To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Rei...To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Reissner–Mindlin shell theory.By utilizing toric surface patches,both trimmed and untrimmed elements of the CAD surfaces are represented through a unified geometric framework,ensuring continuity and an accurate geometric description.Toric-Bernstein basis functions are employed to accurately interpolate the geometry and displacement of the trimmed shell.For singularities and corner points on the toric surface,the normal vector is defined as the unit directional vector from the center of curvature to the corresponding control point.Several numerical examples of polygonal shells are presented to evaluate the effectiveness and robustness of the proposed method.This approach significantly simplifies the treatment of trimmed shell IGA and provides a promising solution for simulating complex shell structures with intricate boundaries.展开更多
In this paper,Isogeometric analysis(IGA)is effectively integrated with machine learning(ML)to investigate the bearing capacity of strip footings in layered soil profiles,with a focus on a sand-over-clay configuration....In this paper,Isogeometric analysis(IGA)is effectively integrated with machine learning(ML)to investigate the bearing capacity of strip footings in layered soil profiles,with a focus on a sand-over-clay configuration.The study begins with the generation of a comprehensive dataset of 10,000 samples from IGA upper bound(UB)limit analyses,facilitating an in-depth examination of various material and geometric conditions.A hybrid deep neural network,specifically the Whale Optimization Algorithm-Deep Neural Network(WOA-DNN),is then employed to utilize these 10,000 outputs for precise bearing capacity predictions.Notably,the WOA-DNN model outperforms conventional ML techniques,offering a robust and accurate prediction tool.This innovative approach explores a broad range of design parameters,including sand layer depth,load-to-soil unit weight ratio,internal friction angle,cohesion,and footing roughness.A detailed analysis of the dataset reveals the significant influence of these parameters on bearing capacity,providing valuable insights for practical foundation design.This research demonstrates the usefulness of data-driven techniques in optimizing the design of shallow foundations within layered soil profiles,marking a significant stride in geotechnical engineering advancements.展开更多
This paper presents,for the first time,an effective numerical approach based on the isogeometric analysis(IGA)and the six-variable quasi-three dimensional(3D)higher-order shear deformation theory(HSDT)to study the fre...This paper presents,for the first time,an effective numerical approach based on the isogeometric analysis(IGA)and the six-variable quasi-three dimensional(3D)higher-order shear deformation theory(HSDT)to study the free vibration characteristics of functionally-graded(FG)graphene origami(GOri)-enabled auxetic metamaterial(GOEAM)plates submerged in a fluid medium.The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors.The velocity potential function and Bernoulli's equation are used to derive the hydrodynamic pressure acting on the plate surface.Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects.The plates are composed of multilayer GOEAMs,with the GOri content varying through the plate's thickness in a layer-wise manner.This design results in graded auxetic growth.The material properties are evaluated by mixing rules and a genetic programming(GP)-assisted micromechanical model.The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton's principle.After validating the convergence and accuracy of the present model,a comprehensive parametric study is carried out to examine the effects of the GOri content,GOri distribution pattern,GOri folding degree,fluid level,immersed depth,and geometric parameter on the natural frequencies of the FG-GOEAM plates.The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10,and then stabilize after the layer number reaches 10.Besides,in general,the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases,while decreases when the GOri folding degree increases.Some additional findings related to the numerical results are presented in the conclusions.It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium.展开更多
This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,whic...This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.展开更多
High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric fini...High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method.Firstly,the physical field is approximated by uniform B-spline interpolation,while geometry is represented by non-uniform rational B-spline interpolation.By introducing a transformation matrix,elements of types C^(0)and C^(1)are constructed in the isogeometric finite element method.Subsequently,the corresponding calculation formats for one-dimensional bars,beams,and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping.The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis,eliminating the need for mesh generation and maintaining flexibility in element construc-tion.Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method.Finally,the test results of several examples show that:(1)Under the same degree and element node numbers,the constructed elements are almost consistent with the results obtained by traditional finite element method;(2)For bar problems with large local field variations and beam problems with variable cross-sections,high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method;(3)The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom,while as degrees of freedom increase,the computational efficiency between the two is similar.展开更多
Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Eule...Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Euler–Bernoulli beam model was utilized,and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral constitution.The governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary conditions.The framework was verified and utilized to analyze the microbeam’s static and dynamic mechanical responses.The present work showed great potential for modeling various types of functionally graded microstructures.展开更多
A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization...A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.展开更多
This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcathete...This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcatheter heart valve replacement(TAVR)procedures.In order to facilitate this exploration,it derives pertinent formulas for 3D multi-material isogeometric hyperelastic analysis based on Hounsfield unit(HU)values,thereby unlocking foundational capabilities for isogeometric analysis in calcified aortic valves.A series of uniaxial and biaxial tensile tests is executed to obtain an accurate constitutive model for calcified active valves.To mitigate discretization errors,methodologies for reconstructing volumetric parametric models,integrating both geometric and material attributes,are introduced.Applying these analytical formulas,constitutive models,and precise analytical models to isogeometric analyses of calcified valves,the research ascertains their close alignment with experimental results through the close fit in displacement-stress curves,compellingly validating the accuracy and reliability of the method.This study presents a step-by-step approach to analyzing themechanical characteristics of patient-specific valves obtained fromCT images,holding significant clinical implications and assisting in the selection of treatment strategies and surgical intervention approaches in TAVR procedures.展开更多
This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstr...This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.展开更多
Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of rob...Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of robust com-putational methods.This paper introduces a Conditional Generation Adversarial Network Isogeometric Analysis(CGAN-IGA)to assess the uncertainty of dielectric solids’mechanical characteristics.IGA is utilized for the precise computation of electric potentials in dielectric,piezoelectric,and flexoelectric materials,leveraging its advantage of integrating seamlessly with Computer-Aided Design(CAD)models to maintain exact geometrical fidelity.The CGAN method is highly efficient in generating models for piezoelectric and flexoelectric materials,specifically adapting to targeted design requirements and constraints.Then,the CGAN-IGA is adopted to calculate the electric potential of optimum models with different parameters to accelerate uncertainty quantification processes.The accuracy and feasibility of this method are verified through numerical experiments presented herein.展开更多
Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a thre...Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.展开更多
Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method ba...Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.展开更多
In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral c...In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.展开更多
We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,an...We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,and the mixed method employs both displacement and pressure unknowns.As benchmarks for what might be considered acceptable accuracy,we employ constant-pressure Abaqus finite elements that are widely used in engineering applications.As a basis of comparisons,we present results for compressible elasticity.All the methods were completely satisfactory for the compressible case.However,results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case.The results for the mixed methods behaved very well for two of the problems we studied,achieving levels of accuracy very similar to those for the compressible case.The third problem,which we consider a“torture test”presented a more complex story for the mixed methods in the nearly-incompressible case.展开更多
Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM...Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM)is applied to compute the unknown structural responses in TO.However,several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO.In order to eliminate the negative influence of the FEM on TO,IsoGeometric Analysis(IGA)has become a promising alternative due to its unique feature that the Computer-Aided Design(CAD)model and Computer-Aided Engineering(CAE)model can be unified into a same mathematical model.In the paper,the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization(ITO)in methods and applications.Finally,some prospects for the developments of ITO in the future are also presented.展开更多
Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a compr...Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.展开更多
Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.A...Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.Adopting a NURBSbased parametric modelling scheme with a small number of design variables,the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method,and demonstrated in this work to give high accuracy and efficiency.Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis,in contrast to the generally complex procedures of typical shape and size sensitivity approaches.展开更多
In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature...In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.展开更多
Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is amo...Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.展开更多
This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented ...This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented to transform a prototype microstructure(PM)for obtaining a series of graded microstructures(GMs),where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability.For the macro scale calculation,the effective mechanical properties can be estimated by means of the numerical homogenization method.By adopting identical non-uniform rational basis splines(NURBS)as basis functions for both parameterized level set model and isogeometric calculation model,the isogeometric analysis(IGA)is integrated into the level set method,which contributes to improving the accuracy and efficiency.Numerical examples demonstrate that,the proposed method is effective in improving the performance and manufacturability.展开更多
基金the National Key Research and Development Projects(Grant Nos.2021YFB3300601,2021YFB3300603,2021YFB3300604)the Fundamental Research Funds for the Central Universities(No.DUT22QN241)is acknowledged.
文摘To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Reissner–Mindlin shell theory.By utilizing toric surface patches,both trimmed and untrimmed elements of the CAD surfaces are represented through a unified geometric framework,ensuring continuity and an accurate geometric description.Toric-Bernstein basis functions are employed to accurately interpolate the geometry and displacement of the trimmed shell.For singularities and corner points on the toric surface,the normal vector is defined as the unit directional vector from the center of curvature to the corresponding control point.Several numerical examples of polygonal shells are presented to evaluate the effectiveness and robustness of the proposed method.This approach significantly simplifies the treatment of trimmed shell IGA and provides a promising solution for simulating complex shell structures with intricate boundaries.
文摘In this paper,Isogeometric analysis(IGA)is effectively integrated with machine learning(ML)to investigate the bearing capacity of strip footings in layered soil profiles,with a focus on a sand-over-clay configuration.The study begins with the generation of a comprehensive dataset of 10,000 samples from IGA upper bound(UB)limit analyses,facilitating an in-depth examination of various material and geometric conditions.A hybrid deep neural network,specifically the Whale Optimization Algorithm-Deep Neural Network(WOA-DNN),is then employed to utilize these 10,000 outputs for precise bearing capacity predictions.Notably,the WOA-DNN model outperforms conventional ML techniques,offering a robust and accurate prediction tool.This innovative approach explores a broad range of design parameters,including sand layer depth,load-to-soil unit weight ratio,internal friction angle,cohesion,and footing roughness.A detailed analysis of the dataset reveals the significant influence of these parameters on bearing capacity,providing valuable insights for practical foundation design.This research demonstrates the usefulness of data-driven techniques in optimizing the design of shallow foundations within layered soil profiles,marking a significant stride in geotechnical engineering advancements.
基金Project supported by the National Natural Science Foundation of China(Nos.12162004 and 11562001)the Doctoral Research Start-up Fund Project at University of South China(No.Y00043-13)。
文摘This paper presents,for the first time,an effective numerical approach based on the isogeometric analysis(IGA)and the six-variable quasi-three dimensional(3D)higher-order shear deformation theory(HSDT)to study the free vibration characteristics of functionally-graded(FG)graphene origami(GOri)-enabled auxetic metamaterial(GOEAM)plates submerged in a fluid medium.The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors.The velocity potential function and Bernoulli's equation are used to derive the hydrodynamic pressure acting on the plate surface.Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects.The plates are composed of multilayer GOEAMs,with the GOri content varying through the plate's thickness in a layer-wise manner.This design results in graded auxetic growth.The material properties are evaluated by mixing rules and a genetic programming(GP)-assisted micromechanical model.The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton's principle.After validating the convergence and accuracy of the present model,a comprehensive parametric study is carried out to examine the effects of the GOri content,GOri distribution pattern,GOri folding degree,fluid level,immersed depth,and geometric parameter on the natural frequencies of the FG-GOEAM plates.The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10,and then stabilize after the layer number reaches 10.Besides,in general,the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases,while decreases when the GOri folding degree increases.Some additional findings related to the numerical results are presented in the conclusions.It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium.
基金support from the National Natural Science Foundation of China(12272075)Liao Ning Revitalization Talents Program(XLYC2001003,XLYC1907119)+1 种基金Fundamental Research Funds for the Central Universities(DUT22QN238)Program for Changjiang Scholars,Innovative Research Team in University(PCSIRT)and 111 Project(B14013)is gratefully acknowledged.
文摘This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.
基金funded by the Zhejiang Province Science and Technology Plan Project under grant number 2023C01069the Hebei Provincial Program on Key Basic Research Project under grant number 23311808Dthe Wenzhou Major Science and Technology Innovation Project of China under grant number ZG2022004。
文摘High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method.Firstly,the physical field is approximated by uniform B-spline interpolation,while geometry is represented by non-uniform rational B-spline interpolation.By introducing a transformation matrix,elements of types C^(0)and C^(1)are constructed in the isogeometric finite element method.Subsequently,the corresponding calculation formats for one-dimensional bars,beams,and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping.The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis,eliminating the need for mesh generation and maintaining flexibility in element construc-tion.Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method.Finally,the test results of several examples show that:(1)Under the same degree and element node numbers,the constructed elements are almost consistent with the results obtained by traditional finite element method;(2)For bar problems with large local field variations and beam problems with variable cross-sections,high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method;(3)The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom,while as degrees of freedom increase,the computational efficiency between the two is similar.
基金support of the present work from the National Natural Science Foundation of China(12172169,12202135,and 12272724)supported by the Fundamental Research Funds for the Central Universities from Hohai University(423142).
文摘Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Euler–Bernoulli beam model was utilized,and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral constitution.The governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary conditions.The framework was verified and utilized to analyze the microbeam’s static and dynamic mechanical responses.The present work showed great potential for modeling various types of functionally graded microstructures.
基金supported by a Major Research Project in Higher Education Institutions in Henan Province,with Project Number 23A560015.
文摘A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.
基金supported by the Natural Science Foundation of China(Project Nos.52075340 and 61972011)the Shanghai Special Research Project on Aging Population and Maternal and Child Health(Project No.2020YJZX0106).
文摘This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcatheter heart valve replacement(TAVR)procedures.In order to facilitate this exploration,it derives pertinent formulas for 3D multi-material isogeometric hyperelastic analysis based on Hounsfield unit(HU)values,thereby unlocking foundational capabilities for isogeometric analysis in calcified aortic valves.A series of uniaxial and biaxial tensile tests is executed to obtain an accurate constitutive model for calcified active valves.To mitigate discretization errors,methodologies for reconstructing volumetric parametric models,integrating both geometric and material attributes,are introduced.Applying these analytical formulas,constitutive models,and precise analytical models to isogeometric analyses of calcified valves,the research ascertains their close alignment with experimental results through the close fit in displacement-stress curves,compellingly validating the accuracy and reliability of the method.This study presents a step-by-step approach to analyzing themechanical characteristics of patient-specific valves obtained fromCT images,holding significant clinical implications and assisting in the selection of treatment strategies and surgical intervention approaches in TAVR procedures.
基金the National Key R&D Program of China(2020YFB1708300)the National Natural Science Foundation of China(52005192)the Project of Ministry of Industry and Information Technology(TC210804R-3).
文摘This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.
文摘Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of robust com-putational methods.This paper introduces a Conditional Generation Adversarial Network Isogeometric Analysis(CGAN-IGA)to assess the uncertainty of dielectric solids’mechanical characteristics.IGA is utilized for the precise computation of electric potentials in dielectric,piezoelectric,and flexoelectric materials,leveraging its advantage of integrating seamlessly with Computer-Aided Design(CAD)models to maintain exact geometrical fidelity.The CGAN method is highly efficient in generating models for piezoelectric and flexoelectric materials,specifically adapting to targeted design requirements and constraints.Then,the CGAN-IGA is adopted to calculate the electric potential of optimum models with different parameters to accelerate uncertainty quantification processes.The accuracy and feasibility of this method are verified through numerical experiments presented herein.
基金support provided by the National Nature Science Foundation of China (Grant Nos.52075340,51875360)Project of Science and Technology Commission of Shanghai Municipality (No.19060502300).
文摘Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.
基金supported by the National Key R&D Program of China(Grant Number 2020YFB1708300)China National Postdoctoral Program for Innovative Talents(Grant Number BX20220124)+1 种基金China Postdoctoral Science Foundation(Grant Number 2022M710055)the New Cornerstone Science Foundation through the XPLORER PRIZE,the Knowledge Innovation Program of Wuhan-Shuguang,the Young Top-Notch Talent Cultivation Program of Hubei Province and the Taihu Lake Innovation Fund for Future Technology(Grant Number HUST:2023-B-7).
文摘Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.
基金The research for this paper was supported by(1)the National Natural Science Foundation of China(Grants Nos.51708429,51708428)the Open Projects Foundation(Grant No.2017-04-GF)of State Key Laboratory for Health and Safety of Bridge Structures+1 种基金Wuhan Institute of Technology Science Found(Grant No.K201734)the science and technology projects of Wuhan Urban and Rural Construction Bureau(Grants Nos.201831,201919).
文摘In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.
基金FF and LDL gratefully acknowledge the financial support of the German Research Foundation(DFG)within the DFG Priority Program SPP 1748“Reliable Simulation Techniques in Solid Mechanics”.AR has been partially supported by the MIUR-PRIN project XFAST-SIMS(No.20173C478 N).
文摘We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,and the mixed method employs both displacement and pressure unknowns.As benchmarks for what might be considered acceptable accuracy,we employ constant-pressure Abaqus finite elements that are widely used in engineering applications.As a basis of comparisons,we present results for compressible elasticity.All the methods were completely satisfactory for the compressible case.However,results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case.The results for the mixed methods behaved very well for two of the problems we studied,achieving levels of accuracy very similar to those for the compressible case.The third problem,which we consider a“torture test”presented a more complex story for the mixed methods in the nearly-incompressible case.
基金Supported by National Key R&D Program of China(Grant No.2020YFB1708304)and Fundamental Research Funds for the Central Universities of the Huazhong University of Science and Technology(Grant No.5003123021)and the Program for HUST Academic Frontier Youth Team(Grant No.2017QYTD04).
文摘Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM)is applied to compute the unknown structural responses in TO.However,several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO.In order to eliminate the negative influence of the FEM on TO,IsoGeometric Analysis(IGA)has become a promising alternative due to its unique feature that the Computer-Aided Design(CAD)model and Computer-Aided Engineering(CAE)model can be unified into a same mathematical model.In the paper,the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization(ITO)in methods and applications.Finally,some prospects for the developments of ITO in the future are also presented.
基金This work was supported by National Natural Science Foundation of China(51705158)the Fundamental Research Funds for the Central Universities(2018MS45)Open Funds of National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials(2018005).
文摘Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.
基金National Natural Science Foundation of China(Grant Nos.51705158 and 51805174)the Fundamental Research Funds for the Central Universities(Grant Nos.2018MS45 and 2019MS059)。
文摘Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.Adopting a NURBSbased parametric modelling scheme with a small number of design variables,the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method,and demonstrated in this work to give high accuracy and efficiency.Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis,in contrast to the generally complex procedures of typical shape and size sensitivity approaches.
文摘In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.
基金Hamid Ghasemi acknowledge the support of the Mechanical Engineering department at Arak University of Technology.Xiaoying Zhuang gratefully acknowledge the financial support by European Research Council for COTOFLEXI project(802205)Harold Park acknowledges the support of the Mechanical Engineering department at Boston University.Timon Rabczuk gratefully acknowledge financial support by the 2019 Foreign Experts Plan of Hebei Province.
文摘Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.
基金National Key R&D Program of China(2018YFB1700803,2018YFB1700804).
文摘This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented to transform a prototype microstructure(PM)for obtaining a series of graded microstructures(GMs),where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability.For the macro scale calculation,the effective mechanical properties can be estimated by means of the numerical homogenization method.By adopting identical non-uniform rational basis splines(NURBS)as basis functions for both parameterized level set model and isogeometric calculation model,the isogeometric analysis(IGA)is integrated into the level set method,which contributes to improving the accuracy and efficiency.Numerical examples demonstrate that,the proposed method is effective in improving the performance and manufacturability.
