Theoretical approach with analytical and numerical procedure for determination initial displacement of a reinforced and prestressed concrete members, simple and cantilever beams, loaded by axial forces and bending mom...Theoretical approach with analytical and numerical procedure for determination initial displacement of a reinforced and prestressed concrete members, simple and cantilever beams, loaded by axial forces and bending moments is <span style="font-family:Verdana;">proposed. It is based on the principle of minimum potential energy with</span><span style="font-family:Verdana;"> equality of internal and external forces. The equations for strain internal energy have been derived, including compressed and tensile concrete and reinforce</span><span style="font-family:Verdana;">ment. The energy equations of the external forces with axial flexural dis</span><span style="font-family:Verdana;">placement effects have been derived from the assumed sinusoidal curve. The trapezoid rule is applied to integrate the segment strain energy. The proposed method uses a non</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">linear stress-strain curve for the concrete and bilinear elastic-plastic relationship for reinforcement;equilibrium conditions at a sectional level to generate the strain energies along the beam. At the end of this article are shown three specific numerical examples with comparative, experimental (two tests)</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">results with the excellent agreement and one calculation result with a great disagreement, by obtaining results of virtual principle method.</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">With this method is avoiding the adoption of an unsure (EJ), as in the case of underestimating or overestimate initial flexural rigidity.</span></span></span>展开更多
Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load...Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load capacity,for which particle jamming is an effective technology for stiffness-tunable robots requiring safe interaction and load capacity.Specific applica-tions,such as rescue scenarios,require quantitative analysis to optimize VSM design parameters,which previous analytical models cannot effectively handle.To address this,a Grey-box model is proposed to analyze the mechanical response of the particle-jamming-based VSM by combining a White-box approach based on the virtual work principle with a Black-box approach that uses a shallow neural network method.The Grey-box model demonstrates a high level of accuracy in predict-ing the VSM force-height mechanical response curves,with errors below 15%in almost 90%of the cases and a maximum error of less than 25%.The model is used to optimize VSM design parameters,particularly those unexplored combinations.Our results from the load capacity and force distribution comparison tests indicate that the VSM,optimized through our methods,quantitatively meets the practical engineering requirements.展开更多
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
The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solv...The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.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
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
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
The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and ele...The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.展开更多
Due to the complex structures of multi-limbed parallel robots,conventional parallel robots generally have limited workspace,complex kinematics,and complex dynamics,which increases the application difficulty of paralle...Due to the complex structures of multi-limbed parallel robots,conventional parallel robots generally have limited workspace,complex kinematics,and complex dynamics,which increases the application difficulty of parallel robot in industrial engineering.To solve the above problems,this paper proposes a single-loop Sch?nflies motion parallel robot with full cycle rotation,the robot can generate Sch?nflies motion by the most simplified structure.The novel Sch?nflies motion parallel robot is a two-limb parallel mechanism with least links and joints,and each limb is driven by a 2-degree of freedom(DOF)cylindrical driver(C-driver).The full cycle rotation of the output link is achieved by“…R-H…”structure,where the revolute(R)and helical(H)joints are coaxial.Mobility,kinematics,workspace and singularity analysis of the novel Sch?nflies motion parallel robot are analyzed.Then,dynamic model is formulated based on the principle of virtual work.Moreover,a pick-and-place task is implemented by the proposed Sch?nflies motion parallel robot and a serial SCARA robot,respectively.The simulation results verify the correctness of the theoretical model.Furthermore,dynamics performances of the proposed Sch?nflies motion parallel robot and a serial SCARA robot are compared,which reveal the performance merits of the proposed Sch?nflies motion parallel robot.展开更多
A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle....A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.展开更多
Plane strain assumption and exponent hardening law are used to investigate the plastic deformation in tube bending. Some theoretical formulae including stress, curvature radius of neutral layer, angle of neutral layer...Plane strain assumption and exponent hardening law are used to investigate the plastic deformation in tube bending. Some theoretical formulae including stress, curvature radius of neutral layer, angle of neutral layer deviation, bending moment, wall thickness variation and crosssection distortion, are developed to explain the phenomena in tube bending and their magnitudes are also determined. During unloading process, the springback angle is deduced using the virtual work principle, and springback radius is also given according to the length of the neutral layer which remains unchanged before and after springback. The theoretical formulae are validated by the experimental results or the validated simulation results in literature, which can be used to auicklv predict the forming aualitv of tube numerical control （NC） bending.展开更多
Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation...Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation,available formulas for the pipe stability are established on the basis of the assumption of uniform deformation along the tube length and symmetrical buckling.This method can predict the nonlinear response of elliptical collapse of steel circular tubes for different ratios of diameter to thickness（D/t）under pure bending or combined bending and external pressure.In these formulas,the strain-displacement relationship is deduced from the nonlinear ring theory,and the Ramberg-Osgood constitutive model is applied to simulate the inelastic material behavior.Meanwhile,the principle of virtual work is adopted to derive the equilibrium equations.A set of equations is solved by the Newton-Raphson method,and the iterative scheme contains nested iteration for the constitutive relation.In order to check the effectiveness of this theoretical method,illustrative examples are presented in this paper.Besides,the numerical simulation is carried out by use of ANSYS.A comparison of the results shows that the theoretical method can provide reasonable prediction for engineering practice.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
The large capacity servo press is traditionally realized by means of redundant actuation, however there exist the over-constraint problem and interference among actuators, which increases the control difficulty and th...The large capacity servo press is traditionally realized by means of redundant actuation, however there exist the over-constraint problem and interference among actuators, which increases the control difficulty and the product cost. A new type of press mechanism with parallel topology is presented to develop the mechanical servo press with high stamping capacity. The dynamic model considering gravity counterbalance is proposed based on the virtual work principle, and then the effect of counterbalance cylinder on the dynamic performance of the servo press is studied. It is found that the motor torque required to operate the press is a lot less than the others when the ratio of the counterbalance force to the gravity of ram is in the vicinity of 1.0. The stamping force of the real press prototype can reach up to 25 MN on the position of 13 mm away from the bottom dead center. The typical deep-drawing process with 1 200 mm stroke at 8 strokes per minute is proposed by means of five order polynomial. On this process condition, the driving torques are calculated based on the above dynamic model and the torque measuring test is also carried out on the prototype. It is shown that the curve trend of calculation torque is consistent to the measured result and that the average error is less than 15%. The parallel mechanism is introduced into the development of large capacity servo press to avoid the over-constraint and interference of traditional redundant actuation, and its dynamic characteristics with gravity counterbalance are presented.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
Soft robots have unique advantages over traditional rigid robots and have broad application prospects in many fields.To expand their bioinspired applications,we propose a novel Soft Pneumatic Actuator(SPA)associated w...Soft robots have unique advantages over traditional rigid robots and have broad application prospects in many fields.To expand their bioinspired applications,we propose a novel Soft Pneumatic Actuator(SPA)associated with spiral configuration inspired by the structure and unwinding motion of the seahorse tail.Diff erent from bending motion of common soft actuators,the spiral SPA can generate unwinding motion as input air pressure increases.First,to explore the eff ect of diff erent initial spiral types on unwinding performance,three typical spiral SPAs are designed and simulated while keeping the outside arc of actuator body constant.Second,a static model of the spiral SPA is established by combining the hyperelastic material model,geometric relationships,and virtual work principle.To improve model accuracy,two geometric correction parameters are employed and their physical significance is analyzed by finite element simulations.Third,a prototype of the logarithmic spiral SPA(Log_spiral SPA)is fabricated and a Fiber Bragg Grating(FBG)sensor array is designed to detect and reconstruct unwinding shapes of the prototype.Finally,the unwinding performance,static model and output force capability of the prototype are tested and verified.Furthermore,we discuss prospects for this novel spiral SPA and test its practical applications in inchworm-like motion,assisting finger rehabilitation and object capture.展开更多
Based on the nonlinear displacement-strain relationship,the virtual work principle method was used to establish the nonlinear equilibrium equations of steel beams with semi-rigid connections under vertical uniform loa...Based on the nonlinear displacement-strain relationship,the virtual work principle method was used to establish the nonlinear equilibrium equations of steel beams with semi-rigid connections under vertical uniform loads and temperature change.Considering the non-uniform temperature distribution across the thickness of beams,the formulas for stresses and vertical displacements were presented.On the basis of a flowchart for analysis of the numerical example,the effect of temperature change on the elastic behavior of steel beams was investigated.It is found that the maximal stress is mainly influenced by axial temperature change,and the maximal vertical displacement is principally affected by temperature gradients.And the effect of temperature gradients on the maximal vertical displacement decreases with the increase of rotational stiffness of joints.Both the maximal stress and vertical displacement decrease with the increase of rotational stiffness of joints.It can be concluded that the effects of temperature changes and rotational stiffness of joints on the elastic behavior of steel beams are significant.However,the influence of rotational stiffness becomes smaller when the rotational stiffness is larger.展开更多
Electromechanical dynamics analysis and simulation on a rollforming equipment with both sides variable cross-section are discussed in this study.The system includes mechanical parts and electromagnetism parts,and it i...Electromechanical dynamics analysis and simulation on a rollforming equipment with both sides variable cross-section are discussed in this study.The system includes mechanical parts and electromagnetism parts,and it is a strongly coupled electromechanical system.Based on a virtual work principle and given power,generalized forces of this system are obtained.By using Lagrange-Maxwell equations,a model of electromechanical dynamics is established.Differential equations of two-phase winding on d-q axis are obtained by Park transformation,which comes from three-phase winding equations on the A-B-C axis.This system is solved with the 4th order Runge-Kutta's method,and discrete solutions of all variables are obtained.Finally,by using Matlab language,the system is simulated.The results show that the proposed method works very well.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
文摘Theoretical approach with analytical and numerical procedure for determination initial displacement of a reinforced and prestressed concrete members, simple and cantilever beams, loaded by axial forces and bending moments is <span style="font-family:Verdana;">proposed. It is based on the principle of minimum potential energy with</span><span style="font-family:Verdana;"> equality of internal and external forces. The equations for strain internal energy have been derived, including compressed and tensile concrete and reinforce</span><span style="font-family:Verdana;">ment. The energy equations of the external forces with axial flexural dis</span><span style="font-family:Verdana;">placement effects have been derived from the assumed sinusoidal curve. The trapezoid rule is applied to integrate the segment strain energy. The proposed method uses a non</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">linear stress-strain curve for the concrete and bilinear elastic-plastic relationship for reinforcement;equilibrium conditions at a sectional level to generate the strain energies along the beam. At the end of this article are shown three specific numerical examples with comparative, experimental (two tests)</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">results with the excellent agreement and one calculation result with a great disagreement, by obtaining results of virtual principle method.</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">With this method is avoiding the adoption of an unsure (EJ), as in the case of underestimating or overestimate initial flexural rigidity.</span></span></span>
基金supported by the National Key R&D Program of China(Grant No.2019YFB1311200).
文摘Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones.Variable Stiffness Module(VSM)offer a solution,balancing flexibility and load capacity,for which particle jamming is an effective technology for stiffness-tunable robots requiring safe interaction and load capacity.Specific applica-tions,such as rescue scenarios,require quantitative analysis to optimize VSM design parameters,which previous analytical models cannot effectively handle.To address this,a Grey-box model is proposed to analyze the mechanical response of the particle-jamming-based VSM by combining a White-box approach based on the virtual work principle with a Black-box approach that uses a shallow neural network method.The Grey-box model demonstrates a high level of accuracy in predict-ing the VSM force-height mechanical response curves,with errors below 15%in almost 90%of the cases and a maximum error of less than 25%.The model is used to optimize VSM design parameters,particularly those unexplored combinations.Our results from the load capacity and force distribution comparison tests indicate that the VSM,optimized through our methods,quantitatively meets the practical engineering requirements.
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The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.
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.
文摘The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.
基金Supported by China Postdoctoral Science Foundation(Grant No.2023M740663)National Natural Science Foundation of China(Grant No.51975039)。
文摘Due to the complex structures of multi-limbed parallel robots,conventional parallel robots generally have limited workspace,complex kinematics,and complex dynamics,which increases the application difficulty of parallel robot in industrial engineering.To solve the above problems,this paper proposes a single-loop Sch?nflies motion parallel robot with full cycle rotation,the robot can generate Sch?nflies motion by the most simplified structure.The novel Sch?nflies motion parallel robot is a two-limb parallel mechanism with least links and joints,and each limb is driven by a 2-degree of freedom(DOF)cylindrical driver(C-driver).The full cycle rotation of the output link is achieved by“…R-H…”structure,where the revolute(R)and helical(H)joints are coaxial.Mobility,kinematics,workspace and singularity analysis of the novel Sch?nflies motion parallel robot are analyzed.Then,dynamic model is formulated based on the principle of virtual work.Moreover,a pick-and-place task is implemented by the proposed Sch?nflies motion parallel robot and a serial SCARA robot,respectively.The simulation results verify the correctness of the theoretical model.Furthermore,dynamics performances of the proposed Sch?nflies motion parallel robot and a serial SCARA robot are compared,which reveal the performance merits of the proposed Sch?nflies motion parallel robot.
文摘A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.
基金the National Natural Science Foundation of China (No.51164030)National Defense Key Disciplines Laboratory of Light Alloy Processing Science and Technology, Nanchang Hangkong University (No.gf201501001) for the support on this research
文摘Plane strain assumption and exponent hardening law are used to investigate the plastic deformation in tube bending. Some theoretical formulae including stress, curvature radius of neutral layer, angle of neutral layer deviation, bending moment, wall thickness variation and crosssection distortion, are developed to explain the phenomena in tube bending and their magnitudes are also determined. During unloading process, the springback angle is deduced using the virtual work principle, and springback radius is also given according to the length of the neutral layer which remains unchanged before and after springback. The theoretical formulae are validated by the experimental results or the validated simulation results in literature, which can be used to auicklv predict the forming aualitv of tube numerical control （NC） bending.
基金supported by the National High Technology Research and Development Programof China(863 Program,Grant No.2006AA09A105)
文摘Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation,available formulas for the pipe stability are established on the basis of the assumption of uniform deformation along the tube length and symmetrical buckling.This method can predict the nonlinear response of elliptical collapse of steel circular tubes for different ratios of diameter to thickness（D/t）under pure bending or combined bending and external pressure.In these formulas,the strain-displacement relationship is deduced from the nonlinear ring theory,and the Ramberg-Osgood constitutive model is applied to simulate the inelastic material behavior.Meanwhile,the principle of virtual work is adopted to derive the equilibrium equations.A set of equations is solved by the Newton-Raphson method,and the iterative scheme contains nested iteration for the constitutive relation.In order to check the effectiveness of this theoretical method,illustrative examples are presented in this paper.Besides,the numerical simulation is carried out by use of ANSYS.A comparison of the results shows that the theoretical method can provide reasonable prediction for engineering practice.
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.
基金supported by National Science and Technology Major Project of China(Grant Nos.2010ZX04017-013,2010ZX04004-112)National Natural Science Foundation of China(Grant No.51205248)+1 种基金Shanghai Municipal Natural Science Foundation of China(Grant No.12ZR1445200)Doctoral Programs Foundation of Ministry of Education of China(Grant No.20120073120060)
文摘The large capacity servo press is traditionally realized by means of redundant actuation, however there exist the over-constraint problem and interference among actuators, which increases the control difficulty and the product cost. A new type of press mechanism with parallel topology is presented to develop the mechanical servo press with high stamping capacity. The dynamic model considering gravity counterbalance is proposed based on the virtual work principle, and then the effect of counterbalance cylinder on the dynamic performance of the servo press is studied. It is found that the motor torque required to operate the press is a lot less than the others when the ratio of the counterbalance force to the gravity of ram is in the vicinity of 1.0. The stamping force of the real press prototype can reach up to 25 MN on the position of 13 mm away from the bottom dead center. The typical deep-drawing process with 1 200 mm stroke at 8 strokes per minute is proposed by means of five order polynomial. On this process condition, the driving torques are calculated based on the above dynamic model and the torque measuring test is also carried out on the prototype. It is shown that the curve trend of calculation torque is consistent to the measured result and that the average error is less than 15%. The parallel mechanism is introduced into the development of large capacity servo press to avoid the over-constraint and interference of traditional redundant actuation, and its dynamic characteristics with gravity counterbalance are presented.
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mainly supported by the National Natural Science Foundation,China(No.U1813216 and No.61903215)The Guangdong Natural Science Foundation,China(No.2018A030310679)+1 种基金The Basic Research Program of Shenzhen,China(No.JCYJ20180306174321766)The Open Project of Shenzhen Institute of Artificial Intelligence and Robotics for Society,China(No.ACO1202005004)。
文摘Soft robots have unique advantages over traditional rigid robots and have broad application prospects in many fields.To expand their bioinspired applications,we propose a novel Soft Pneumatic Actuator(SPA)associated with spiral configuration inspired by the structure and unwinding motion of the seahorse tail.Diff erent from bending motion of common soft actuators,the spiral SPA can generate unwinding motion as input air pressure increases.First,to explore the eff ect of diff erent initial spiral types on unwinding performance,three typical spiral SPAs are designed and simulated while keeping the outside arc of actuator body constant.Second,a static model of the spiral SPA is established by combining the hyperelastic material model,geometric relationships,and virtual work principle.To improve model accuracy,two geometric correction parameters are employed and their physical significance is analyzed by finite element simulations.Third,a prototype of the logarithmic spiral SPA(Log_spiral SPA)is fabricated and a Fiber Bragg Grating(FBG)sensor array is designed to detect and reconstruct unwinding shapes of the prototype.Finally,the unwinding performance,static model and output force capability of the prototype are tested and verified.Furthermore,we discuss prospects for this novel spiral SPA and test its practical applications in inchworm-like motion,assisting finger rehabilitation and object capture.
基金Project(50478075) supported by the National Natural Science Foundation of ChinaProject(YBJJ0817) supported by Scientific Research Foundation of Graduate School of Southeast University
文摘Based on the nonlinear displacement-strain relationship,the virtual work principle method was used to establish the nonlinear equilibrium equations of steel beams with semi-rigid connections under vertical uniform loads and temperature change.Considering the non-uniform temperature distribution across the thickness of beams,the formulas for stresses and vertical displacements were presented.On the basis of a flowchart for analysis of the numerical example,the effect of temperature change on the elastic behavior of steel beams was investigated.It is found that the maximal stress is mainly influenced by axial temperature change,and the maximal vertical displacement is principally affected by temperature gradients.And the effect of temperature gradients on the maximal vertical displacement decreases with the increase of rotational stiffness of joints.Both the maximal stress and vertical displacement decrease with the increase of rotational stiffness of joints.It can be concluded that the effects of temperature changes and rotational stiffness of joints on the elastic behavior of steel beams are significant.However,the influence of rotational stiffness becomes smaller when the rotational stiffness is larger.
基金Supported by the National Science and Technology Support Program(No.2011BAG03B03)Inner Mongolia University of Technology Science and Research Projects of China(No.X201338)
文摘Electromechanical dynamics analysis and simulation on a rollforming equipment with both sides variable cross-section are discussed in this study.The system includes mechanical parts and electromagnetism parts,and it is a strongly coupled electromechanical system.Based on a virtual work principle and given power,generalized forces of this system are obtained.By using Lagrange-Maxwell equations,a model of electromechanical dynamics is established.Differential equations of two-phase winding on d-q axis are obtained by Park transformation,which comes from three-phase winding equations on the A-B-C axis.This system is solved with the 4th order Runge-Kutta's method,and discrete solutions of all variables are obtained.Finally,by using Matlab language,the system is simulated.The results show that the proposed method works very well.
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.
