Table of Content

10 December 2022, Volume 33 Issue 23

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Time Domain Dynamics Topology Optimization of Functionally Gradient Material Structures with Self-weight Load

WEN Guilin, CHEN Gaoxi, WANG Hongxin, XUE Liang, WEI Peng, LIU Jie,

2022, 33(23):  2774-2782.  DOI: 10.3969/j.issn.1004-132X.2022.23.001

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 A time domain dynamics topology optimization design method of FGM with self-weight load was developed. A structural self-weight distribution strategy of FGM-SIMP gradient materials was proposed under the framework of solid isotropic material with penalization（SIMP）. The dynamics topology optimization formulations were established with minimum dynamic compliance as the optimization objective and structural volume as the constraints. The sensitivity was derived in the time domain based on the adjoint method and solved by the method of moving asymptotes（MMA）. The topology optimization design of FGM structures with self-weight load was systematically analyzed through 2D and 3D typical numerical examples. Besides， the effects of the self-weight loads and the direction of material gradient distribution on the topology optimization results were deeply discussed. It is found that the self-weight loads and the direction of material gradient distributions have a significant influence on the optimal configuration and dynamic stiffness of the FGM structures. Finally， taking homogeneous materials（a special case of FGM）as an example， the validity of the proposed method was verified by numerical simulations and experiments， it is found that the proposed method may effectively improve the resonance frequency and dynamic stiffness. 

Topological Dynamics Optimization of Constrained Damping Plates Based on Bilinear Material Interpolation Model

HE HonglinZ, HAO Weipeng, YU Zhihao, LONG Yufan, YAN Yinqi, LI Ji

2022, 33(23):  2783-2789，2878.  DOI: 10.3969/j.issn.1004-132X.2022.23.002

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Aimed to reduce vibrations and weights， a dynamics optimization method of damping plates was proposed. An optimization model of damping plates was presented taking the difference between a moving constant and the modal loss factor as objective function， density of damping layers elements as design variables， the volume usage of damping materials and the modal frequencies as constraints. A convex approximation function for objective function was provided with sequential convex programming method， and the Lagrange multiplier method was employed to solve the function so that a globally optimized damping layer layout was obtained. The sensitivity of objective function to design variables was derived using the relation of the modal loss factor and modal strain energy， and the iterative formulas of these variables were derived from K-T condition. The bilinear interpolation functions were used to punish the variables to make them converge to 0 or 1. The optimization programs were programmed and implemented for a cantilever damping plate. It is shown that the 1st order modal loss factor increases 52.29% and the proportion of gray element is as 1.78%， when the volume usage of damping materials is limited to 50%. Better vibration suppression property of the optimized plates is demonstrated by harmonic response analysis. The optimized damping layout from bilinear interpolation may make full use of the energy dissipation of damping materials and reduce the number of gray damping elements largely. 

Study on Mechanics Properties and Numerical Convergence of Gyroid Cellular Structures

JIANG Chuangyu, ZHANG Baoqiang, CHEN Yun, WANG Cunfu, LUO Huageng, HU Jiexiang, CAO Longchao

2022, 33(23):  2790-28000.  DOI: 10.3969/j.issn.1004-132X.2022.23.003

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In order to reveal the corresponding relationship between TPMS structure design and mechanics property parameters， the mechanics properties of Gyroid cellular structure（GCS） with different arrangements and the numerical convergence of meshes with different parameters were studied. GCS specimens with fixed volume fraction and unit size were designed. Based on the voxelization model with changing mesh parameters， the convergence analyses of GCS were conducted by finite element method. The correctness of the simulation was verified by tensile test of specimen. Finally， the mechanics properties of the GCS in different arrangements were studied in tensile and bending conditions. Results show that the relative errors of tensile strength and load limit between simulation and experiment are all less than 1.5%. Based on the voxelization method， the number of elements during convergence  may be significantly reduced by adjusting the Jacobian parameters. Quantitative analyses of mechanics properties of variable thickness GCS were conducted. In tensile tests， for 4×4×4 structures， the maximum variation of equivalent elastic modulus along the thickness direction may reach 14.41%. In bending tests， for 20×4×4 structures， the maximum difference of equivalent elastic modulus is as 21.25%. 

Efficient Multigrid Isogeometric Topology Optimization under Bézier Element Stiffness Mapping

DING Yandong, LUO Nianmeng, YANG Aodi, WANG Shuting, ZHU Haoran, XIE Xianda

2022, 33(23):  2801-2810.  DOI: 10.3969/j.issn.1004-132X.2022.23.004

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 Isogeometric topology optimization（ITO） utilized B-spline or NURBS as the shape function of unknow physical field of CAE， which avoided the low-accuracy problems of traditional FEM-based topology optimization due to the C0 continuity of Lagrange basis function. Through the inheritance between design variables on different hierarchies， the calculation efficiency of ITO might be significantly improved， while it still suffered from the problems of huge memory burden and complicated pre-processing processes with respect to the elemental stiffness matrices of all elements. To resolve these problems， the multigrid ITO method was put forward based on Bézier element stiffness mapping herein. The standard Bézier element stiffness matrix and the Bézier extraction matrices of all hierarchies were used to express the elemental stiffness matrix of an arbitrary B-spline element on arbitrary grid-level equivalently， which optimized the data storage structure and pre-processing processes for multigrid ITO. Numerical example results show that compared with conventional multigrid ITO method， the proposed method obtains identical optimization processes and results， but significantly reduces the storage burden and pre-processing time of the B-spline elements stiffness matrices. Therefore， the effectiveness of the proposed method was verified. 

An Efficient Isogeometric Topology Optimization Method Using DOF Reduction and Convergence Acceleration

YANG Yuhao, ZHENG Wei, WANG Yingjun,

2022, 33(23):  2811-2821.  DOI: 10.3969/j.issn.1004-132X.2022.23.005

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 In order to improve the efficiency of isogeometric topology optimization（ITO）， an efficient ITO method was proposed， which accelerated ITO from DOF reduction and convergence acceleration. The DOF reduction algorithm included DOF reduction based on displacement changes and empty elements， and the convergence acceleration algorithm included design variable reduction and gray-scale suppression. Through 2D and 3D cases， it is demonstrated that the speedup ratio of the proposed efficient ITO method may reach to 1.56～6.02 compared with traditional ITO when optimization accuracy is ensured， which significantly improves the efficiency of ITO and provides a strong support for the efficient and high-quality design of product structures. 

Topology Optimization Design of Aero-engine External System Brackets for Additive Manufacturing

MENG Liang, ZHONG Mingzhe, LI Wenbiao, XIA Liang, GAO Tong, ZHU Jihong, ZHANG Weihong,

2022, 33(23):  2822-2832.  DOI: 10.3969/j.issn.1004-132X.2022.23.006

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The mechanics properties of aero-engine external system supports under critical loading conditions were analyzed. The support smoothness under two kinds of ultimate load conditions was used as objective function. The topology optimization design and performance check of external system supports for additive manufacturing were conducted using transverse isotropic model of additive manufacturing materials. The results of the mechanics test of metal laser additive manufacturing samples shows that， compared with the initial structure， the support design for additive manufacturing has a 15% less material usage， the stiffness increases by about 20%， and the first-order natural frequency improves by 15%. The structural strength increases significantly. The integrated additive manufacturing with 1 external system support， 2 piping supports and 4 rivets was realized herein， which effectively improves the quality and efficiency of engine assembly. The ground static load and engine ignition tests were successfully passed. 

Optimization Design of TiO2 Porous Ceramic Structures for Catalyst Carrier Applications

ZOU Wuyou, DU Chun, AI Jianping, SHAN Bin

2022, 33(23):  2833-2843.  DOI: 10.3969/j.issn.1004-132X.2022.23.007

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Based on additive manufacturing， the periodic lattice structure of porous ceramics might effectively solve the problems of the poor recyclability of traditional powder catalysts and the low catalytic efficiency of bulk catalysts. Due to the complex relationship among structural characteristic parameters and application performance， the accurate and rapid design of periodic lattice structures remained a great challenge. Aiming at this challenge， a set of simulation models was constructed for porous ceramics， TiO2 ceramic samples with fine porous structure were successfully prepared by 3D printing technology， and the simulation models were verified and modified through experiments. The working mechanism of structural parameter on performance was further explored by using single-factor optimization analysis method， and angles a=153.4°， b=90°， c=45° were selected as the optimal parameters for periodic lattice structure design and optimization. The comparison results show that the pressure drop of the optimized porous structures decreases by 57.2% and the surface area increases by 25.3%. This paper provides a new structure design method for the applications of porous ceramics in the field of catalyst carrier applications. 

Design and Manufacture Method of Bionic Porous Structures for Orthopedic Implants

JIAO Chen, CHAO Long, ZHU Lei, SHEN Lida, LIANG Huixin, DAI Ning, WANG Changjiang, SUN Jun

2022, 33(23):  2844-2850.  DOI: 10.3969/j.issn.1004-132X.2022.23.008

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The selective laser melting and ceramic digital light processing methods were adopted to fabricate metal scaffolds and ceramic scaffolds with porous structures. The compression test was employed to evaluate the mechanics behaviors of the scaffolds. The in vitro cultivation of MC3T3E1 cells was used to evaluate the biocompatibility of the scaffolds. The test results show that the irregularity and porosity are influential to the mechanics properties and biocompatibility； metal scaffolds have better mechanics properties， while ceramic scaffoldsis are closer to the cancellous bones； the irregular pores show better performance of cell adhesion which improves the biocompatibility of the scaffolds. 

A Substructure-based Co-optimization Method for Macro-micro Structures

WU Zijun, XIAO Renbin

2022, 33(23):  2851-2858.  DOI: 10.3969/j.issn.1004-132X.2022.23.009

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 The integrated structural macro-microscopic design was achieved by using the reduction of substructural degrees of freedom， which required the pre-establishment of samples of different substructural configurations. The macroscopic structure optimization might only be interpolated in predefined microscopic configurations， which restricted the optimization space of structural macro and microscopic. A macro-micro collaborative method was proposed for the design of periodic structures by combining substructure degree of freedom reduction and inverse theory. Using the solid isotropic material with penalization（SIMP） method and the substructure method， a substructure-based macro-micro collaborative framework for periodic structures was constructed. The correlation between the material volume variation of macrostructures and microscopic periodic cell was analyzed， and the matching of optimization parameters was given such as penalty factor and variable filter radius at two scales. Then， the sensitivity values of the design variables in the macroscopic structures and microscopic periodic structures were calculated in combination with the traditional structural flexibility minimum optimization model， and the co-design of macro and micro structures was realized. The effectiveness of the proposed method was verified by the design of the cantilever beam structures. 

Design and Mechanics Property Analysis for Different Graded Irregular Porous Structures

TANG Yongfeng, LU Ping, LIU Bin, JIANG Kaiyong, YAN Binggong, LIU Jiawei, HAN Wei,

2022, 33(23):  2859-2866.  DOI: 10.3969/j.issn.1004-132X.2022.23.010

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 Four different type graded irregular porous structures were designed based on the Voronoi diagram， and the four graded porous structure examples were prepared by the stereolithography molding technology. The longitudinal（load direction parallels to the graded direction）and transverse（load direction perpendiculars to the graded direction）compression tests were carried out on the four graded porous structures to study their deformation characteristics and mechanics properties. The results show that the deformation characteristics of the graded porous structures are similar to that of the uniform porous structure during transverse compression processes， and the deformation characteristics of layer-by-layer collapse are exhibited during longitudinal compression processes. In the case of similar porosity， different graded types may affect the mechanics properties in the longitudinal compression processes but have little effect on the mechanics properties in the transverse compression processes. Decreasing the average porosity of the graded porous structures may improve the mechanics properties of the structures. Finally， combining the iso-stress composite model and the Voigt model， the elastic modulus of the graded porous structures were predicted in the longitudinal and transverse compression processes respectively， and most of the relative errors between the predicted results and the experimental ones are less than 10%. 

Optimization Design Method for Graded Hollow Cellular Structures

TIAN Qihua, SHU Zhengtao, FU Junjian, DU Yixian, ZHOU Xiangman, TIAN Lei

2022, 33(23):  2867-2878.  DOI: 10.3969/j.issn.1004-132X.2022.23.011

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To realize the parametric modeling and improve load-bearing capacity of hollow cellular structures， an optimization design method for graded hollow cellular structures was proposed. The implicit modeling of hollow cellular unit cell was realized by the Boolean operation of I-Wrapped Package（I-WP）triply periodic minimal surfaces（TPMS）with different level parameters. The numerical homogenization method was applied to evaluate the effective elastic properties of hollow cellular structures. By introducing the affine concept of convex optimization theory， the hybrid level set function（LSF）was constructed to realize the parametric modeling of the graded hollow cellular structures. A graded hollow cellular structures topology optimization model was established with the maximum stiffness based on the HLSM. The optimality criteria（OC）was used to solve the model to obtain a cellular structure with superior continuity. The finite element method was performed to analyze the mechanical performance of the optimized structures. Then selective laser sintering（SLS）technology was used to manufacture specimens and the mechanics experiments were carried out. Numerical examples and experimental results show that this method may effectively realize the parametric design of hollow cellular structures， and significantly improve the load-bearing performance of the structures. 

Topology-size-material Joint Optimization Design of Long-pan Unsupported Decks

CUI Yupeng, YU Yang, YU Jianxing, LI Zhenmian,

2022, 33(23):  2879-2887，2897.  DOI: 10.3969/j.issn.1004-132X.2022.23.012

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 A concept-detailed joint design framework was proposed to carry out an integrated topology-size-material optimization study regarding stiffness， deformation， and dynamic vibration performance for a long-span unsupported deck under the spatial constraint. The dimensionality reduction processing strategy for the topology design domain of the stiffened panel was applied to address the issues of disconnected 3D solid units and low computational efficiency of the long-span deck. A TSC method， taking into account the efficiency of iteration and the approximation of the global optimal solution， was presented and applied to the concept design of the long-span deck in terms of strain energy， multi-case displacement， and first-order dynamic frequency. The effectiveness of the TSC method was demonstrated by 480 examples for maximizing the stiffness of stiffened panels. The size/material integrated design approach was suggested and combined with the automation technology for the detailed design of the long-span deck concept structure for engineering fabrication， i.e.， optimization of the combination of cross-sectional dimensions of curved T-beams， panel thickness， and material elastic modulus. The results show that the curved long-span unsupported deck obtained efficiently by the concept-detailed joint design framework possesses both spatial and performance（stiffness， deformation， dynamic vibration）benefits compared to the conventional long-span deck. 

Lightweight Design of Front and Middle Shield Structures Based on Topology Optimization and Kriging Model

JIA Lianhui, LI Xiaoke, YUAN Wenzheng, HE Wenbin, LIAO Zhaojin

2022, 33(23):  2888-2897.  DOI: 10.3969/j.issn.1004-132X.2022.23.013

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The front and middle shield was an important part of shield machines. Because of the large structural size and complex service environment， it was very important to carry out lightweight design on the premise of ensuring structural strength. Aiming at the front and middle shield of a slurry balance shield， a lightweight design method was proposed herein based on topology optimization and size optimization. Firstly， topology optimization was used in the front and middle shield structural design， and secondary design was carried out based on the topology optimization results. Then， the size optimization model of the front and middle shields was built after the secondary design， where the structural parameters that had great impacts on the mass， maximum deformation and maximum stress of the front and middle shields were selected as design variables by orthogonal experiment and analysis of variance. The optimal Latin hypercube design and finite element analysis method were used to obtain 45 groups of sample points， thereby a Kriging agent model with design variables-performance responses implicit relation were constructed. Finally， the size optimization model of the front and middle shields was solved by the sequential quadratic programming（SQP） algorithm， and the optimal size parameter groups were obtained. The verification results show that， the mass of the front and middle shields decreases by 30 t（with a drop of 3.1%）after topology optimization and size optimization.