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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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Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on

Junjie ZHAN, Yangjun LUO

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 201-212 doi: 10.1007/s11465-019-0529-y

摘要： This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties, which are described using a non-probabilistic bounded field model. Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bounded coefficients on the basis of the series expansion method. Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume. The nest optimization problem is solved using a gradient-based optimization algorithm. Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.

关键词： compliant mechanisms     robust topology optimization     hinges     uncertainty     bounded field    

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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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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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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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Target-oriented robust optimization of a microgrid system investment model

Lanz UY, Patric UY, Jhoenson SIY, Anthony Shun Fung CHIU, Charlle SY

《能源前沿（英文）》 2018年 第12卷 第3期   页码 440-455 doi: 10.1007/s11708-018-0563-1

摘要：

An emerging alternative solution to address energy shortage is the construction of a microgrid system. This paper develops a mixed-integer linear programming microgrid investment model considering multi-period and multi-objective investment setups. It further investigates the effects of uncertain demand by using a target-oriented robust optimization (TORO) approach. The model was validated and analyzed by subjecting it in different scenarios. As a result, it is seen that there are four factors that affect the decision of the model: cost, budget, carbon emissions, and useful life. Since the objective of the model is to maximize the net present value (NPV) of the system, the model would choose to prioritize the least cost among the different distribution energy resources (DER). The effects of load uncertainty was observed through the use of Monte Carlo simulation. As a result, the deterministic model shows a solution that might be too optimistic and might not be achievable in real life situations. Through the application of TORO, a profile of solutions is generated to serve as a guide to the investors in their decisions considering uncertain demand. The results show that pessimistic investors would have lower NPV targets since they would invest more in storage facilities, incurring more electricity stock out costs. On the contrary, an optimistic investor would tend to be aggressive in buying electricity generating equipment to meet most of the demand, however risking more storage stock out costs.

关键词： microgrid     renewable resources     robust optimization     target-oriented robust optimization    

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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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Reliability-based robust design optimization of vehicle components, Part I: Theory

Yimin ZHANG

《机械工程前沿（英文）》 2015年 第10卷 第2期   页码 138-144 doi: 10.1007/s11465-015-0333-2

摘要：

The reliability-based design optimization, the reliability sensitivity analysis and robust design method are employed to present a practical and effective approach for reliability-based robust design optimization of vehicle components. A procedure for reliability-based robust design optimization of vehicle components is proposed. Application of the method is illustrated by reliability-based robust design optimization of axle and spring. Numerical results have shown that the proposed method can be trusted to perform reliability-based robust design optimization of vehicle components.

关键词： vehicle components     reliability-based design optimization     reliability-based sensitivity analysis     multi-objective optimization     robust design    

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Reliability-based robust design optimization of vehicle components, Part II: Case studies

Yimin ZHANG

《机械工程前沿（英文）》 2015年 第10卷 第2期   页码 145-153 doi: 10.1007/s11465-015-0334-1

摘要：

The reliability-based optimization, the reliability-based sensitivity analysis and robust design method are employed to propose an effective approach for reliability-based robust design optimization of vehicle components in Part I. Applications of the method are further discussed for reliability-based robust optimization of vehicle components in this paper. Examples of axles,torsion bar, coil and composite springs are illustrated for numerical investigations. Results have shown the proposed method is an efficient method for reliability-based robust design optimization of vehicle components.

关键词： vehicle axles and springs     reliability-based design optimization     reliability-based sensitivity analysis     multi-objective optimization     robust design    

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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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Distributionally robust optimization of home energy management system based on receding horizon optimization

Jidong WANG, Boyu CHEN, Peng LI, Yanbo CHE

《能源前沿（英文）》 2020年 第14卷 第2期   页码 254-266 doi: 10.1007/s11708-020-0665-4

摘要： This paper investigates the scheduling strategy of schedulable load in home energy management system (HEMS) under uncertain environment by proposing a distributionally robust optimization (DRO) method based on receding horizon optimization (RHO-DRO). First, the optimization model of HEMS, which contains uncertain variable outdoor temperature and hot water demand, is established and the scheduling problem is developed into a mixed integer linear programming (MILP) by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables. Combined with RHO, the MILP is solved in a rolling fashion using the latest update data related to uncertain variables. The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort. Furthermore, compared with the robust optimization (RO) method, the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.

关键词： distributionally robust optimization (DRO)     home energy management system (HEMS)     receding horizon optimization (RHO)     uncertainties    

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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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标题 作者 时间 类型 操作

Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

期刊论文

Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on

Junjie ZHAN, Yangjun LUO

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

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

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

Target-oriented robust optimization of a microgrid system investment model

Lanz UY, Patric UY, Jhoenson SIY, Anthony Shun Fung CHIU, Charlle SY

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

Reliability-based robust design optimization of vehicle components, Part I: Theory

Yimin ZHANG

期刊论文

Reliability-based robust design optimization of vehicle components, Part II: Case studies

Yimin ZHANG

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

Distributionally robust optimization of home energy management system based on receding horizon optimization

Jidong WANG, Boyu CHEN, Peng LI, Yanbo CHE

期刊论文

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文