The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of ...The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of AI-empowered frameworks,including data-driven methods,physics-informed neural networks,and neural operators.While these approaches have demonstrated significant promise,challenges remain in terms of robustness,generalisation,and computational efficiency.We delineate four promising research directions:(1)Modular neural architectures inspired by traditional computational mechanics,(2)physics informed neural operators for resolution-invariant operator learning,(3)intelligent frameworks for multiphysics and multiscale biomechanics problems,and(4)structural optimisation strategies based on physics constraints and reinforcement learning.These directions represent a shift toward foundational frameworks that combine the strengths of physics and data,opening new avenues for the modelling,simulation,and optimisation of complex physical systems.展开更多
This paper takes the assessment and evaluation of computational mechanics course as the background,and constructs a diversified course evaluation system that is student-centered and integrates both quantitative and qu...This paper takes the assessment and evaluation of computational mechanics course as the background,and constructs a diversified course evaluation system that is student-centered and integrates both quantitative and qualitative evaluation methods.The system not only pays attention to students’practical operation and theoretical knowledge mastery but also puts special emphasis on the cultivation of students’innovative abilities.In order to realize a comprehensive and objective evaluation,the assessment and evaluation method of the entropy weight model combining TOPSIS(Technique for Order Preference by Similarity to Ideal Solution)multi-attribute decision analysis and entropy weight theory is adopted,and its validity and practicability are verified through example analysis.This method can not only comprehensively and objectively evaluate students’learning outcomes,but also provide a scientific decision-making basis for curriculum teaching reform.The implementation of this diversified course evaluation system can better reflect the comprehensive ability of students and promote the continuous improvement of teaching quality.展开更多
Jumping robots are highly capable of overcoming obstacles.However,their explosive force,short duration,and variable trajectories pose significant challenges in achieving stable landings in complex environments.Traditi...Jumping robots are highly capable of overcoming obstacles.However,their explosive force,short duration,and variable trajectories pose significant challenges in achieving stable landings in complex environments.Traditional approaches rely heavily on sophisticated algorithms and electronic sensor feedback systems to ensure landing stability,which increases the implementation complexity.Inspired by the process by which humans complete jumps and achieve stable landings in complex environments,this study proposes a novel landing control method for jumping robots.By designing a mechanically coupled perception-control structure based on mechanical logic computing,the robot simulates the real-time transmission of neural signals triggered by the ground reaction force(GRF)in human reflex loops,thereby simplifying traditional control approaches.Through the collaboration of a flexible mechanical spine and a bistable foot module,the robot achieves an average height of 16.8 cm and a distance of 25.36 cm in consecutive stable jumps.It also demonstrates reliable landing performance on challenging terrain including slopes and cobblestone surfaces.This paper proposes a novel landing control method for jumping robots that simplifies traditional control approaches.The method enables stable landings on complex terrain through a mechanically coupled perception-control structure.This approach has potential applications in tasks requiring mobility over uneven terrain,such as search and rescue.展开更多
In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to...In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.展开更多
Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles（MAVs） design,we propose a comprehensive computational framework,whic...Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles（MAVs） design,we propose a comprehensive computational framework,which integrates aerodynamics,flight dynamics,vehicle stability and maneuverability.This framework consists of（1） a Navier-Stokes unsteady aerodynamic model;（2） a linear finite element model for structural dynamics;（3） a fluidstructure interaction（FSI） model for coupled flexible wing aerodynamics aeroelasticity;（4） a free-flying rigid body dynamic（RBD） model utilizing the Newtonian-Euler equations of 6DoF motion;and（5） flight simulator accounting for realistic wing-body morphology,flapping-wing and body kinematics,and a coupling model accounting for the nonlinear 6DoF flight dynamics and stability of insect flapping flight.Results are presented based on hovering aerodynamics with rigid and flexible wings of hawkmoth and fruitfly.The present approach can support systematic analyses of bio- and bio-inspired flight.展开更多
Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularl...Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.展开更多
Most of granular materials are highly heteroge- neous, composed of voids and particles with different sizes and shapes. Geological matter, soil and clay in nature, geo-structure, concrete, etc. are practical ex- ample...Most of granular materials are highly heteroge- neous, composed of voids and particles with different sizes and shapes. Geological matter, soil and clay in nature, geo-structure, concrete, etc. are practical ex- amples among them. From the microscopic view, a lo- cal region in the medium is occupied by particles with small but finite sizes and granular material is naturally modeled as an assembly of discrete particles in contacts On the other hand, the local region is identified with a material point in the overall structure and this discon- tinuous medium can then be represented by an effective continuum on the macroscopic level展开更多
This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need muc...This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.展开更多
We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure tha...We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure that is advantageous in not requiring repeated forward model solves andhas good scalability to large number of differential operators. However it has strict data typerequirements needing the ability to directly represent the operators through the available data.The second is a Bayesian inference framework highly valuable for providing uncertaintyquantification, and flexible for accommodating sparse and noisy data that may also be indirectquantities of interest. However, it also requires repeated forward solutions of the PDE modelswhich is expensive and hinders scalability. We provide illustrations of results on a model problemfor pattern formation dynamics, and discuss merits of the presented methods.展开更多
This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to o...This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to obtain a static equilibrium state of an elastic structure. Preliminary numerical experiments illustrate that, compared with existing methods, the proposed method finds a reasonable solution even if data points distribute coarsely in a given material data set.展开更多
In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes ...In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.展开更多
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi...This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.展开更多
Nature and technology often adopt structures that can be described as tubular helical assemblies.However,the role and mechanisms of these structures remain elusive.In this paper,we study the mechanical response under ...Nature and technology often adopt structures that can be described as tubular helical assemblies.However,the role and mechanisms of these structures remain elusive.In this paper,we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchholf rods,arranged in pairs with opposite chirality and connected by pin joints,both analytically and numerically.We first focus on compression and find that,whereas a single helical rod would buckle,the rods of the assembly deform coherently as stable helical shapes wound around a common axis.Moreover,we investigate the response of the assembly under different boundary conditions,highlighting the emergence of a central region where rods remain circular helices.Secondly,we study the effects of different hypotheses on the elastic properties of rods,i.e.,stress-free rods when straight versus when circular helices,Kirchhoff’s rod model versus Sadowsky’s ribbon model.Summing up,our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods,as well as some interesting features,and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology.展开更多
Using the method presented recently [Phys.Rev.A 77（2008）014306; Phys.Lett.A 369（2007）377], the transformation operator （TO） is explicitly given for teleporting an arbitrary three-qubit state with a six-qubit cha...Using the method presented recently [Phys.Rev.A 77（2008）014306; Phys.Lett.A 369（2007）377], the transformation operator （TO） is explicitly given for teleporting an arbitrary three-qubit state with a six-qubit channel and Bell-state measurements. A criterion on whether such quantum teleportation can be perfectly realized is educed in terms of TO. Moreover, six instantiations on TO and criterion are concisely shown.展开更多
Prevailing ambient wind is the main reason thatcauses inlet flow rate(air mass flow rate)decreasingand air flowing backward to the air-cooled condenserfans upward to the wind,hence a set of wind guidingnets is designe...Prevailing ambient wind is the main reason thatcauses inlet flow rate(air mass flow rate)decreasingand air flowing backward to the air-cooled condenserfans upward to the wind,hence a set of wind guidingnets is designed to improve the detrimental effect.Fig.1 shows four typical units of a 1000MW directair-cooled condenser(DACC)and a set of windguiding nets installed under its edge upward to theambient wind.As shown in Fig.2,the fan inlet flowrate decreases as the prevailing ambient wind velocityincreasing,especially for the first two units upward tothe wind.展开更多
We propose a scheme for the probabilistic teleportation of an unknown two-particle state of general formation in ion trap. It is shown that one can realize experimentally this teleportation protocol of two-particle st...We propose a scheme for the probabilistic teleportation of an unknown two-particle state of general formation in ion trap. It is shown that one can realize experimentally this teleportation protocol of two-particle state with presently available techniques.展开更多
Based on superconducting charge qubits （SCCQs） coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degene...Based on superconducting charge qubits （SCCQs） coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.展开更多
A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses,strains, strain rates and f...A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses,strains, strain rates and failure stress, as compared to previously reported models with two states.Model is used to perform deformation and failure simulations of carbon nanotubes and carbon nanotube/epoxy nanocomposites. The model capability of capturing the strain rate dependent deformation and failure has been demonstrated through predictions against uniaxial test data taken from literature. The predicted results show a good agreement between data set taken from literature and simulations.展开更多
In this work,a physics-informed neural network(PINN)designed specifically for analyzing digital mate-rials is introduced.This proposed machine learning(ML)model can be trained free of ground truth data by adopting the...In this work,a physics-informed neural network(PINN)designed specifically for analyzing digital mate-rials is introduced.This proposed machine learning(ML)model can be trained free of ground truth data by adopting the minimum energy criteria as its loss function.Results show that our energy-based PINN reaches similar accuracy as supervised ML models.Adding a hinge loss on the Jacobian can constrain the model to avoid erroneous deformation gradient caused by the nonlinear logarithmic strain.Lastly,we discuss how the strain energy of each material element at each numerical integration point can be calculated parallelly on a GPU.The algorithm is tested on different mesh densities to evaluate its com-putational efficiency which scales linearly with respect to the number of nodes in the system.This work provides a foundation for encoding physical behaviors of digital materials directly into neural networks,enabling label-free learning for the design of next-generation composites.展开更多
This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
基金supported by the Australian Research Council(Grant No.IC190100020)the Australian Research Council Indus〓〓try Fellowship(Grant No.IE230100435)the National Natural Science Foundation of China(Grant Nos.12032014 and T2488101)。
文摘The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of AI-empowered frameworks,including data-driven methods,physics-informed neural networks,and neural operators.While these approaches have demonstrated significant promise,challenges remain in terms of robustness,generalisation,and computational efficiency.We delineate four promising research directions:(1)Modular neural architectures inspired by traditional computational mechanics,(2)physics informed neural operators for resolution-invariant operator learning,(3)intelligent frameworks for multiphysics and multiscale biomechanics problems,and(4)structural optimisation strategies based on physics constraints and reinforcement learning.These directions represent a shift toward foundational frameworks that combine the strengths of physics and data,opening new avenues for the modelling,simulation,and optimisation of complex physical systems.
基金2024 Key Project of Teaching Reform Research and Practice in Higher Education in Henan Province“Exploration and Practice of Training Model for Outstanding Students in Basic Mechanics Discipline”(2024SJGLX094)Henan Province“Mechanics+X”Basic Discipline Outstanding Student Training Base2024 Research and Practice Project of Higher Education Teaching Reform in Henan University of Science and Technology“Optimization and Practice of Ability-Oriented Teaching Mode for Computational Mechanics Course:A New Exploration in Cultivating Practical Simulation Engineers”(2024BK074)。
文摘This paper takes the assessment and evaluation of computational mechanics course as the background,and constructs a diversified course evaluation system that is student-centered and integrates both quantitative and qualitative evaluation methods.The system not only pays attention to students’practical operation and theoretical knowledge mastery but also puts special emphasis on the cultivation of students’innovative abilities.In order to realize a comprehensive and objective evaluation,the assessment and evaluation method of the entropy weight model combining TOPSIS(Technique for Order Preference by Similarity to Ideal Solution)multi-attribute decision analysis and entropy weight theory is adopted,and its validity and practicability are verified through example analysis.This method can not only comprehensively and objectively evaluate students’learning outcomes,but also provide a scientific decision-making basis for curriculum teaching reform.The implementation of this diversified course evaluation system can better reflect the comprehensive ability of students and promote the continuous improvement of teaching quality.
基金Supported by New Chongqing Innovative Young Talent Project(Grant No.2024NSCQ-qncxX0468)Natural Science Foundation of Chongqing(Grant No.CSTB2022NSCQ-MSX1283)Dreams Foundation of Jianghuai Advanced Technology Center(Grant No.2023-ZM01Z007).
文摘Jumping robots are highly capable of overcoming obstacles.However,their explosive force,short duration,and variable trajectories pose significant challenges in achieving stable landings in complex environments.Traditional approaches rely heavily on sophisticated algorithms and electronic sensor feedback systems to ensure landing stability,which increases the implementation complexity.Inspired by the process by which humans complete jumps and achieve stable landings in complex environments,this study proposes a novel landing control method for jumping robots.By designing a mechanically coupled perception-control structure based on mechanical logic computing,the robot simulates the real-time transmission of neural signals triggered by the ground reaction force(GRF)in human reflex loops,thereby simplifying traditional control approaches.Through the collaboration of a flexible mechanical spine and a bistable foot module,the robot achieves an average height of 16.8 cm and a distance of 25.36 cm in consecutive stable jumps.It also demonstrates reliable landing performance on challenging terrain including slopes and cobblestone surfaces.This paper proposes a novel landing control method for jumping robots that simplifies traditional control approaches.The method enables stable landings on complex terrain through a mechanically coupled perception-control structure.This approach has potential applications in tasks requiring mobility over uneven terrain,such as search and rescue.
基金The project is supported by National Natural Science Foundation of China
文摘In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.
基金supported by a PRESTO-JST program,the Grant-in-Aid for Scientific Research JSPS.Japan(18656056 and 18100002).
文摘Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles（MAVs） design,we propose a comprehensive computational framework,which integrates aerodynamics,flight dynamics,vehicle stability and maneuverability.This framework consists of（1） a Navier-Stokes unsteady aerodynamic model;（2） a linear finite element model for structural dynamics;（3） a fluidstructure interaction（FSI） model for coupled flexible wing aerodynamics aeroelasticity;（4） a free-flying rigid body dynamic（RBD） model utilizing the Newtonian-Euler equations of 6DoF motion;and（5） flight simulator accounting for realistic wing-body morphology,flapping-wing and body kinematics,and a coupling model accounting for the nonlinear 6DoF flight dynamics and stability of insect flapping flight.Results are presented based on hovering aerodynamics with rigid and flexible wings of hawkmoth and fruitfly.The present approach can support systematic analyses of bio- and bio-inspired flight.
文摘Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.
文摘Most of granular materials are highly heteroge- neous, composed of voids and particles with different sizes and shapes. Geological matter, soil and clay in nature, geo-structure, concrete, etc. are practical ex- amples among them. From the microscopic view, a lo- cal region in the medium is occupied by particles with small but finite sizes and granular material is naturally modeled as an assembly of discrete particles in contacts On the other hand, the local region is identified with a material point in the overall structure and this discon- tinuous medium can then be represented by an effective continuum on the macroscopic level
文摘This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.
基金We acknowledge the support of Defense Advanced Research Projects Agency(Grant HR00111990S2)Toyota Research Institute(Award#849910).
文摘We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure that is advantageous in not requiring repeated forward model solves andhas good scalability to large number of differential operators. However it has strict data typerequirements needing the ability to directly represent the operators through the available data.The second is a Bayesian inference framework highly valuable for providing uncertaintyquantification, and flexible for accommodating sparse and noisy data that may also be indirectquantities of interest. However, it also requires repeated forward solutions of the PDE modelswhich is expensive and hinders scalability. We provide illustrations of results on a model problemfor pattern formation dynamics, and discuss merits of the presented methods.
基金supported by JSPS KAKENHI (Grants 17K06633 and 18K18898)
文摘This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to obtain a static equilibrium state of an elastic structure. Preliminary numerical experiments illustrate that, compared with existing methods, the proposed method finds a reasonable solution even if data points distribute coarsely in a given material data set.
文摘In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122205 and 11772119)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.
基金Open access funding provided by Scuola Superiore Sant’Anna within the CRUI-CARE Agreement.
文摘Nature and technology often adopt structures that can be described as tubular helical assemblies.However,the role and mechanisms of these structures remain elusive.In this paper,we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchholf rods,arranged in pairs with opposite chirality and connected by pin joints,both analytically and numerically.We first focus on compression and find that,whereas a single helical rod would buckle,the rods of the assembly deform coherently as stable helical shapes wound around a common axis.Moreover,we investigate the response of the assembly under different boundary conditions,highlighting the emergence of a central region where rods remain circular helices.Secondly,we study the effects of different hypotheses on the elastic properties of rods,i.e.,stress-free rods when straight versus when circular helices,Kirchhoff’s rod model versus Sadowsky’s ribbon model.Summing up,our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods,as well as some interesting features,and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology.
基金Supported by the New Century Excellent Talent Project （NCET） of the Ministry of Education of China under Grant No NCET-06-0554, the National Natural Science Foundation of China under Grant Nos 10975001, 60677001, 10747146 and 10874122, the Science-Technology Fund of Anhui Province for Outstanding Youth under Grant No 06042087, the Key Fund of the Ministry of Education of China under Grant No 206063, the General Fund of the Educational Committee of Anhui Province under Grant No 2006KJ260B, the Natural Science Foundation of Guangdong Province under Grant Nos 06300345 and 7007806, and the Talent Foundation of High Education of Anhui Province for Outstanding Youth under Grant No 2009SQRZ018.
文摘Using the method presented recently [Phys.Rev.A 77（2008）014306; Phys.Lett.A 369（2007）377], the transformation operator （TO） is explicitly given for teleporting an arbitrary three-qubit state with a six-qubit channel and Bell-state measurements. A criterion on whether such quantum teleportation can be perfectly realized is educed in terms of TO. Moreover, six instantiations on TO and criterion are concisely shown.
文摘Prevailing ambient wind is the main reason thatcauses inlet flow rate(air mass flow rate)decreasingand air flowing backward to the air-cooled condenserfans upward to the wind,hence a set of wind guidingnets is designed to improve the detrimental effect.Fig.1 shows four typical units of a 1000MW directair-cooled condenser(DACC)and a set of windguiding nets installed under its edge upward to theambient wind.As shown in Fig.2,the fan inlet flowrate decreases as the prevailing ambient wind velocityincreasing,especially for the first two units upward tothe wind.
基金Supported by the National Natural Science Foundation of China under Grant No 10971247, and the Hebei Natural Science Foundation of China under Grant No F2009000311.
文摘We propose a scheme for the probabilistic teleportation of an unknown two-particle state of general formation in ion trap. It is shown that one can realize experimentally this teleportation protocol of two-particle state with presently available techniques.
基金Supported by the National Natural Science Foundation of China under Grant No 10574126, the Hunan Provincial Natural Science Foundation under Grant No 06jj50014 and Key Foundation of the Education Commission of Hunan Province under Grant No 06A055.
文摘Based on superconducting charge qubits （SCCQs） coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.
文摘A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses,strains, strain rates and failure stress, as compared to previously reported models with two states.Model is used to perform deformation and failure simulations of carbon nanotubes and carbon nanotube/epoxy nanocomposites. The model capability of capturing the strain rate dependent deformation and failure has been demonstrated through predictions against uniaxial test data taken from literature. The predicted results show a good agreement between data set taken from literature and simulations.
文摘In this work,a physics-informed neural network(PINN)designed specifically for analyzing digital mate-rials is introduced.This proposed machine learning(ML)model can be trained free of ground truth data by adopting the minimum energy criteria as its loss function.Results show that our energy-based PINN reaches similar accuracy as supervised ML models.Adding a hinge loss on the Jacobian can constrain the model to avoid erroneous deformation gradient caused by the nonlinear logarithmic strain.Lastly,we discuss how the strain energy of each material element at each numerical integration point can be calculated parallelly on a GPU.The algorithm is tested on different mesh densities to evaluate its com-putational efficiency which scales linearly with respect to the number of nodes in the system.This work provides a foundation for encoding physical behaviors of digital materials directly into neural networks,enabling label-free learning for the design of next-generation composites.
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
