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Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

《机械工程前沿（英文）》 2022年 第17卷 第2期 doi: 10.1007/s11465-022-0683-5

摘要： Piezoelectric actuators have received substantial attention among the industry and academia due to quick responses, such as high output force, high stiffness, high accuracy, and precision. However, the design of piezoelectric actuators always suffers from the emergence of several localized hinges with only one-node connection, which have difficulty satisfying manufacturing and machining requirements (from the over- or under-etching devices). The main purpose of the current paper is to propose a robust isogeometric topology optimization (RITO) method for the design of piezoelectric actuators, which can effectively remove the critical issue induced by one-node connected hinges and simultaneously maintain uniform manufacturability in the optimized topologies. In RITO, the isogeometric analysis replacing the conventional finite element method is applied to compute the unknown electro elastic fields in piezoelectric materials, which can improve numerical accuracy and then enhance iterative stability. The erode–dilate operator is introduced in topology representation to construct the eroded, intermediate, and dilated density distribution functions by non-uniform rational B-splines. Finally, the RITO formulation for the design of piezoelectric materials is developed, and several numerical examples are performed to test the effectiveness and efficiency of the proposed RITO method.

关键词： piezoelectric actuator     isogeometric topology optimization     uniform manufacturability     robust formulation     density distribution function    

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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 222-234 doi: 10.1007/s11465-019-0534-1

摘要： Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

关键词： topology optimization     level set method     isogeometric analysis     eigenfrequency    

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Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

《机械工程前沿（英文）》 2016年 第11卷 第4期   页码 328-343 doi: 10.1007/s11465-016-0403-0

摘要：

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.

关键词： isogeometric analysis     topology optimization     level set method     arbitrary geometric constraint     trimmed element    

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Massively efficient filter for topology optimization based on the splitting of tensor product structure

《机械工程前沿（英文）》 2022年 第17卷 第4期 doi: 10.1007/s11465-022-0710-6

摘要： In this work, we put forward a massively efficient filter for topology optimization (TO) utilizing the splitting of tensor product structure. With the aid of splitting technique, the traditional weight matrices of B-splines and non-uniform rational B-spline implicit filters are decomposed equivalently into two or three submatrices, by which the sensitivity analysis is reformulated for the nodal design variables without altering the optimization process. Afterwards, an explicit sensitivity filter, which is decomposed by the splitting pipeline as that applied to implicit filter, is established in terms of the tensor product of the axial distances between adjacent element centroids, and the corresponding sensitivity analysis is derived for elemental design variables. According to the numerical results, the average updating time for the design variables is accelerated by two-order-of-magnitude for the decomposed filter compared with the traditional filter. In addition, the memory burden and computing time of the weight matrix are decreased by six- and three-order-of-magnitude for the decomposed filter. Therefore, the proposed filter is massively improved by the splitting of tensor product structure and delivers a much more efficient way of solving TO problems in the frameworks of isogeometric analysis and finite element analysis.

关键词： topology optimization     isogeometric analysis     finite element analysis     tensor product structure     sensitivity analysis    

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Isogeometric topology optimization based on energy penalization for symmetric structure

Xianda XIE, Shuting WANG, Ming YE, Zhaohui XIA, Wei ZHAO, Ning JIANG, Manman XU

《机械工程前沿（英文）》 2020年 第15卷 第1期   页码 100-122 doi: 10.1007/s11465-019-0568-4

摘要： We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.

关键词： topology optimization     moving morphable component     isogeometric analysis     energy penalization method     symmetric constraint    

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从计算机辅助设计到人辅助设计——一种等几何拓扑优化方法

王英俊, 肖蜜, 夏兆辉, 李培根, 高亮

《工程（英文）》 2023年 第22卷 第3期   页码 94-105 doi: 10.1016/j.eng.2022.07.013

摘要：

本文提出了一种新的设计模式——人辅助设计，以取代传统的计算机辅助设计。在人辅助设计中，计算机可以通过一种新的等几何拓扑优化自动完成整个产品设计，而人类仅需协助轻微修改设计以满足要求。文中提出了一种嵌入域等几何拓扑优化用于设计具有不规则设计域的复杂模型，并且可以基于分层等几何拓扑优化结果自动生成优化结果的可编辑几何模型。测试了三个算例以验证所提出的等几何拓扑优化模式，包括一个具有规则设计域的3D悬臂梁，一个具有不规则设计域的汽车零件和一个具有多尺度结构的MBB梁。结果表明，所提出的等几何拓扑优化模式可以自动生成高质量的优化模型。因此，该技术具有成为革命性技术的巨大潜力，可以将当前设计模式由计算机辅助设计转变为人辅助设计。

关键词： 人辅助设计     CAD/CAE一体化     等几何分析     结构优化     等几何拓扑优化    

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Implicit Heaviside filter with high continuity based on suitably graded THB splines

《机械工程前沿（英文）》 2022年 第17卷 第1期   页码 14-14 doi: 10.1007/s11465-021-0670-2

摘要： The variable density topology optimization (TO) method has been applied to various engineering fields because it can effectively and efficiently generate the conceptual design for engineering structures. However, it suffers from the problem of low continuity resulting from the discreteness of both design variables and explicit Heaviside filter. In this paper, an implicit Heaviside filter with high continuity is introduced to generate black and white designs for TO where the design space is parameterized by suitably graded truncated hierarchical B-splines (THB). In this approach, the fixed analysis mesh of isogeometric analysis is decoupled from the design mesh, whose adaptivity is implemented by truncated hierarchical B-spline subjected to an admissible requirement. Through the intrinsic local support and high continuity of THB basis, an implicit adaptively adjusted Heaviside filter is obtained to remove the checkboard patterns and generate black and white designs. Threefold advantages are attained in the proposed filter: a) The connection between analysis mesh and adaptive design mesh is easily established compared with the traditional adaptive TO method using nodal density; b) the efficiency in updating design variables is remarkably improved than the traditional implicit sensitivity filter based on B-splines under successive global refinement; and c) the generated black and white designs are preliminarily compatible with current commercial computer aided design system. Several numerical examples are used to verify the effectiveness of the proposed implicit Heaviside filter in compliance and compliant mechanism as well as heat conduction TO problems.

关键词： topology optimization     truncated hierarchical B-spline     isogeometric analysis     black and white designs     Heaviside filter    

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Solving topology optimization problems by the Guide-Weight method

Xinjun LIU, Zhidong LI, Liping WANG, Jinsong WANG

《机械工程前沿（英文）》 2011年 第6卷 第1期   页码 136-150 doi: 10.1007/s11465-010-0126-6

摘要：

Finding a good solution method for topology optimization problems is always paid attention to by the research field because they are subject to the large number of the design variables and to the complexity that occurs because the objective and constraint functions are usually implicit with respect to design variables. Guide-Weight method, proposed first by Chen in 1980s, was effectively and successfully used in antenna structures’ optimization. This paper makes some improvement to it so that it possesses the characteristics of both the optimality criteria methods and the mathematical programming methods. When the Guide-Weight method is applied into topology optimization, it works very well with unified and simple form, wide availability and fast convergence. The algorithm of the Guide-Weight method and the improvement on it are described; two formulations of topology optimization solved by the Guide-Weight method combining with SIMP method are presented; subsequently, three numerical examples are provided, and comparison of the Guide-Weight method with other methods is made.

关键词： Guide-Weight method     topology optimization     SIMP method    

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Multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

《机械工程前沿（英文）》 2023年 第18卷 第4期 doi: 10.1007/s11465-023-0768-9

摘要： This study proposes a B-spline-based multiresolution and multimaterial topology optimization (TO) design method for fail-safe structures (FSSs), aiming to achieve efficient and lightweight structural design while ensuring safety and facilitating the postprocessing of topological structures. The approach involves constructing a multimaterial interpolation model based on an ordered solid isotropic material with penalization (ordered-SIMP) that incorporates fail-safe considerations. To reduce the computational burden of finite element analysis, we adopt a much coarser analysis mesh and finer density mesh to discretize the design domain, in which the density field is described by the B-spline function. The B-spline can efficiently and accurately convert optimized FSSs into computer-aided design models. The 2D and 3D numerical examples demonstrate the significantly enhanced computational efficiency of the proposed method compared with the traditional SIMP approach, and the multimaterial TO provides a superior structural design scheme for FSSs. Furthermore, the postprocessing procedures are significantly streamlined.

关键词： multiresolution     multimaterial     topology optimization     fail-safe structure     B-spline    

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Controlling interstory drift ratio profiles via topology optimization strategies

《结构与土木工程前沿（英文）》 2023年 第17卷 第2期   页码 165-178 doi: 10.1007/s11709-022-0892-3

摘要： An approach to control the profiles of interstory drift ratios along the height of building structures via topology optimization is proposed herein. The theoretical foundation of the proposed approach involves solving a min–max optimization problem to suppress the maximum interstory drift ratio among all stories. Two formulations are suggested: one inherits the bound formulation and the other utilizes a p-norm function to aggregate all individual interstory drift ratios. The proposed methodology can shape the interstory drift ratio profiles into inverted triangular or quadratic patterns because it realizes profile control using a group of shape weight coefficients. The proposed formulations are validated via a series of numerical examples. The disparity between the two formulations is clear. The optimization results show the optimal structural features for controlling the interstory drift ratios under different requirements.

关键词： interstory drift ratio     aggregation function     bound formulation     min–max problem     topology optimization    

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Robust topology optimization of multi-material lattice structures under material and load uncertainties

Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 141-152 doi: 10.1007/s11465-019-0531-4

摘要： Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions. This work proposes a density-based robust topology optimization method for meso- or macro-scale multi-material lattice structures under any combination of material and load uncertainties. The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials, and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty. By formulating the objective function as a weighted sum of the mean and standard deviation of compliance, the tradeoff between optimality and robustness can be studied and controlled. Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach. The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.

关键词： robust topology optimization     lattice structures     multi-material     material uncertainty     load uncertainty     univariate dimension reduction    

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A MATLAB code for the material-field series-expansion topology optimization method

《机械工程前沿（英文）》 2021年 第16卷 第3期   页码 607-622 doi: 10.1007/s11465-021-0637-3

摘要： This paper presents a MATLAB implementation of the material-field series-expansion (MFSE) topo-logy optimization method. The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology. With the series-expansion method for bounded fields, this material field is described with the characteristic base functions and the corresponding coefficients. Compared with the conventional density-based method, the MFSE method decouples the topological description and the finite element discretization, and greatly reduces the number of design variables after dimensionality reduction. Other features of this method include inherent control on structural topological complexity, crisp structural boundary description, mesh independence, and being free from the checkerboard pattern. With the focus on the implementation of the MFSE method, the present MATLAB code uses the maximum stiffness optimization problems solved with a gradient-based optimizer as examples. The MATLAB code consists of three parts, namely, the main program and two subroutines (one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer). The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail. The code is intended for researchers who are interested in this method and want to get started with it quickly. It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.

关键词： MATLAB implementation     topology optimization     material-field series-expansion method     bounded material field     dimensionality reduction    

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Manufacturing cost constrained topology optimization for additive manufacturing

Jikai LIU, Qian CHEN, Xuan LIANG, Albert C. TO

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 213-221 doi: 10.1007/s11465-019-0536-z

摘要： This paper presents a manufacturing cost constrained topology optimization algorithm considering the laser powder bed additive manufacturing process. Topology optimization for additive manufacturing was recently extensively studied, and many related topics have been addressed. However, metal additive manufacturing is an expensive process, and the high manufacturing cost severely hinders the widespread use of this technology. Therefore, the proposed algorithm in this research would provide an opportunity to balance the manufacturing cost while pursuing the superior structural performance through topology optimization. Technically, the additive manufacturing cost model for laser powder bed-based process is established in this paper and real data is collected to support this model. Then, this cost model is transformed into a level set function-based expression, which is integrated into the level set topology optimization problem as a constraint. Therefore, by properly developing the sensitivity result, the metallic additive manufacturing part can be optimized with strictly constrained manufacturing cost. Effectiveness of the proposed algorithm is proved by numerical design examples.

关键词： topology optimization     manufacturing cost     additive manufacturing     powder bed    

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Efficient, high-resolution topology optimization method based on convolutional neural networks

Liang XUE, Jie LIU, Guilin WEN, Hongxin WANG

《机械工程前沿（英文）》 2021年 第16卷 第1期   页码 80-96 doi: 10.1007/s11465-020-0614-2

摘要： Topology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the super-resolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

关键词： topology optimization     convolutional neural network     high resolution     density-based    

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Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

《机械工程前沿（英文）》 2020年 第15卷 第3期   页码 390-405 doi: 10.1007/s11465-020-0588-0

摘要： The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

关键词： level set method     topology optimization     density-based method     level set band    

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标题 作者 时间 类型 操作

Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

期刊论文

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

期刊论文

Massively efficient filter for topology optimization based on the splitting of tensor product structure

期刊论文

Isogeometric topology optimization based on energy penalization for symmetric structure

Xianda XIE, Shuting WANG, Ming YE, Zhaohui XIA, Wei ZHAO, Ning JIANG, Manman XU

期刊论文

从计算机辅助设计到人辅助设计——一种等几何拓扑优化方法

王英俊, 肖蜜, 夏兆辉, 李培根, 高亮

期刊论文

Implicit Heaviside filter with high continuity based on suitably graded THB splines

期刊论文

Solving topology optimization problems by the Guide-Weight method

Xinjun LIU, Zhidong LI, Liping WANG, Jinsong WANG

期刊论文

Multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

期刊论文

Controlling interstory drift ratio profiles via topology optimization strategies

期刊论文

Robust topology optimization of multi-material lattice structures under material and load uncertainties

Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN

期刊论文

A MATLAB code for the material-field series-expansion topology optimization method

期刊论文

Manufacturing cost constrained topology optimization for additive manufacturing

Jikai LIU, Qian CHEN, Xuan LIANG, Albert C. TO

期刊论文

Efficient, high-resolution topology optimization method based on convolutional neural networks

Liang XUE, Jie LIU, Guilin WEN, Hongxin WANG

期刊论文

Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

期刊论文