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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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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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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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Topology optimization of piezoelectric bi-material actuators with velocity feedback control

Mariana MORETTI, Emílio C. N. SILVA

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 190-200 doi: 10.1007/s11465-019-0537-y

摘要： In recent years, the new technologies and discoveries on manufacturing materials have encouraged researchers to investigate the appearance of material properties that are not naturally available. Materials featuring a specific stiffness, or structures that combine non-structural and structural functions are applied in the aerospace, electronics and medical industry fields. Particularly, structures designed for dynamic actuation with reduced vibration response are the focus of this work. The bi-material and multifunctional concepts are considered for the design of a controlled piezoelectric actuator with vibration suppression by means of the topology optimization method (TOM). The bi-material piezoelectric actuator (BPEA) has its metallic host layer designed by the TOM, which defines the structural function, and the electric function is given by two piezo-ceramic layers that act as a sensor and an actuator coupled with a constant gain active velocity feedback control (AVFC). The AVFC, provided by the piezoelectric layers, affects the structural damping of the system through the velocity state variables readings in time domain. The dynamic equation analyzed throughout the optimization procedure is fully elaborated and implemented. The dynamic response for the rectangular four-noded FE analysis is obtained by the Newmark’s time-integration method, which is applied to the physical and the adjoint systems, given that the adjoint formulation is needed for the sensitivity analysis. A gradient-based optimization method is applied to minimize the displacement energy output measured at a predefined degree-of-freedom of the BPEA when a transient mechanical load is applied. Results are obtained for different control gain values to evaluate their influence on the final topology.

关键词： topology optimization method     bi-material piezoactuator     active velocity feedback control     time-domain transient analysis     host structure design     vibration suppression    

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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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Module-based method for design and analysis of reconfigurable parallel robots

Fengfeng XI, Yuwen LI, Hongbo WANG

《机械工程前沿（英文）》 2011年 第6卷 第2期   页码 151-159 doi: 10.1007/s11465-011-0121-6

摘要：

This paper presents a method for the design and analysis of reconfigurable parallel robots. The inherent modularity in a parallel robot lends itself as a natural candidate for reconfiguration. By taking the branches as building blocks, many modular parallel robots can be constructed, from which a reconfigurable parallel robot can be realized. Among three types of reconfigurations, namely, geometry morphing, topology morphing, and group morphing, the method presented here is for the last two reconfigurations, thereby advancing the current research that is mainly limited to geometry morphing. It is shown that the module-based method not only provides a systematic way of designing a reconfigurable parallel robot, but also offers a unified modeling for robot analysis. Two examples are provided, one showing the topology morphing and the other showing the group morphing.

关键词： reconfigurable parallel robot     topology morphing     group morphing    

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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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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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Data-driven distribution network topology identification considering correlated generation power of distributed

《能源前沿（英文）》 2022年 第16卷 第1期   页码 121-129 doi: 10.1007/s11708-021-0780-x

摘要： This paper proposes a data-driven topology identification method for distribution systems with distributed energy resources (DERs). First, a neural network is trained to depict the relationship between nodal power injections and voltage magnitude measurements, and then it is used to generate synthetic measurements under independent nodal power injections, thus eliminating the influence of correlated nodal power injections on topology identification. Second, a maximal information coefficient-based maximum spanning tree algorithm is developed to obtain the network topology by evaluating the dependence among the synthetic measurements. The proposed method is tested on different distribution networks and the simulation results are compared with those of other methods to validate the effectiveness of the proposed method.

关键词： power distribution network     data-driven     topology identification     distributed energy resource     maximal information coefficient    

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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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Connected morphable components-based multiscale topology optimization

Jiadong DENG, Claus B. W. PEDERSEN, Wei CHEN

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 129-140 doi: 10.1007/s11465-019-0532-3

摘要： The advances of manufacturing techniques, such as additive manufacturing, have provided unprecedented opportunities for producing multiscale structures with intricate latticed/cellular material microstructures to meet the increasing demands for parts with customized functionalities. However, there are still difficulties for the state-of-the-art multiscale topology optimization (TO) methods to achieve manufacturable multiscale designs with cellular materials, partially due to the disconnectivity issue when tiling material microstructures. This paper attempts to address the disconnectivity issue by extending component-based TO methodology to multiscale structural design. An effective linkage scheme to guarantee smooth transitions between neighboring material microstructures (unit cells) is devised and investigated. Associated with the advantages of components-based TO, the number of design variables is greatly reduced in multiscale TO design. Homogenization is employed to calculate the effective material properties of the porous materials and to correlate the macro/structural scale with the micro/material scale. Sensitivities of the objective function with respect to the geometrical parameters of each component in each material microstructure have been derived using the adjoint method. Numerical examples demonstrate that multiscale structures with well-connected material microstructures or graded/layered material microstructures are realized.

关键词： multiscale topology optimization     morphable component     material microstructure     homogenization    

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Feasible workspace regions for general two-revolute manipulator

Conghui LIANG, Marco CECCARELLI

《机械工程前沿（英文）》 2011年 第6卷 第4期   页码 397-408 doi: 10.1007/s11465-011-0228-9

摘要：

In this paper, a topology is presented for feasible workspace regions in general two-revolute manipulators. The design problem and concept of feasible workspace regions have been discussed as linked to each other. Design equations are formulated by arbitrarily prescribing four workspace boundary points. The so-called feasible workspace regions are the intersection of three different sub-regions, which are given by constraint curves as function of the relative positions of three workspace boundary points. By using a parametric study, all topologies for three sub-regions are figured out. Corresponding areas in cross section plane are determined for prescribing the position of a feasible workspace point as function of the topology for sub-regions. A classification has been proposed to determine and to characterize the combination of the topologies for those sub-regions. All topologies for feasible workspace regions are figured out and they are discussed as a design tool. Three general cases are analyzed in details to characterize workspace design capabilities for general two-revolute manipulators.

关键词： workspace     two-revolute manipulators     topology analysis     design    

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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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标题 作者 时间 类型 操作

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

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

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

Topology optimization of piezoelectric bi-material actuators with velocity feedback control

Mariana MORETTI, Emílio C. N. SILVA

期刊论文

Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

期刊论文

Module-based method for design and analysis of reconfigurable parallel robots

Fengfeng XI, Yuwen LI, Hongbo WANG

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

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

Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN

期刊论文

Data-driven distribution network topology identification considering correlated generation power of distributed

期刊论文

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

期刊论文

Connected morphable components-based multiscale topology optimization

Jiadong DENG, Claus B. W. PEDERSEN, Wei CHEN

期刊论文

Feasible workspace regions for general two-revolute manipulator

Conghui LIANG, Marco CECCARELLI

期刊论文

Controlling interstory drift ratio profiles via topology optimization strategies

期刊论文