The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical ...The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.展开更多
4-node, 8-node and 8（4）-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite ...4-node, 8-node and 8（4）-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.展开更多
A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in it...A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in its formulation for describing the load deformation of bedded rocks. It is shown that such a continuum based code is valuable for assessing the feasibility of introducing LTCC in any mine. Various LTCC parameters, for example chock convergences, top coal failure behavior, strata cavingmechanism, abutment stresses and vertical stresses, were evaluated for a mine using COSFLOW.展开更多
In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat ro...In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.展开更多
On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. T...On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.展开更多
In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern framework, they used the nonli...In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern framework, they used the nonlinear Spencer sequence instead of the nonlinear Janet sequence for the Lie groupoid defining the group of rigid motions of space. Following H. Weyl, our purpose is to compute for the first time the linear and nonlinear Spencer sequences for the Lie groupoid defining the conformal group of space-time in order to provide the mathematical foundations of both electromagnetism (EM) and gravitation (GR), with the only experimental need to measure the EM and GR constants. With a manifold of dimension n ≥ 3, the difficulty is to deal with the n nonlinear transformations that have been called “elations” by E. Cartan in 1922. Using the fact that dimension n = 4 has very specific properties for the computation of the Spencer cohomology, we also prove that there is no conceptual difference between the (nonlinear) Cosserat EL field or induction equations and the (linear) Maxwell EM field or induction equations. As for gravitation, the dimension n = 4 also allows to have a conformal factor defined everywhere but at the central attractive mass because the inversion law of the isotropy subgroupoid made by second order jets transforms attraction into repulsion. The mathematical foundations of both electromagnetism and gravitation are thus only depending on the structure of the conformal pseudogroup of space-time.展开更多
This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstru...This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.展开更多
This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory....This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory.The unmodeled dynamics of the system are considered,and an adaptive neural network controller is designed using the backstepping method and radial basis function neural network.The stability of the closed-loop system and the boundedness of the tracking error are verified using Lyapunov theory.The simulation results show that our approach is a good solution to the motion constraint problem of the line-driven soft robotic arm.展开更多
Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigate展开更多
Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and comp...Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.展开更多
A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding r...A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy princi- ple of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.展开更多
To obviate the complexities of the straight forward couple stress finite element method,the penalty-based couple stress finite element method(named PcouFEM)within the framework of the Cosserat continuum is utilized to...To obviate the complexities of the straight forward couple stress finite element method,the penalty-based couple stress finite element method(named PcouFEM)within the framework of the Cosserat continuum is utilized to obtain the approximate solution by relaxing the C1 continuity.To examine the performance of the PcouFEM,three well known numerical examples are investigated.For the analysis on stress concentration around the circular hole of the plane strain specimen,it was found that as long as the penalty factor G_(c) is not less than 5 times the shear modulus of the classical continuum G(i.e.,G_(c)≥5G),the stress concentration factors calculated by the PcouFEM with the reduced integration scheme agree well with the analytical solutions.For the strain localization analysis in the uniaxial compression test,it was observed that by applying the PcouFEM,the pathologically mesh-dependent problem associated with the conventional FEM can be alleviated or even removed,and based on numerical simulations,it is recommended to define 5G≤G_(c)≤10G from the perspective of numerical accuracy.For the soil slope subjected to an eccentric load through the rigid strip footing,it was found that the mesh-dependent problem of the shear band simulation can be largely alleviated by applying the PcouFEM.展开更多
This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that co...This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that converge to the point of the dislocation and by a residual force distributed around that point. The plate deformation caused by the dislocation is calculated using the Finite Element Method. We also discuss the effect of the dislocation on the cavities present in the Cosserat plates.展开更多
Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling c...Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling can be accurate and effective.While for other cases,such as soft robots or robot-environment interactions,the constant curvature assumption can be inaccurate.To model the complex deformation of continuum robots,the geometrically exact beam theory(may also be called the Cosserat rod theory)has been used to develop computational mechanics models.Different from previous computational models that used finite difference schemes for the spatial discretization,here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots.Several numerical examples are presented to show the accuracy,efficiency,and applicability of our new computational model for tendon-driven continuum robots.展开更多
Mainly for the problems that the configuration of the mobile cable on the satellite is very easy to change,the motion trajectory and dynamic characteristics of the cable can not be accu-rately predicted,which affects ...Mainly for the problems that the configuration of the mobile cable on the satellite is very easy to change,the motion trajectory and dynamic characteristics of the cable can not be accu-rately predicted,which affects the laying quality seriously,the dynamic modeling and simulation of mobile cable on the satellite are carried out.On the basis of referring to the previous papers,the existing mathematical model is improved.The equations of the base vector of the cable section principal axis coordinate system with respect to the arc coordinate s,the distribution force of cable balance equation,the matrix expression of the base vector after the rotation motion transformation in the section principal axis coordinate system,the angular velocity of cable,the section elastic strain and velocity calculation equations are given,and the Cosserat dynamic modeling of the mobile cable is established.Finally,the dynamic simulation model of the mobile cable assembly of the kinematic mechanism is established,and the changes of the force and torque on the cable con-straint end are obtained,which provides a reference for the dynamic modeling and simulation of the mobile cable on satellite.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10472067)
文摘The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.
基金The project supported by the National Natural Science Foundation of China(10225212,50178016,10421002)the Program for Changjiang Scholars and Innovative Research Team in University of China
文摘4-node, 8-node and 8（4）-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.
文摘A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in its formulation for describing the load deformation of bedded rocks. It is shown that such a continuum based code is valuable for assessing the feasibility of introducing LTCC in any mine. Various LTCC parameters, for example chock convergences, top coal failure behavior, strata cavingmechanism, abutment stresses and vertical stresses, were evaluated for a mine using COSFLOW.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262019 and 10972143)
文摘In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.
基金supported by the National Natural Science Foundation of China (90715011, 10672033 and 10590354) the National Key Basic Research and Development Program (2002CB412709) the Australia Research Council through the ARC International Fellowship Offered at University of Newcastle (LX0666274)
文摘On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.
文摘In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern framework, they used the nonlinear Spencer sequence instead of the nonlinear Janet sequence for the Lie groupoid defining the group of rigid motions of space. Following H. Weyl, our purpose is to compute for the first time the linear and nonlinear Spencer sequences for the Lie groupoid defining the conformal group of space-time in order to provide the mathematical foundations of both electromagnetism (EM) and gravitation (GR), with the only experimental need to measure the EM and GR constants. With a manifold of dimension n ≥ 3, the difficulty is to deal with the n nonlinear transformations that have been called “elations” by E. Cartan in 1922. Using the fact that dimension n = 4 has very specific properties for the computation of the Spencer cohomology, we also prove that there is no conceptual difference between the (nonlinear) Cosserat EL field or induction equations and the (linear) Maxwell EM field or induction equations. As for gravitation, the dimension n = 4 also allows to have a conformal factor defined everywhere but at the central attractive mass because the inversion law of the isotropy subgroupoid made by second order jets transforms attraction into repulsion. The mathematical foundations of both electromagnetism and gravitation are thus only depending on the structure of the conformal pseudogroup of space-time.
基金the National Natural Science Foundation of China through Contract/Grant Numbers 12002245,12172263 and 11772237Chongqing Jiaotong University through Contract/Grant Number F1220038.
文摘This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.
基金supported by the National Natural Science Foundation of China(62103039,62073030)the Scientific and Technological Innovation Foundation of Shunde Graduate School+8 种基金University of Science and Technology Beijing(USTB)(BK21BF003)the Korea Institute of Energy Technology Evaluation and Planning through the Auspices of the Ministry of TradeIndustry and EnergyRepublic of Korea(20213030020160)the Science and Technology Planning Project of Guangzhou City(202102010398,202201010758)the Guangzhou University-Hong Kong University of Science and Technology Joint Research Collaboration Fund(YH202205)Beijing Top Discipline for Artificial Intelligent Science and EngineeringUniversity of Science and Technology Beijing。
文摘This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory.The unmodeled dynamics of the system are considered,and an adaptive neural network controller is designed using the backstepping method and radial basis function neural network.The stability of the closed-loop system and the boundedness of the tracking error are verified using Lyapunov theory.The simulation results show that our approach is a good solution to the motion constraint problem of the line-driven soft robotic arm.
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigate
基金Supported by National Natural Science Foundation of China(Grant No.51875033)Fundamental Research Funds for the Central Universities of China(Grant No.2021YJS137).
文摘Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.
基金Project supported by the National Natural Sciences Foundation (Nos. 50679013,10421202 and 10225212)the Program for Changjiang Scholars and Innovative Research Team in Universities of China (PCSIRT)the National Key Basic Research Special Foundation of China (No. 2005CB321704)
文摘A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy princi- ple of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.
基金Project(2021YFF0306302)supported by the National Key R&D Program of ChinaProjects(42002277,41972279,42172299)supported by the National Natural Science Foundation of China+2 种基金Projects(2020M680321,2021T140046)supported by the China Postdoctoral Science FoundationProjects(2020-zz-081,2021-zz-116)supported by the Beijing Postdoctoral Research Foundation,ChinaProject(X21074)supported by the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture,China。
文摘To obviate the complexities of the straight forward couple stress finite element method,the penalty-based couple stress finite element method(named PcouFEM)within the framework of the Cosserat continuum is utilized to obtain the approximate solution by relaxing the C1 continuity.To examine the performance of the PcouFEM,three well known numerical examples are investigated.For the analysis on stress concentration around the circular hole of the plane strain specimen,it was found that as long as the penalty factor G_(c) is not less than 5 times the shear modulus of the classical continuum G(i.e.,G_(c)≥5G),the stress concentration factors calculated by the PcouFEM with the reduced integration scheme agree well with the analytical solutions.For the strain localization analysis in the uniaxial compression test,it was observed that by applying the PcouFEM,the pathologically mesh-dependent problem associated with the conventional FEM can be alleviated or even removed,and based on numerical simulations,it is recommended to define 5G≤G_(c)≤10G from the perspective of numerical accuracy.For the soil slope subjected to an eccentric load through the rigid strip footing,it was found that the mesh-dependent problem of the shear band simulation can be largely alleviated by applying the PcouFEM.
文摘This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that converge to the point of the dislocation and by a residual force distributed around that point. The plate deformation caused by the dislocation is calculated using the Finite Element Method. We also discuss the effect of the dislocation on the cavities present in the Cosserat plates.
基金support from the National Natural Science Foundation of China(NSFC Grant No.12072143).J.L.acknowledges the funding support from the National Natural Science Foundation of China(NSFC Grant No.12172160).C.C.acknowledges the financial support from the U.S.National Science Foundation(ECCS-2024649).
文摘Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling can be accurate and effective.While for other cases,such as soft robots or robot-environment interactions,the constant curvature assumption can be inaccurate.To model the complex deformation of continuum robots,the geometrically exact beam theory(may also be called the Cosserat rod theory)has been used to develop computational mechanics models.Different from previous computational models that used finite difference schemes for the spatial discretization,here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots.Several numerical examples are presented to show the accuracy,efficiency,and applicability of our new computational model for tendon-driven continuum robots.
基金supported by National Defense Basic Scientific Research Funding Project(No.JCKY2022203C048)Equipment Advanced Research Funding Program(No.41423010401).
文摘Mainly for the problems that the configuration of the mobile cable on the satellite is very easy to change,the motion trajectory and dynamic characteristics of the cable can not be accu-rately predicted,which affects the laying quality seriously,the dynamic modeling and simulation of mobile cable on the satellite are carried out.On the basis of referring to the previous papers,the existing mathematical model is improved.The equations of the base vector of the cable section principal axis coordinate system with respect to the arc coordinate s,the distribution force of cable balance equation,the matrix expression of the base vector after the rotation motion transformation in the section principal axis coordinate system,the angular velocity of cable,the section elastic strain and velocity calculation equations are given,and the Cosserat dynamic modeling of the mobile cable is established.Finally,the dynamic simulation model of the mobile cable assembly of the kinematic mechanism is established,and the changes of the force and torque on the cable con-straint end are obtained,which provides a reference for the dynamic modeling and simulation of the mobile cable on satellite.
