The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving ...The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving the Fredholm integral equation to obtain the eigenvalues and eigenfunctions of the covariance functions of the random fields.The collocation method,which has fewer integral operations,is more efficient in accomplishing the task than the timeconsuming Galerkin method,and it is more suitable for engineering applications with complex geometries and a large number of elements.With the help of isogeometric analysis that preserves accurate geometry in analysis,the isogeometric collocation method can efficiently achieve the results with sufficient accuracy.An adaptive moment abscissa is proposed to calculate the coordinates of the collocation points to further improve the accuracy of the collocation method.The adaptive moment abscissae led to more accurate results than the classical Greville abscissae when using the moment parameter optimized with intelligent algorithms.Numerical and engineering examples illustrate the advantages of the proposed isogeometric collocation method based on the adaptive moment abscissae over existing methods in terms of accuracy and efficiency.展开更多
Inspired by the structural adaptations of natural biological organisms,helicoidal composite architectures have shown significant potential for enhancing toughness,strength,and weight efficiency in engineering applicat...Inspired by the structural adaptations of natural biological organisms,helicoidal composite architectures have shown significant potential for enhancing toughness,strength,and weight efficiency in engineering applications.However,temperature and moisture's adverse effects pose challenges during service,potentially compromising their overall performance.This study meticulously analyzes the buckling and vibration behavior of carbon nanotube(CNT)-reinforced bioinspired helicoidal composite plates under different hygrothermal conditions.A novel aspect of this study lies in the proposition of a multiscale analysis combining the analytical and numerical techniques to assess the effects of temperature,moisture,weight fraction of CNTs,layup configurations of bioinspired designs,aspect ratios,loading and boundary conditions,and geometric shapes of bioinspired helicoidal composite structures on their vibration and buckling characteristics.In this context,the stiffness properties are computed with the Halpin-Tsai model,incorporating the size-dependent features of CNTs along with their waviness and agglomeration.In addition,the Chamis micro-mechanical equations are used to determine the elastic properties of individual layers constituting bioinspired composites,considering the effects of temperature and moisture.The kinematics of the laminated bioinspired structures are captured with the third-order shear deformation theory(TSDT)within the isogeometric framework employing the non-uniform rational B-splines(NURBSs)as the basis functions.The isogeometric framework ensures higher-order inter-element continuity and provides an exact geometric representation,offering various advantages over the traditional finite element method.The developed framework is validated against the existing literature,and thereafter several numerical examples are presented,providing valuable insights for the design and optimization of bioinspired composite structures,with potential benefits for various engineering fields,including marine and aerospace sectors.展开更多
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
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
In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a s...In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.展开更多
Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear ...Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.展开更多
A general and new explicit isogeometric topology optimisation approach with moving morphable voids(MMV)is proposed.In this approach,a novel multiresolution scheme with two distinct discretisation levels is developed t...A general and new explicit isogeometric topology optimisation approach with moving morphable voids(MMV)is proposed.In this approach,a novel multiresolution scheme with two distinct discretisation levels is developed to obtain high-resolution designs with a relatively low computational cost.Ersatz material model based on Greville abscissae collocation scheme is utilised to represent both the Young’s modulus of the material and the density field.Two benchmark examples are tested to illustrate the effectiveness of the proposed method.Numerical results show that high-resolution designs can be obtained with relatively low computational cost,and the optimisation can be significantly improved without introducing additional DOFs.展开更多
This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structu...This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structures,are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations.Bezier extraction technique is employed to accelerate the evaluation of NURBS basis functions.We adopt a radial integration method to address the additional domain integrals.The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis.展开更多
This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate ...This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.展开更多
This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced ...This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.展开更多
This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications.In isogeometric analysis,mult...This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications.In isogeometric analysis,multi-patch structure is not easy to achieve high continuity between neighboring patches which will reduce the advantage of isogeometric analysis in a sense.The proposed method can achieve high continuity at surface stitching region with low geometric error,and this technique exploits constructing the approximate surface with several control points are from original surfaces,which guarantees the local feature of the surface can be well-preserved with high precision.With the proposed approximating method,isogeometric analysis results using the new single-patch can be obtained efficiently compared with the original multi-patch structure.Several examples are presented to illustrate the effectiveness,accuracy and efficiency of the proposed method.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.U22A6001 and 52375273)Major Project of Science and Technology Innovation 2030(Grant No.2021ZD0113100)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ24E050005)。
文摘The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving the Fredholm integral equation to obtain the eigenvalues and eigenfunctions of the covariance functions of the random fields.The collocation method,which has fewer integral operations,is more efficient in accomplishing the task than the timeconsuming Galerkin method,and it is more suitable for engineering applications with complex geometries and a large number of elements.With the help of isogeometric analysis that preserves accurate geometry in analysis,the isogeometric collocation method can efficiently achieve the results with sufficient accuracy.An adaptive moment abscissa is proposed to calculate the coordinates of the collocation points to further improve the accuracy of the collocation method.The adaptive moment abscissae led to more accurate results than the classical Greville abscissae when using the moment parameter optimized with intelligent algorithms.Numerical and engineering examples illustrate the advantages of the proposed isogeometric collocation method based on the adaptive moment abscissae over existing methods in terms of accuracy and efficiency.
文摘Inspired by the structural adaptations of natural biological organisms,helicoidal composite architectures have shown significant potential for enhancing toughness,strength,and weight efficiency in engineering applications.However,temperature and moisture's adverse effects pose challenges during service,potentially compromising their overall performance.This study meticulously analyzes the buckling and vibration behavior of carbon nanotube(CNT)-reinforced bioinspired helicoidal composite plates under different hygrothermal conditions.A novel aspect of this study lies in the proposition of a multiscale analysis combining the analytical and numerical techniques to assess the effects of temperature,moisture,weight fraction of CNTs,layup configurations of bioinspired designs,aspect ratios,loading and boundary conditions,and geometric shapes of bioinspired helicoidal composite structures on their vibration and buckling characteristics.In this context,the stiffness properties are computed with the Halpin-Tsai model,incorporating the size-dependent features of CNTs along with their waviness and agglomeration.In addition,the Chamis micro-mechanical equations are used to determine the elastic properties of individual layers constituting bioinspired composites,considering the effects of temperature and moisture.The kinematics of the laminated bioinspired structures are captured with the third-order shear deformation theory(TSDT)within the isogeometric framework employing the non-uniform rational B-splines(NURBSs)as the basis functions.The isogeometric framework ensures higher-order inter-element continuity and provides an exact geometric representation,offering various advantages over the traditional finite element method.The developed framework is validated against the existing literature,and thereafter several numerical examples are presented,providing valuable insights for the design and optimization of bioinspired composite structures,with potential benefits for various engineering fields,including marine and aerospace sectors.
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.
基金supported by the Natural Science Foundation of China(Project Nos.61972011 and 61572056).
文摘In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.
基金support by the Natural Science Foundation of China(Project Nos.61972011 and 61572056).
文摘Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.
基金National Natural Science Foundation of China under Grant Nos.51675525 and 11725211.
文摘A general and new explicit isogeometric topology optimisation approach with moving morphable voids(MMV)is proposed.In this approach,a novel multiresolution scheme with two distinct discretisation levels is developed to obtain high-resolution designs with a relatively low computational cost.Ersatz material model based on Greville abscissae collocation scheme is utilised to represent both the Young’s modulus of the material and the density field.Two benchmark examples are tested to illustrate the effectiveness of the proposed method.Numerical results show that high-resolution designs can be obtained with relatively low computational cost,and the optimisation can be significantly improved without introducing additional DOFs.
基金funded by National Natural Science Foundation of China(NSFC)under Grant Nos.11702238,51904202,and 11902212Nanhu Scholars Program for Young Scholars of XYNU.
文摘This paper presents an isogeometric boundary element method(IGABEM)for transient heat conduction analysis.The Non-Uniform Rational B-spline(NURBS)basis functions,which are used to construct the geometry of the structures,are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations.Bezier extraction technique is employed to accelerate the evaluation of NURBS basis functions.We adopt a radial integration method to address the additional domain integrals.The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis.
基金This research is funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant number 107.02-2019.330.
文摘This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.
基金The authors thank the financial support of National Natural Science Foundation of China(NSFC)under Grant(Nos.51904202,11902212,11901578).
文摘This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.
基金This research was supported by the National Nature Science Foundation of China under Grant Nos.61602138,61772163 and 61761136010the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization(Grant No.U1909210)Zhejiang Provincial Science and Technology Program in China(2018C01030).
文摘This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications.In isogeometric analysis,multi-patch structure is not easy to achieve high continuity between neighboring patches which will reduce the advantage of isogeometric analysis in a sense.The proposed method can achieve high continuity at surface stitching region with low geometric error,and this technique exploits constructing the approximate surface with several control points are from original surfaces,which guarantees the local feature of the surface can be well-preserved with high precision.With the proposed approximating method,isogeometric analysis results using the new single-patch can be obtained efficiently compared with the original multi-patch structure.Several examples are presented to illustrate the effectiveness,accuracy and efficiency of the proposed method.
