A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is ...A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary f...By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.展开更多
According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In thi...According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.展开更多
Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dyna...Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.展开更多
Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is r...Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.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 investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
The eagle strategy algorithm is combined with particle swarm optimization in this paper.The new algorithm,denoted as the ES-PSO,is implemented by interfacing Etabs structural analysis codes.ES-PSO is used to optimize ...The eagle strategy algorithm is combined with particle swarm optimization in this paper.The new algorithm,denoted as the ES-PSO,is implemented by interfacing Etabs structural analysis codes.ES-PSO is used to optimize the RC ribbed floor system,including floor and underground garage roof.By considering the effects of reinforcement,the principle of virtual work is applied to calculate the deflections of components.Construction cost is taken as the objective function and the constraint conditions are required to satisfy.Accordingly,the optimal layout,the optimal sections of the beams and slabs and the corresponding reinforcements are obtained for different column grids.In this investigation,the RC ribbed floor system is optimized according to the Chinese standard,whose column grids are 8.4 m and 8.4 m.The performance of the ES-PSO algorithm is good enough,which can be applied to practical engineering.The paper can also provide a basis for subsequent optimization design of monolithic structures.展开更多
In this research,mechanical stress,static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented.The kinematic relations are developed based on higherorder sinusoi...In this research,mechanical stress,static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented.The kinematic relations are developed based on higherorder sinusoidal shear deformation theory.Thickness stretching formulation is accounted for more accurate analysis.The total transverse deflection is divided into bending,shear and thickness stretching parts in which the third term is responsible for change of deflection along the thickness direction.The axisymmetric formulations are derived through principle of virtual work.A parametric study is presented to investigate variation of stress and strain components along the thickness and longitudinal directions.To explore effect of thickness stretching model on the static results,a comparison between the present results with the available results of literature is presented.As an important output,effect of micro-scale parameter is studied on the static stress and strain distribution.展开更多
Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient ...Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient temperature, and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation. However, the material stress-strain relationship is very complicated at elevated temperature, and its form is not unique, which brings great difficulty to the derivation of element stiffness equation. Referring to the derivation method of element stiffness equation at ambient temperature, by using the continuous function of stress-strain-temperature at elevated temperature, and based on the principle of virtual work, the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper, which provide basis for finite element analysis on structures at elevated temperature.展开更多
According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s g...According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot＇s inertia matrix in the workspace is studied. The method has computationa＇, advantage of numerical accuracy for the Delta robot and can be parallelized easily.展开更多
For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distr...For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distribution on the strip. The electrostatic force on each side of the rectangular shield wall is achieved by using the principle of virtual work. The result is easy to be obtained by computerized calculation.展开更多
Understanding the relationship between normal stiffness and permeability in rock fractures under high and true-triaxial in situ stress conditions is critical to assess hydro-mechanical coupling in the Earth's crus...Understanding the relationship between normal stiffness and permeability in rock fractures under high and true-triaxial in situ stress conditions is critical to assess hydro-mechanical coupling in the Earth's crust.Previous data on stiffness–permeability relations are measured under uniaxial stress states as well as under normal stress.However,many projects involve faulted formations with complex three-dimensional(3D)stress states or significant changes to the original stress state.We rectified this by following the permeability evolution using a true-triaxial stress-permeability apparatus as well as independently applying a spectrum of triaxial stresses from low to high.The relationship between permeability and fracture normal stiffness was quantified using constraints based on the principle of virtual work.The impacts of fracture-lateral and fracture-normal stresses on permeability and normal stiffness evolution were measured.It was found that permeability decreases with increasing fracture-lateral and fracture-normal stresses as a result of Poisson confinement,independent of the orientation of the fracture relative to the stresses.The lateral stresses dominated the evolution of normal stiffness at lower normal stresses(σ_(3)=10 MPa)and played a supplementary role at higher normal stresses(σ_(3)>10 MPa).Moreover,correlations between the evolution of permeability and normal stiffness were extended beyond the low-stiffness,high-permeability region to the high-stiffness,low-permeability region under high fracture-lateral stresses(10–80 MPa)with fracture-normal stress(10–50 MPa)conditions.Again,high lateral stresses further confined the fracture and therefore reduced permeability and increased normal stiffness,which exceeded the previous reported stiffness under no lateral stress conditions.This process enabled us to identify a fundamental change in the flow regime from multi-channel to isolated channelized flow.These results provide important characterizations of fracture permeability in the deep crust,including recovery from deep shale-gas reservoirs.展开更多
We examine the electromechanical field and charge redistribution within a flexoelectric semiconductor(FS)nanobeam,accounting for bending,fundamental thickness-shear,and antisymmetric thickness-stretch deformations.The...We examine the electromechanical field and charge redistribution within a flexoelectric semiconductor(FS)nanobeam,accounting for bending,fundamental thickness-shear,and antisymmetric thickness-stretch deformations.The coupled gov-erning equations include microstructure,flexoelectric,and semiconductor effects,highlighting the interplay between me-chanical displacement,electric potential,and charge carriers.For applications in flexoelectronic devices,the static bending of a simply supported FS beam induced by uniform pressure and wave propagation in an unbounded FS beam are analytically addressed using the derived framework.The effects of antisymmetric thickness-stretch on mechanical displacements and electron concentration perturbation,as well as size dependence of microstructure and flexoelectric effects,are identified.An interesting finding reveals that wave frequencies of the antisymmetric thickness-stretch mode,as anticipated by the proposed model,are larger compared to those of the model neglecting flexoelectric and semiconductor effects.For the first time,the cutoff frequency of antisymmetric thickness-stretch impacted by the two features is explained mathematically.These findings are beneficial for enhancing the performance of flexoelectronic sensors and electroacoustic devices.展开更多
This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity...This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.展开更多
An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit...An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit-Hartenberg.The model of the equivalent contact forces exerted by the object on the finger is proposed.By the principle of virtual work,the static equilibrium of finger is established.The force Jacobian matrix of finger is calculated,and then the joint torques of the finger when grasping objects are obtained.The theory and structure of the force feedback datagolve are introduced.Based on the theory of motion stabilization of four-bar linkage,the flexion angles of joints are measured.The torques on finger joints caused by the output forces of pneumatic artificial muscles are calculated.The output forces of pneumatic artificial muscle,whose values are controlled by its inner pressure,can be calculated by the joint torques of the finger when grasping objects.The arms of force,driving torques and the needed output forces of pneumatic muscle are calculated for each joint of the index finger.The criterion of output force of pneumatic muscle is given.展开更多
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo,some basic principles in the linear theory of piezoelectric micropolar elas...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo,some basic principles in the linear theory of piezoelectric micropolar elastodynamics can be established systematically.In this paper,an important integral relation in terms of convolutions is given,which can be considered as the generalized principle of virtual work in mechanics.Based on this relation,it is not only possible to obtain the principle of virtual work and the reciprocal theorem,but also to systematically derive the complementary functionals for the eleven-field,nine-field and six-field simplified Gurtin-type variational principles and the potential energy-functional for the three-field one in the linear theory of piezoelectric micropolar elastodynamics by the generalized Legendre transformations given in this paper.Furthermore,with this approach,the intrinsic relationships among various principles can be explained clearly.展开更多
The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, an...The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.展开更多
In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power...In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power as well as the generalized Piola theorem. Adding the boundary conditions presented here to the results by Gao Jian and Dai Tianmin,the mixed boundary_value problem of the non_local asymmetric linear elasticity are formulated.展开更多
Owing to their inherent great flexibility, good compliance, excellent adaptability, and safe interactivity, soft robots have shown great application potential. The advantages of light weight, high efficiency, non-poll...Owing to their inherent great flexibility, good compliance, excellent adaptability, and safe interactivity, soft robots have shown great application potential. The advantages of light weight, high efficiency, non-polluting characteristic, and environmental adaptability provide pneumatic soft robots an important position in the field of soft robots. In this paper, a soft robot with 10 soft modules, comprising three uniformly distributed endoskeleton pneumatic artificial muscles, was developed. The robot can achieve flexible motion in 3D space. A novel kinematic modeling method for variable-curvature soft robots based on the minimum energy method was investigated, which can accurately and efficiently analyze forward and inverse kinematics. Experiments show that the robot can be controlled to move to the desired position based on the proposed model. The prototype and modeling method can provide a new perspective for soft robot design, modeling, and control.展开更多
基金Supported by National Natural Science Foundation of China (No. 50375106) andKey Laboratory of Intelligent Manufacturing at Shantou University Grant (No. Imstu-2002-11).
文摘A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
文摘By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.
基金The project supported by the Foundation of Zhongshan University Advanced Research Center
文摘According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.
基金Supported by National Natural Science Foundation of China(Grant No.51175422)
文摘Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.
文摘Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.
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 investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
文摘The eagle strategy algorithm is combined with particle swarm optimization in this paper.The new algorithm,denoted as the ES-PSO,is implemented by interfacing Etabs structural analysis codes.ES-PSO is used to optimize the RC ribbed floor system,including floor and underground garage roof.By considering the effects of reinforcement,the principle of virtual work is applied to calculate the deflections of components.Construction cost is taken as the objective function and the constraint conditions are required to satisfy.Accordingly,the optimal layout,the optimal sections of the beams and slabs and the corresponding reinforcements are obtained for different column grids.In this investigation,the RC ribbed floor system is optimized according to the Chinese standard,whose column grids are 8.4 m and 8.4 m.The performance of the ES-PSO algorithm is good enough,which can be applied to practical engineering.The paper can also provide a basis for subsequent optimization design of monolithic structures.
文摘In this research,mechanical stress,static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented.The kinematic relations are developed based on higherorder sinusoidal shear deformation theory.Thickness stretching formulation is accounted for more accurate analysis.The total transverse deflection is divided into bending,shear and thickness stretching parts in which the third term is responsible for change of deflection along the thickness direction.The axisymmetric formulations are derived through principle of virtual work.A parametric study is presented to investigate variation of stress and strain components along the thickness and longitudinal directions.To explore effect of thickness stretching model on the static results,a comparison between the present results with the available results of literature is presented.As an important output,effect of micro-scale parameter is studied on the static stress and strain distribution.
基金the National Natural Science Foundation of China(No.50578093)
文摘Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient temperature, and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation. However, the material stress-strain relationship is very complicated at elevated temperature, and its form is not unique, which brings great difficulty to the derivation of element stiffness equation. Referring to the derivation method of element stiffness equation at ambient temperature, by using the continuous function of stress-strain-temperature at elevated temperature, and based on the principle of virtual work, the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper, which provide basis for finite element analysis on structures at elevated temperature.
基金Supported by National Natural Science Foundation of China (No. 50375106) , the State Scholarship Fund (No. 2004812032) and Key Laboratory of Intelligent Manufacturing at Shantou University ( No. Imstu-2002-11).
文摘According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot＇s inertia matrix in the workspace is studied. The method has computationa＇, advantage of numerical accuracy for the Delta robot and can be parallelized easily.
基金Funded by the Key Research Foundation of Sichuan Education Commission(No. 2002A046 )
文摘For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distribution on the strip. The electrostatic force on each side of the rectangular shield wall is achieved by using the principle of virtual work. The result is easy to be obtained by computerized calculation.
基金funded by the joint fund of the National Key Research and Development Program of China(Grant No.2021YFC2902101)National Natural Science Foundation of China(Grant No.52374084)+1 种基金the 111 Project(Grant No.B17009)DE acknowledges support from the G.Albert Shoemaker endowment.
文摘Understanding the relationship between normal stiffness and permeability in rock fractures under high and true-triaxial in situ stress conditions is critical to assess hydro-mechanical coupling in the Earth's crust.Previous data on stiffness–permeability relations are measured under uniaxial stress states as well as under normal stress.However,many projects involve faulted formations with complex three-dimensional(3D)stress states or significant changes to the original stress state.We rectified this by following the permeability evolution using a true-triaxial stress-permeability apparatus as well as independently applying a spectrum of triaxial stresses from low to high.The relationship between permeability and fracture normal stiffness was quantified using constraints based on the principle of virtual work.The impacts of fracture-lateral and fracture-normal stresses on permeability and normal stiffness evolution were measured.It was found that permeability decreases with increasing fracture-lateral and fracture-normal stresses as a result of Poisson confinement,independent of the orientation of the fracture relative to the stresses.The lateral stresses dominated the evolution of normal stiffness at lower normal stresses(σ_(3)=10 MPa)and played a supplementary role at higher normal stresses(σ_(3)>10 MPa).Moreover,correlations between the evolution of permeability and normal stiffness were extended beyond the low-stiffness,high-permeability region to the high-stiffness,low-permeability region under high fracture-lateral stresses(10–80 MPa)with fracture-normal stress(10–50 MPa)conditions.Again,high lateral stresses further confined the fracture and therefore reduced permeability and increased normal stiffness,which exceeded the previous reported stiffness under no lateral stress conditions.This process enabled us to identify a fundamental change in the flow regime from multi-channel to isolated channelized flow.These results provide important characterizations of fracture permeability in the deep crust,including recovery from deep shale-gas reservoirs.
基金supported by the National Natural Science Foundation of China(Grant No.12002086(Gongye Zhang))Fundamental Research Funds for the Central Universities(Grant No.2242022R40040(Gongye Zhang))Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX24_0365(Ziwen Guo)).
文摘We examine the electromechanical field and charge redistribution within a flexoelectric semiconductor(FS)nanobeam,accounting for bending,fundamental thickness-shear,and antisymmetric thickness-stretch deformations.The coupled gov-erning equations include microstructure,flexoelectric,and semiconductor effects,highlighting the interplay between me-chanical displacement,electric potential,and charge carriers.For applications in flexoelectronic devices,the static bending of a simply supported FS beam induced by uniform pressure and wave propagation in an unbounded FS beam are analytically addressed using the derived framework.The effects of antisymmetric thickness-stretch on mechanical displacements and electron concentration perturbation,as well as size dependence of microstructure and flexoelectric effects,are identified.An interesting finding reveals that wave frequencies of the antisymmetric thickness-stretch mode,as anticipated by the proposed model,are larger compared to those of the model neglecting flexoelectric and semiconductor effects.For the first time,the cutoff frequency of antisymmetric thickness-stretch impacted by the two features is explained mathematically.These findings are beneficial for enhancing the performance of flexoelectronic sensors and electroacoustic devices.
基金The project supported by the National Natural Science Foundation of China(10132010 and 10472089)
文摘This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.
基金This project is supported by National Natural Science Foundation of China(No.50375034).
文摘An exoskeleton force feedback dataglove is developed,which uses the pneumatic artificial muscles as actuators.On the basis of the simplified hand model,the motion equation is deduced according to the theory of Denavit-Hartenberg.The model of the equivalent contact forces exerted by the object on the finger is proposed.By the principle of virtual work,the static equilibrium of finger is established.The force Jacobian matrix of finger is calculated,and then the joint torques of the finger when grasping objects are obtained.The theory and structure of the force feedback datagolve are introduced.Based on the theory of motion stabilization of four-bar linkage,the flexion angles of joints are measured.The torques on finger joints caused by the output forces of pneumatic artificial muscles are calculated.The output forces of pneumatic artificial muscle,whose values are controlled by its inner pressure,can be calculated by the joint torques of the finger when grasping objects.The arms of force,driving torques and the needed output forces of pneumatic muscle are calculated for each joint of the index finger.The criterion of output force of pneumatic muscle is given.
基金was supported by the National Natural Science Foundation of China(Grant No.10772203)
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo,some basic principles in the linear theory of piezoelectric micropolar elastodynamics can be established systematically.In this paper,an important integral relation in terms of convolutions is given,which can be considered as the generalized principle of virtual work in mechanics.Based on this relation,it is not only possible to obtain the principle of virtual work and the reciprocal theorem,but also to systematically derive the complementary functionals for the eleven-field,nine-field and six-field simplified Gurtin-type variational principles and the potential energy-functional for the three-field one in the linear theory of piezoelectric micropolar elastodynamics by the generalized Legendre transformations given in this paper.Furthermore,with this approach,the intrinsic relationships among various principles can be explained clearly.
文摘The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.
文摘In this paper, the equations of motion and all boundary conditions as well as the energy equation for non_local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power as well as the generalized Piola theorem. Adding the boundary conditions presented here to the results by Gao Jian and Dai Tianmin,the mixed boundary_value problem of the non_local asymmetric linear elasticity are formulated.
基金the National Natural Science Foundation of China(Grant Nos.51975566,61821005,and U1908214)the Key Research Program of Frontier Sciences,CAS,China(Grant No.ZDBS-LY-JSC011).
文摘Owing to their inherent great flexibility, good compliance, excellent adaptability, and safe interactivity, soft robots have shown great application potential. The advantages of light weight, high efficiency, non-polluting characteristic, and environmental adaptability provide pneumatic soft robots an important position in the field of soft robots. In this paper, a soft robot with 10 soft modules, comprising three uniformly distributed endoskeleton pneumatic artificial muscles, was developed. The robot can achieve flexible motion in 3D space. A novel kinematic modeling method for variable-curvature soft robots based on the minimum energy method was investigated, which can accurately and efficiently analyze forward and inverse kinematics. Experiments show that the robot can be controlled to move to the desired position based on the proposed model. The prototype and modeling method can provide a new perspective for soft robot design, modeling, and control.
