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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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Thermo-elastic extended meshfree method for fracture without crack tip enrichment

A. ASADPOUR

《结构与土木工程前沿（英文）》 2015年 第9卷 第4期   页码 441-447 doi: 10.1007/s11709-015-0319-5

摘要： This is the first manuscript presenting an extended meshfree method for thermo- elastic fracture which does not exploit a crack tip enrichment. The crack is modeled by partition of unity enrichment of the displacement and temperature field. Only a step function is employed that facilitates the implementation. To ensure that crack tip is at the correct position, a Lagrange multiplier field ahead of the crack tip is introduced along a line. The Lagrange multiplier nodal parameters are discretised with the available meshfree functions. Two benchmark examples illustrate the efficiency of the method.

关键词： meshfree method     thermo-elasticity    

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A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

Dongdong WANG, Jiarui WANG, Junchao WU, Junjun DENG, Ming SUN

《结构与土木工程前沿（英文）》 2019年 第13卷 第2期   页码 337-352 doi: 10.1007/s11709-018-0467-5

摘要： A three-dimensional two-level gradient smoothing meshfree method is presented for rainfall induced landslide simulations. The two-level gradient smoothing for meshfree shape function is elaborated in the three-dimensional Lagrangian setting with detailed implementation procedure. It is shown that due to the successive gradient smoothing operation without the requirement of derivative computation in the present formulation, the two-level smoothed gradient of meshfree shape function is capable of achieving a given influence domain more efficiently than the standard gradient of meshfree shape function. Subsequently, the two-level smoothed gradient of meshfree shape function is employed to discretize the weak form of coupled rainfall seepage and soil motion equations in a nodal integration format, as provides an efficient three-dimensional regularized meshfree formulation for large deformation rainfall induced landslide simulations. The exponential damage and pressure dependent plasticity relationships are utilized to describe the failure evolution in landslides. The plastic response of soil is characterized by the true effective stress measure, which is updated according to the rotationally neutralized objective integration algorithm. The effectiveness of the present three-dimensional two-level gradient smoothing meshfree method is demonstrated through numerical examples.

关键词： meshfree method     landslide     rainfall     three-dimensional two-level gradient smoothing     nodal integration    

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A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

《结构与土木工程前沿（英文）》 2019年 第13卷 第2期   页码 380-396 doi: 10.1007/s11709-018-0471-9

摘要： In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.

关键词： phase field method     FEniCS     brittle fracture     crack propagation     variational theory of fracture    

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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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Non-convex sparse optimization-based impact force identification with limited vibration measurements

《机械工程前沿（英文）》 2023年 第18卷 第3期 doi: 10.1007/s11465-023-0762-2

摘要： Impact force identification is important for structure health monitoring especially in applications involving composite structures. Different from the traditional direct measurement method, the impact force identification technique is more cost effective and feasible because it only requires a few sensors to capture the system response and infer the information about the applied forces. This technique enables the acquisition of impact locations and time histories of forces, aiding in the rapid assessment of potentially damaged areas and the extent of the damage. As a typical inverse problem, impact force reconstruction and localization is a challenging task, which has led to the development of numerous methods aimed at obtaining stable solutions. The classical ℓ2 regularization method often struggles to generate sparse solutions. When solving the under-determined problem, ℓ2 regularization often identifies false forces in non-loaded regions, interfering with the accurate identification of the true impact locations. The popular ℓ1 sparse regularization, while promoting sparsity, underestimates the amplitude of impact forces, resulting in biased estimations. To alleviate such limitations, a novel non-convex sparse regularization method that uses the non-convex ℓ1−2 penalty, which is the difference of the ℓ1 and ℓ2 norms, as a regularizer, is proposed in this paper. The principle of alternating direction method of multipliers (ADMM) is introduced to tackle the non-convex model by facilitating the decomposition of the complex original problem into easily solvable subproblems. The proposed method named ℓ1−2-ADMM is applied to solve the impact force identification problem with unknown force locations, which can realize simultaneous impact localization and time history reconstruction with an under-determined, sparse sensor configuration. Simulations and experiments are performed on a composite plate to verify the identification accuracy and robustness with respect to the noise of the ℓ1−2-ADMM method. Results indicate that compared with other existing regularization methods, the ℓ1−2-ADMM method can simultaneously reconstruct and localize impact forces more accurately, facilitating sparser solutions, and yielding more accurate results.

关键词： impact force identification     inverse problem     sparse regularization     under-determined condition     alternating direction method of multipliers    

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

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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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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拟共形映射图像特征匹配 Article

Chun-xue WANG, Li-gang LIU

《信息与电子工程前沿（英文）》 2017年 第18卷 第5期   页码 644-657 doi: 10.1631/FITEE.1500411

摘要： 本文展示了一种从两幅图像的候选匹配点集中选取几何一致匹配点组并排除离群数据（outliers）的全自动方法。在给出包含离群数据的尺度不变特征转换（Scale-invariant feature transform, SIFT）候选匹配点集合的前提下，本文旨在通过在全部微分同胚空间中搜索映射，选择匹配点子集以保留更多的几何信息。该问题可转化为包含Beltrami系数（BC）项和拟共形映射的约束最优化问题。该问题可通过变量分裂迭代算法有效求解。算法的迭代涉及线性系统和线性约束凸二次规划两子问题。本文算法简洁，对离群数据有鲁棒性。实验结果表明，与现有方法相比，本算法能够获得更多的正确匹配点。

关键词： 特征匹配；拟共形映射；分裂算法    

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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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dynamic analysis of functionally graded fluid-infiltrated porous skew and elliptical nanoplates using an isogeometric

《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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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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埋地热油管道运行参数的准周期变化

崔慧

《中国工程科学》 2006年 第8卷 第1期   页码 51-53

摘要：

从理论上分析了在大气温度变化的影响下埋地热油管道的运行参数以及周围土壤环境均随季节变化而呈现准周期变化规律，在分析大量实际运行数据的基础上，进一步验证了该规律的合理性，建议在有关管道的节能降耗、优化运行以及经济清蜡等问题的研究中，应该考虑运行参数的滞后影响。

关键词： 热油管道     大气温度     土壤环境     准周期    

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标题 作者 时间 类型 操作

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

Hanjie ZHANG,Junzhao WU,Dongdong WANG

期刊论文

Thermo-elastic extended meshfree method for fracture without crack tip enrichment

A. ASADPOUR

期刊论文

A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

Dongdong WANG, Jiarui WANG, Junchao WU, Junjun DENG, Ming SUN

期刊论文

A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

期刊论文

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文

Non-convex sparse optimization-based impact force identification with limited vibration measurements

期刊论文

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

Yingjun WANG,David J. BENSON

期刊论文

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

Zhen-Pei WANG, Zhifeng XIE, Leong Hien POH

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

拟共形映射图像特征匹配

Chun-xue WANG, Li-gang LIU

期刊论文

Robust isogeometric topology optimization for piezoelectric actuators with uniform manufacturability

期刊论文

dynamic analysis of functionally graded fluid-infiltrated porous skew and elliptical nanoplates using an isogeometric

期刊论文

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

期刊论文

Isogeometric analysis based on geometric reconstruction models

期刊论文

埋地热油管道运行参数的准周期变化

崔慧

期刊论文