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Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Ordnance Equipment Engineering is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the Formula Student Racing Car, the frame is a fundamental component that supports the body. The frame's anti-deformation ability will impact the four-wheel positioning parameters of the car, which subsequently affect the car's stability. The quality of the frame directly determines the power and efficiency of the racing car, making the frame crucial to the overall race performance. Therefore, researching lightweight frame design is particularly important to enhance frame performance and reduce its total weight. In this paper, based on the variable density method, the global topology optimization of the frame is carried out to obtain the distribution of the frame material, realize the efficient utilization of the material, and improve the torsional stiffness of the frame. Compared with the previous local topology optimization, the global topology optimization involves a wider range, and the results are more accurate. Based on the adjoint variable method, the sensitivity analysis of the frame is carried out to obtain the influence level of each design variable. The size of the frame is optimized according to the variables with high influence levels. After optimization, the total mass of the frame is reduced by 12.8%; the performance in terms of maximum displacement and maximum stress is improved; and the lightweight design of the frame is realized as a whole. [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]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Featured Application: The developed topology optimization approach may give a potential design idea for body shape drag reduction of micro underwater vehicles and other underwater equipment worked in low speed. This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape. [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]

Copyright of Journal of Ordnance Equipment Engineering is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Copyright of Food & Machinery is the property of Food & Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to improve the structural performance of the aero-engine gearbox housing and reduce the adverse effects of the engine bad working conditions on the supporting components， the topology optimization theory based on variable density method is adopted， and the minimum flexibility index and weighted average transverse eigenvalue are taken as the target number， and the coupling of thermal-elastohydrodynamic-lubrication effects of the supporting components are considered. Taking the maximum deformation less than 0.15 mm and the equivalent stress less than the material stress as the constraint conditions， the topology optimization design of the aero-engine gearbox housing is carried out. According to the topology optimization results， the geometric reconstruction of the housing structure is carried out， and the strength， stiffness and mass of the shell structure before and after optimization are compared and analyzed. The results show that， after optimization， the housing mass is reduced from 5.53 kg to 5.107 kg， the weight is reduced by 7.6%， the maximum deflection of the housing is reduced from 0.173 1 mm to 0.127 mm， the deformation is reduced by 26.6%， the maximum equivalent stress of the housing is reduced from 124 MPa to 116.9 MPa， the stress is reduced by 5.7%.The maximum deformation and equivalent stress of the housing are effectively reduced， and the strength and stiffness of the housing are significantly improved. It is of great significance to improve the reliability and service life of aero-engine central transmission shell.

Objective: To improve the comprehensive performance of starter press machine. Methods: Based on the finite element analysis method for die box component modal and harmonic response analysis, and based on the finite element model by using variable density method was carried out on the die box component topology optimization, and the topology structure was also improved, which will improved the quality of the die box components and 1 order natural frequency as the optimization goal. The multi-objective optimization design was carried out based on non-dominated sorting genetic algorithm. Results: In the fourth mode, large torsional deformation appeared on the overall edge of the die box components, which did not meet the requirements of stiffness performance. The highest speed of the servo motor was close to the first-order critical speed, and the probability of low-frequency coupling resonance was very large. At the same time, the region where the response peak occurs was basically the same as the region where the deformation occurs in the modal analysis, which verified the accuracy of the dynamic characteristic results. After optimization, the mass of the die box component decreased by 15.13%, and the first four natural frequencies increasd by 14.09%, 14.14%, 3.54% and 10.37%, respectively. Conclusion: The dynamic characteristics of the starter press machine mainly affect its production efficiency and starter press quality. Under the optimized die box component, the starter press machine has good dynamic performance and achieves the goal of lightweight design.

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The variable density method has become an effective method to solve the topology optimization problem of continuum structure due to its advantages such as few design variables and high efficiency. Aiming at the problem of the gray unit and sawtooth boundary in the optimization process of the variable density method, a post-processing method of variable density method for continuum topology optimization is proposed in this paper. The topology optimization model is binarized and the sawtooth shape boundary line is extracted, and the target discrete corner point set is obtained, used as the sample point for curve fitting to obtain the optimized structure with smooth boundary. Experimental results show that this method effectively avoids the zigzag boundary and intermediate density of the optimization result, and improves the manufacturability of the optimization result under the premise of ensuring that the structural performance is within the allowable range.

Taking a hydrogen-fueled truck frame as the research object, based on the topology optimization theory of variable density method, the goal of maximizing the static multi-working stiffness and improving the dynamic low-order natural frequency of the frame is realized. The attachments of the frame were retained, and the topological optimization space was established according to the original frame outline size. A multi-objective topology optimization was carried out by using the isotropic material penalty function to obtain the best frame structure layout, and then the new frame structure was designed. The results show that the middle bearing capacity of the new frame is better than that of the original frame which has been verified by modal testing, and the maximum stress decreases by 35.6%. The first-order natural frequency increases by 1.9 Hz, which can avoid the maximum excitation energy region of the road. Meanwhile, the frame weight is reduced by 7.8%, which realizes the specialized and lightweight design of a hydrogen-fueled truck frame.

In the Formula Student Racing Car, the frame is a fundamental component that supports the body. The frame’s anti-deformation ability will impact the four-wheel positioning parameters of the car, which subsequently affect the car’s stability. The quality of the frame directly determines the power and efficiency of the racing car, making the frame crucial to the overall race performance. Therefore, researching lightweight frame design is particularly important to enhance frame performance and reduce its total weight. In this paper, based on the variable density method, the global topology optimization of the frame is carried out to obtain the distribution of the frame material, realize the efficient utilization of the material, and improve the torsional stiffness of the frame. Compared with the previous local topology optimization, the global topology optimization involves a wider range, and the results are more accurate. Based on the adjoint variable method, the sensitivity analysis of the frame is carried out to obtain the influence level of each design variable. The size of the frame is optimized according to the variables with high influence levels. After optimization, the total mass of the frame is reduced by 12.8%; the performance in terms of maximum displacement and maximum stress is improved; and the lightweight design of the frame is realized as a whole.

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.

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]

In structural strength topology optimization based on the variable density method, there are gray cells in the optimization result, making it difficult to accurately predict the structural stress which changes greatly before and after post-processing. This paper uses a filter-projection-based structural parameterization method to achieve a continuous decrease in the proportion of structural intermediate density units during the iterative optimization process. By studying the influence of the main optimization parameters of the structural ratio strength problem on the optimization process and structural strength optimization, a novel optimization strategy of structural topology optimization followed by approximate shape optimization is proposed, which realizes the accurate control of the change of structural stress during the optimization process, achieveing structural strength optimization while improving the stability of the optimization process. Typical optimization examples verify the rationality and practicability of the proposed optimization method.

Topology optimization and additive manufacturing are of particular importance in solving the problems of stress concentration, excessive steel consumption, and excessive displacement in spatial structure joints. In this work, we investigate the best topological form for such joints under multi-objective topology optimization (MTO). We conducted a single-objective topology optimization (STO) analysis on the joint first, in the optimization process, the influences of penalty parameters, minimum member size, symmetry constraints, and the checkerboard phenomenon were comprehensively considered. Through comparative analysis, the optimal values for various load conditions were obtained, according to the optimal value obtained by STO, the MTO calculation of joint is carried out by using the compromise programming method. Then, the Nurbs modeling method is used to redesign the preliminarily optimized result, and the smooth joint is obtained. The mechanical performance of single-condition and multi-condition, MTO and STO, MTO joint and hollow sphere joint are compared with the same steel consumption. The results show that the mechanical performance of the joint obtained by MTO is more uniform than those obtained by STO, and the mechanical performance of the joint obtained by MTO is better than those of hollow sphere joint under the same steel consumption. Finally, the optimized joints were fabricated via additive manufacturing, which produced joints with novel shapes, smooth surfaces, and light weights. [ABSTRACT FROM AUTHOR]

According to the characteristics of the cyclic ring structure, this paper deals with a topology optimization method based on the dynamical Hertz contact theory to simulate the material distribution. A piecewise linear plasticity material model is utilized by considering the relative design of materials as design variables. Using the cellular automata unit state information to update the design variables, the Hertz contact theory is employed to determine the angle of the design domain substructure. The number of substructures within the structure of the suction to the maximum is considered as the optimization objective function. Through exploiting the method presented in this article, the topology optimization configurations of the cyclic ring structure with different mass fractions are verified with the results of the finite element approach and thereafter the crashworthiness simulation analyses are performed. The results show that the topology optimization problems of crashworthiness of cyclic structures can be suitably solved by using the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape.

In order to achieve the goal of lightweight design of the scallop sheller, the buckling characteristics was analyzed by ANSYS Workbench 18.0. The buckling eigenvalue and the mode diagram were obtained through simulation analysis to determine the critical stress value and the buckling location when sheller instability occurred. On this basis, topology optimization was performed based on the optimization criteria of the variable density method, and the buckling characteristics before and after optimization were compared. The topology optimization results show that the overall structure is reduced by 12.5%, and the maximum deformation almost stays same. The research ensures that the structure meets normal working conditions and achieves the lightweight requirements of scallop sheller. [ABSTRACT FROM AUTHOR]

In order to improve the precision and quality of electrochemical machining of complex surface/cavity parts, the design of horizontal electrochemical machine tool which can realize the compound feeding motion of straight line and rotation is carried out. In this paper, UG software is used to build three-dimensional model of horizontal machine tool, and the simplified model is imported into ANSYS Workbench software for static analysis. The structural stiffness of the machine tool is analyzed based on deformation and stress distribution nephograms. The first six natural frequencies and modes of motion platform are determined by modal analysis, and the optimal design is carried out by using the variable density topology optimization method. Finally, the design is redesigned on the basis of considering the technological characteristics of the structure, and the lightweight design goal of the machine tool is achieved. The developed electrochemical machining machine has sufficient stiffness and stability, which can satisfy the requirements of actual machining. The research results have certain reference value to the design and application of electrochemical machining tool.

Copyright of Light Industry Machinery is the property of Light Industry Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The stacker crane is a long-and-thin structure with a large length-to-width ratio. It is difficult to obtain a topology configuration with good period properties using traditional optimization methods. While the mathematical model of periodic topology optimization-in which the elements' relative densities are selected as design variables, and mean compliance as the objective function-is established. To find a topology configuration with a good period property, an additional constraint condition must be imported into the mathematical model. According to the optimization criteria method, the iterative formula of design variables is derived in the virtual sub domain. To verify the capability and availability of the proposed method, periodic topology optimization of a single-mast stacker crane is investigated in this paper. The results show that configurations with good periodicity can be obtained when the number of sub domains is varied. After considering mean compliance and complexity, the optimal configuration has eight periods. A preliminary lightweight design scheme is proposed based on this configuration of a stacker crane, which is a periodic feature structure.

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]

Copyright of Journal of Beijing University of Technology is the property of Journal of Beijing University of Technology, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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.

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]

For super-light materials, based on the application of boundary conditions of macrostructure to those of unit cell with microstructure, topolopy optimization of the unit cell with microstructure was solved by using the finite element model, variable density approach and optimization criteria method. The optimization model based on volume constraint and strain energy was aimed to gain the unit cell with maximal stiffness. Topology optimization was achieved through repeating the progress of using optimization criteria method, changing the relative density of each element, and saving elements whose density values are lower than the threshold for next step's iterative computation. By adopting the appropriate penalty factor and threshold to control iterative, the convergence rate and precision was improved. Optimization results show that by applying this method, optimal microstructure of the unit cell can be obtained to gain the porous material with maximal stiffness under the same volume constraint, while the cost and the weight of the structure are lowered down. [ABSTRACT FROM AUTHOR]