THE VIRTUAL WORK PRINCIPLE AND LINEAR COMPLEMEN-TARY METHOD FOR COUPLING ANALYSIS OF ELASTO-PLASTIC DAMAGE STRUCTURE

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.

NEW PRINCIPLES OF WORK AND ENERGY AS WELLAS POWER AND ENERGY RATE FORCONTINUUM FIELD THEORIES

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

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) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional 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.e. 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.

A FINITE ELEMENT—MATHEMATICAL PROGRAMMING METHOD FOR ELASTOPLASTIC PROBLEMS BASED ON THE PRINCIPLE OF VIRTUAL WORK

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.

THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY

This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.

ON SOME BASIC PRINCIPLES IN DYNAMIC THEORY OF ELASTIC MATERIALS WITH VOIDS

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.

DYNAMIC PRINCIPLE FOR INTERACTION BETWEEN HEART AND ARTERIAL SYSTEM

Various steady models for interaction between heart and arterial system have been given in liter- ature,In our recent study,a dynamic principle,i.e.the principle of least cardiac work is proposed,and a dy- namic model for interaction of heart and arterial system is established.Preliminary results of our experiments show that both the principle and the model are consistent with the physiological phenomena.It reveals that the pres- ent analysis may offer a new measure for the study of dynamic process of interaction between heart and arterial system.

Mechanical stress and deformation analyses of pressurized cylindrical shells based on a higher-order modeling

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.

Analysis on Buckling Performance of Submarine Pipelines During Deepwater 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.

Dynamic Modeling and Experiment of a New Type of Parallel Servo Press Considering Gravity Counterbalance

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.

Third-order polynomial model for analyzing stickup state laminated structure in flexible electronics

Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weight, can be folded,twisted, flipped inside-out, or be pasted onto other surfaces of arbitrary shapes. In this paper, an analytical model is presented to study the mechanics of laminated hard-soft structures in flexible electronics under a stickup state. Thirdorder polynomials are used to describe the displacement field,and the principle of virtual work is adopted to derive the governing equations and boundary conditions. The normal strain and the shear stress along the thickness direction in the bimaterial region are obtained analytically, which agree well with the results from finite element analysis. The analytical model can be used to analyze stickup state laminated structures, and can serve as a valuable reference for the failure prediction and optimal design of flexible electronics in the future.

A New Kind of Pilot Controlled Proportional Direction Valve with Internal Flow Feedback

Proportional direction valve is one of the most fundamental elements in electronic-hydraulic control technique. Its function is to control the operating speed, direction, position, and strength of output force of the hydraulic actuator continuously. Considering the different application and the cost, the existing technique mainly includes the internal feedback valve used in open loop system, and the electronic closed loop controlled valve used in closed loop system. Because of their different mechanical structure and the gre at different in performance, it brings inconvenience for customer to select, also inconvenience for enterprise to produce. Aiming at this problem, the idea of combining the above two kinds of valves into one body is proposed first, and then the new valve＇s structure to realize this target is designed. The idea intends to apply the displacement pilot flow feedback control principle in present 2-position 2-way valve system to the proportional direction valve of 3-position 4-way system. Newly designed feed forward controller can decouple the interference between the internal feedback and the electronic closed loop. Redundant conversion is designed to electronic switch mode. Experiment on dynamic and static characteristic of new proportional direction valve in internal feedback control mode and electronic closed loop control mode is discussed to prove the new theory is correct. Although the new valve is of excellent dynamic response characteristic, its steady control characteristic in open loop control mode needs to be improved further. The research results prepare one new fundamental element for electronic-hydraulic control technology.

Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

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.

Study on generalized magneto-thermoelastic problems by FEM in time domain

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.

Performance analysis of a 2-stroke micro free-piston swing engine

The micro free-piston swing engine （MFPSE） is a new structure, free-piston internal combustion engine. The dynamic model integrated MFPSE with a power generator and thermodynamic models in compression, power and scavenge processes based on the open thermodynamic systems were presented. A simulation was executed at given geometric parameters and initial conditions. The results manifest that the working principle of MFPSE is feasible.

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅰ)──MICROPOLAR THERMOELASTICITY

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.

FORCE FEEDBACK DATAGLOVE BASED ON PNEUMATIC ARTIFICIAL MUSCLES

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.

THE MIXED BOUNDARY-VALUE PROBLEM FOR NON-LOCAL ASYMMETRIC ELASTICITY

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.

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

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.

Solar Shutters based on Photovoltaic Power Generation

This paper introduces a set of electrical energy-saving system for commercial office buildings,aiming at making better use of solar energy and photovoltaic power generation.Solar energy is a renewable energy source,which is inexhaustible clean energy and has great commercial application value.Based on this fact,we plan to design a unique and novel solar shutter in combination with the daily observation and the shape of solar panels.The shutter blades are equipped with an automatic light tracking system,and the angle of the blades can be adjusted in time through photoresistor induction,that is,as much solar energy as possible can be converted into electric energy for load use,and at the same time,comfortable light can be provided for the house.In essence,the system is a small photovoltaic power generation system,which runs all day with high-efficiency based on automatic sun tracking.Among them,the basic operation route includes:solar position detection,computer data processing,photovoltaic and electric volt energy conversion,circuit connection,etc.From the current debugging results,the shutter has the characteristics of humanization,high efficiency,cleanliness and so on.Through this energy-saving system,we hope to maximize the use of solar energy in the premise of low cost,so as to achieve the purpose of energy saving.