problem, a topology optimization method for compliant amplification mechanisms with low parasitic displacement was proposed. Based on the variable density topology optimization method, the topology optimization model of the compliant amplification mechanism was established with the goal of increasing the output displacement and reducing the parasitic displacement. Volume ratio was set as constraint condition. The optimization criterion method were used to solve the problem and topology optimized amplification mechanisms (TOAMs) were obtained. Simultaneously, the configuration characteristics and displacement amplification ratios of the mechanism under different virtual spring stiffnesses were compared. To verify the validity of the method, the performance of the TOAM and the typical amplification mechanism (TAM) were compared using finite element simulation. The displacement amplification ratio is 5.95 and 3.17, and the relative parasitic displacement is 0.6% and 10.27%, respectively. Finally, the performance of the TOAM and the TAM was verified by experiments. The displacement amplification ratio is 5.72 and 3.06, and the relative parasitic displacement is 0.95% and 10.64%, respectively. Simulation and experimental results show that the TOAM has a larger displacement amplification ratio and a lower parasitic displacement, which verifies the validity of this method. [ABSTRACT FROM AUTHOR]

Aiming at the numerical instability problems including boundary diffusion and slender rod structure of the optimization results in the structural topology optimization based on variable density method, a partitioned weighted sensitivity filtering method based on the variable density method was proposed. Firstly, the sensitivity filtering area was divided into two parts: inner and outer. Then, the values of the optimization parameters such as the weighting factor correction coefficient, the penalty factor, and the minimum filter radius were determined to perform weighting processing on the inner and outer regions respectively by using different weighting factors, so that the regions close to the center obtained higher sensitivity values and the regions far from the center obtained lower sensitivity values, and then a topology optimization structure with clear boundaries was obtained. Finally, after the metrics of topology optimization were introduced, the feasibility and effectiveness of the method in solving boundary diffusion and slender rod problems were verified by typical examples. The research results show that the method improves the number of iterations, gray value, discrete rate and gray rate, which can improve the optimization efficiency and the manufacturability of the optimized structure, and is beneficial to model extraction and reconstruction during post-processing. Compared with other optimization methods, it has certain advantages in solving boundary diffusion and slender rod problems. [ABSTRACT FROM AUTHOR]

Aiming at topology optimization of multi-material continuum structures, based on the development of 3 D printing technology, the technology of material made up of a variety of different materials mixed in any proportion was investigated. Based on the topological optimization method of variable density method, a topological optimization model and its calculation method for two-material hybrid structure was proposed. In this model, the elements densities were used as the design variables, and the mixing ratios of two materials in the elements were added as the design variables. The developed method was verified by two examples. The results indicate that this method can optimize the structure topology and obtain the mixture ratios of two materials, so as to realize the material and structure integrated topology optimization based on the interpolation model for solid isotropic material with penalization. [ABSTRACT FROM AUTHOR]

Aiming at the lightweight design target of the head structure of grinding and polishing machine for the blade surface grinding of aeroengine’s overall blade disk, the variable density method for topological optimization design was applied to the grinding head support plate. Based on the static and dynamic analysis of the grinding head structure, the theory of topological optimization of variable density method was studied. Based on the topologically optimized material distribution results, the lightweight structure and size optimization of the grinding head structure were carried out, and the final design parameters of the grinding head structure were obtained.The results showed that the mass of the optimized grinding head structure is reduced by 8.74%, and the dynamic and static mechanical properties of the structure are advanced, that is, the lightweight design of the grinding head structure is well achieved. [ABSTRACT FROM AUTHOR]

Conceptual design plays a key role in product design, but traditional methods of designing gear shaping machine lead to a poor control of our design result. In order to get a clear concept and accurate design, this paper presents a novel method for the design of the concept prototype and structure prototype of YKW51250 gear shaping machine, which saves a great deal of design cost and shorts product conceptual design cycle. With variable density method, topology optimization was carried out for property YKW51250 gear shaping machine based on Hyper- Works. The original YKW51250 gear shaping machine and the improved one in constraint state are compared based on an experiment with the system of LMS Test. Lab. Finally, the first vibration frequency in the improved YKW51250 gear shaping machine is 27.9 Hz, which is increased by as much as 30.3% compared with the original YKW51250 machine tool. Meanwhile, the mass is decreased by more than 5%. In this way, not only the design requirements are satisfied, but it provides an important technical message for conceptual design. The research results provide the basis during the research and development of the gear shaping machine and references in research of other machine tools and equipment. [ABSTRACT FROM AUTHOR]

An objective function defined by minimum compliance of topology optimization for 3D continuum structure was established to search optimal material distribution constrained by the predetermined volume restriction. Based on the improved SIMP (solid isotropic microstructures with penalization) model and the new sensitivity filtering technique, basic iteration equations of 3D finite element analysis were deduced and solved by optimization criterion method. All the above procedures were written in MATLAB programming language, and the topology optimization design examples of 3D continuum structure with reserved hole were examined repeatedly by observing various indexes, including compliance, maximum displacement, and density index. The influence of mesh, penalty factors, and filter radius on the topology results was analyzed. Computational results showed that the finer or coarser the mesh number was, the larger the compliance, maximum displacement, and density index would be. When the filtering radius was larger than 1.0, the topology shape no longer appeared as a chessboard problem, thus suggesting that the presented sensitivity filtering method was valid. The penalty factor should be an integer because iteration steps increased greatly when it is a noninteger. The above modified variable density method could provide technical routes for topology optimization design of more complex 3D continuum structures in the future. [ABSTRACT FROM AUTHOR]