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Static and dynamic analysis of functionally graded fluid-infiltrated porous skew and elliptical nanoplatesusing an isogeometric approach

《结构与土木工程前沿（英文）》 2023年 第17卷 第3期   页码 477-502 doi: 10.1007/s11709-023-0918-5

摘要： The analysis of static bending and free and forced vibration responses of functionally graded fluid-infiltrated porous (FGFP) skew and elliptical nanoplates placed on Pasternak’s two-parameter elastic foundation is performed for the first time using isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBSs) basis function. Three types of porosity distributions affect the mechanical characteristics of materials: symmetric distribution, upper asymmetric distribution, and lower asymmetric distribution. The stress–strain relationship for Biot porous materials was determined using the elastic theory. The general equations of motion of the nanoplates were established using the four-unknown shear deformation plate theory in conjunction with the nonlocal elastic theory and Hamilton’s principle. A computer program that uses IGA to determine the static bending and free and forced vibration of a nanoplate was developed on MATLAB software platform. The accuracy of the computational program was validated via numerical comparison with confidence assertions. This set of programs presents the influence of the following parameters on the static bending and free and forced vibrations of nanoplates: porosity distribution law, porosity coefficient and geometrical parameters, elastic foundation, deviation angle, nonlocal coefficient, different boundary conditions, and Skempton coefficients. The numerical findings demonstrated the uniqueness of the FGFP plate’s behavior when the porosities are saturated with liquid compared with the case without liquid. The findings of this study have significant implications for engineers involved in the design and fabrication of the aforementioned type of structures. Furthermore, this can form the basis for future research on the mechanical responses of the structures.

关键词： static bending     free and forced vibrations     nonlocal theory     isogeometric analysis     fluid-infiltrated porous nanoplates    

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A frequency error estimation for isogeometric analysis of Kirchhoff–Love cylindrical shells

《结构与土木工程前沿（英文）》 doi: 10.1007/s11709-023-0006-x

摘要： A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions. By analyzing the discrete isogeometric equations with the aid of harmonic wave assumption, the frequency error measures are rationally derived for the quadratic and cubic formulations for Kirchhoff–Love cylindrical shells. In particular, the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shells is naturally embedded into the frequency error measures without the need of explicit frequency expressions, which usually are not trivial for the shell problems. In accordance with these theoretical findings, the 2nd and 4th orders of frequency accuracy are attained for the isogeometric schemes using quadratic and cubic basis functions, respectively. Numerical results not only thoroughly verify the theoretical convergence rates of frequency solutions, but also manifest an excellent magnitude match between numerical and theoretical frequency errors for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells.

关键词： isogeometric analysis     Kirchhoff–Love cylindrical shell     free vibration     frequency error     convergence    

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Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

Hanjie ZHANG,Junzhao WU,Dongdong WANG

《结构与土木工程前沿（英文）》 2015年 第9卷 第4期   页码 405-419 doi: 10.1007/s11709-015-0310-1

摘要： The free vibration analysis of cracked thin plates via a quasi-convex coupled isogeometric-meshfree method is presented. This formulation employs the consistently coupled isogeometric-meshfree strategy where a mixed basis vector of the convex B-splines is used to impose the consistency conditions throughout the whole problem domain. Meanwhile, the rigid body modes related to the mixed basis vector and reproducing conditions are also discussed. The mixed basis vector simultaneously offers the consistent isogeometric-meshfree coupling in the coupled region and the quasi-convex property for the meshfree shape functions in the meshfree region, which is particularly attractive for the vibration analysis. The quasi-convex meshfree shape functions mimic the isogeometric basis function as well as offer the meshfree nodal arrangement flexibility. Subsequently, this approach is exploited to study the free vibration analysis of cracked plates, in which the plate geometry is exactly represented by the isogeometric basis functions, while the cracks are discretized by meshfree nodes and highly smoothing approximation is invoked in the rest of the problem domain. The efficacy of the present method is illustrated through several numerical examples.

关键词： meshfree method     isogeometric analysis     quasi-convex isogeometric-meshfree method     free vibration     cracked thin plate    

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Isogeometric analysis based on geometric reconstruction models

《机械工程前沿（英文）》 2021年 第16卷 第4期   页码 782-797 doi: 10.1007/s11465-021-0648-0

摘要： In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.

关键词： isogeometric analysis     reconstruction model     level set function     trimmed element     point cloud    

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Isogeometric analysis of coupled thermo-elastodynamic problems under cyclic thermal shock

Asghar AMANI DASHLEJEH

《结构与土木工程前沿（英文）》 2019年 第13卷 第2期   页码 397-405 doi: 10.1007/s11709-018-0473-7

摘要： The isogeometric analysis (IGA) method was extended for the solution of the coupled thermo-elastodynamic equations. The dimensionless formulation was accepted in discretization of the uncoupled and coupled thermoelasticity equations and the Generalized Newmark method was used in the time integration procedure. First, the performance of the proposed method was verified against a two-dimensional benchmark example subjected to constant thermal shock with available exact analytical solutions. Then a two-dimensional half-space benchmark example under thermal shock was solved. Finally, cyclic thermal shock (CTS) loading was applied on the half-space problem. The results dedicated that IGA can be used as a suitable approach in the analysis of the general thermomechanical problems.

关键词： isogeometric analysis     coupled thermo-elastodynamic     dynamic analysis     generalized newmark     cyclic thermal shock    

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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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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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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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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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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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Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

Tran Quoc THAI, Timon RABCZUK, Xiaoying ZHUANG

《结构与土木工程前沿（英文）》 2020年 第14卷 第2期   页码 267-279 doi: 10.1007/s11709-019-0567-x

摘要： We present a cohesive zone model for delamination in thin shells and composite structures. The isogeometric (IGA) thin shell model is based on Kirchhoff-Love theory. Non-Uniform Rational B-Splines (NURBS) are used to discretize the exact mid-surface of the shell geometry exploiting their C -continuity property which avoids rotational degrees of freedom. The fracture process zone is modeled by interface elements with a cohesive law. Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.

关键词： cohesive zone model     IGA     Kirchhoff-Love model     thin shell analysis     delamination    

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An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivityanalysis

Zhen-Pei WANG, Zhifeng XIE, Leong Hien POH

《机械工程前沿（英文）》 2020年 第15卷 第2期   页码 279-293 doi: 10.1007/s11465-019-0575-5

摘要： In structural design optimization involving transient responses, time integration scheme plays a crucial role in sensitivity analysis because it affects the accuracy and stability of transient analysis. In this work, the influence of time integration scheme is studied numerically for the adjoint shape sensitivity analysis of two benchmark transient heat conduction problems within the framework of isogeometric analysis. It is found that (i) the explicit approach ( = 0) and semi-implicit approach with <0.5 impose a strict stability condition of the transient analysis; (ii) the implicit approach ( =1) and semi-implicit approach with > 0.5 are generally preferred for their unconditional stability; and (iii) Crank–Nicolson type approach ( =0.5) may induce a large error for large time-step sizes due to the oscillatory solutions. The numerical results also show that the time-step size does not have to be chosen to satisfy the critical conditions for all of the eigen-frequencies. It is recommended to use for unconditional stability, such that the oscillation condition is much less critical than the Crank–Nicolson scheme, and the accuracy is higher than a fully implicit approach.

关键词： isogeometric shape optimization     design-dependent boundary condition     transient heat conduction     implicit time integration     adjoint method    

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15th International Congress for Stereology and Image Analysis 第十五届国际体视学与图像分析学术会议

会议日期： 2019年05月27日

会议地点： 丹麦/奥胡斯

主办单位： 国际体视学与图像分析学会(ISSIA)

标题 作者 时间 类型 操作

Static and dynamic analysis of functionally graded fluid-infiltrated porous skew and elliptical nanoplatesusing an isogeometric approach

期刊论文

A frequency error estimation for isogeometric analysis of Kirchhoff–Love cylindrical shells

期刊论文

Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

Hanjie ZHANG,Junzhao WU,Dongdong WANG

期刊论文

Isogeometric analysis based on geometric reconstruction models

期刊论文

Isogeometric analysis of coupled thermo-elastodynamic problems under cyclic thermal shock

Asghar AMANI DASHLEJEH

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

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

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

Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

期刊论文

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

期刊论文

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

Tran Quoc THAI, Timon RABCZUK, Xiaoying ZHUANG

期刊论文

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivityanalysis

Zhen-Pei WANG, Zhifeng XIE, Leong Hien POH

期刊论文

15th International Congress for Stereology and Image Analysis 第十五届国际体视学与图像分析学术会议

2019年05月27日

会议信息