Showing papers on "Virtual work published in 2009"
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23 Nov 2009TL;DR: Theoretical work hardening properties of elastic and inelastic deformation have been studied in this article, where the authors present a uniqueness theorem for elastic deformation and limit analysis and limiting equilibrium.
Abstract: Preface 1. Stress and strain 2. Elastic and inelastic material behaviour 3. Yield 4. Plastic flow 5. Collapse load theorems 6. Slip line analysis 7. Work hardening behaviour A. Non-Cartesian coordinate systems B. Mohr's circles C. Principles of virtual work D. Extremum principles E. Drucker's stability postulate F. The associated flow rule G. A uniqueness theorem for elastic-plastic deformation H. Theorems of limit analysis I. Limit analysis and limiting equilibrium.
262 citations
129 citations
01 Jan 2009
TL;DR: In this paper, a refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline.
Abstract: A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.
119 citations
TL;DR: In this paper, a Lagrange multiplier method is proposed to solve 2D Coulomb frictional contact problems in the context of large deformations, where the constraints are imposed in a weak integral sense along the contact surface.
116 citations
TL;DR: In this article, the first 3D C1 element was constructed, which is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity.
Abstract: In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C1 finite elements and their perceived computational cost. In this context, the lack of three-dimensional C1 elements is of particular concern. In this paper we present a new C1 hexahedral element which, to the best of our knowledge, is the first three-dimensional C1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good-quality solutions. Copyright © 2008 John Wiley & Sons, Ltd.
110 citations
TL;DR: In this paper, the authors review two concepts that appear in the theory that governs the interaction between electric fields and deformable media, namely the "Maxwell stress" and the "total stress".
91 citations
TL;DR: This conceptual research develops a theoretical model of individual virtual competence and describes its role in the communication process, which underpins effective knowledge transfer in virtual settings and considers the antecedent role that prior experience in virtual activity plays in aiding workers to develop virtual competence, which in turn engenderseffective knowledge transfer.
Abstract: Economic forces, competitive pressures and technological advances have created an environment within which firms have developed new ways of organizing (e.g. virtual work settings) and managing their resources (e.g. knowledge management) in order to maintain and improve firm performance. Extant research has highlighted the challenges associated with managing knowledge in virtual settings. However, researchers are still struggling to provide effective guidance to practitioners in this field. We believe that a better understanding of individual virtual competency is a potential avenue for managing the complexity of knowledge transfer in virtual settings. In particular, we suggest that optimal knowledge transfers can be achieved by individuals armed with the right personal capabilities and skills for virtual work, particularly when those knowledge transfers are emergent, bottom-up and cannot be specified a priori. The virtual competency exhibited by individuals can be the key to overcoming the constraints of knowledge transfers with such characteristics because underlying competency can facilitate effective action in unfamiliar and novel situations. In this conceptual research, we develop a theoretical model of individual virtual competence and describe its role in the communication process, which underpins effective knowledge transfer in virtual settings. Additionally, we consider the antecedent role that prior experience in virtual activity plays in aiding workers to develop virtual competence, which in turn engenders effective knowledge transfer. We conclude with implications for future research and for practicing managers.
84 citations
TL;DR: In this paper, a virtual power format was used to deduce all balance and imbalance laws of thermomechanics, and the basic balance laws turn out to be those for momentum and entropy.
Abstract: It is shown that a virtual power format slightly more general than usual may be employed to deduce all balance and imbalance laws of thermomechanics. An essential role is played by the notion of thermal displacement; the basic balance laws turn out to be those for momentum and entropy. In consequence of these balances and of two axioms of thermodynamical nature—namely, conservation of internal action in cyclic processes and dissipative nature of ordinary processes—balance of energy and inbalance of entropy are arrived at.
73 citations
TL;DR: In this paper, a semi-analytical solution method is developed for stress analysis of single-lap hybrid (bolted/bonded) joints of composite laminates under in-plane as well as lateral loading.
71 citations
TL;DR: The inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices to lead to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion.
Abstract: In this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here 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. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.
67 citations
TL;DR: In this article, the necessary similarity conditions for free vibrations of orthogonally stiffened cylindrical shells are developed using the similitude theory, and different examples are solved to validate the scaling laws numerically and experimentally.
Abstract: In this paper, the necessary similarity conditions, or scaling laws, for free vibrations of orthogonally stiffened cylindrical shells are developed using the similitude theory. The Donnell-type nonlinear strain–displacement relations along with the smearing theory are used to model the structure. Then the principle of virtual work is used to analyze the free vibration of the stiffened shell. After non-dimensionalizing the derived formulations, the scaling laws are developed, using the similitude theory. Then, different examples are solved to validate the scaling laws numerically and experimentally. The obtained results show the effectiveness of the derived formulations.
TL;DR: In this article, the authors extend the theory of dimensional regularization to pre-fractal media with lower and upper cut-offs, in which D is also the order of fractional integrals employed to state global balance laws.
Abstract: This paper further continues the recently begun extension of continuum mechanics and thermodynamics to fractal porous media which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution lengthscale R. The focus is on pre-fractal media (i.e., those with lower and upper cut-offs) through a theory based on dimensional regularization, in which D is also the order of fractional integrals employed to state global balance laws. In effect, the global forms of governing equations may be cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing coefficients involving D, d and R. Here we first generalize the principles of virtual work, virtual displacement and virtual stresses, which in turn allow us to extend the minimum energy theorems of elasticity theory. Next, we generalize the extremum principles of elasto-plastic and rigid-plastic bodies. In all the cases, the derived relations depend explicitly on D, d and R, and, upon setting D = 3 and d = 2, they reduce to conventional forms of governing equations for continuous media with Euclidean geometries.
TL;DR: In this article, the 3-RRR Agile Wrist spherical parallel robot with three identical legs was developed and the principle of virtual work was used in the inverse dynamic problem.
Abstract: Recursive matrix relations for kinematics and dynamics of the 3-RRR Agile Wrist spherical parallel robot are established in this paper The prototype of the robot is a three-degrees-of-freedom mechanism with three identical legs Controlled by concurrent torques, which are generated by some electric motors, the active elements of the robot have three independent rotations Knowing the rotation motion of the moving platform, we develop first the inverse kinematical problem and determine the velocities and accelerations Further, the principle of virtual work is used in the inverse dynamic problem Matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model
TL;DR: In this article, the second order statistics of post buckling load of shear deformable laminated composite plates resting on linear elastic foundation with random system properties were derived using the principal of virtual work.
TL;DR: In this article, the authors established recursive matrix relations for kinematics and dynamics of the commonly known 3-RPR planar parallel robots, where three identical planar legs connecting to the moving platform are located in the same plane.
TL;DR: In this paper, the authors employ a new finite element formulation for dynamics analysis of a viscoelastic flexible multibody system, which can relax the small deformation assumption in the traditional finite element implementation.
Abstract: This paper employs a new finite element formulation for dynamics analysis of a viscoelastic flexible multibody system. The viscoelastic constitutive equation used to describe the behavior of the system is a three-parameter fractional derivative model. Based on continuum mechanics, the three-parameter fractional derivative model is modified and the proposed new fractional derivative model can reduce to the widely used elastic constitutive model, which meets the continuum mechanics law strictly for pure elastic materials. The system equations of motion are derived based on the absolute nodal coordinate formulation (ANCF) and the principle of virtual work, which can relax the small deformation assumption in the traditional finite element implementation. In order to implement the viscoelastic model into the absolute nodal coordinate, the Grunwald definition of the fractional derivative is employed. Based on a comparison of the HHT-I3 method and the Newmark method, the HHT-I3 method is used to solve the equations of motion. Another particularity of the proposed method based on the ANCF method lies in the storage of displacement history only during the integration process, reducing the numerical computation considerably. Numerical examples are presented in order to analyze the effects of the truncation number of the Grunwald series (fading memory phenomena) and the value of several fractional model parameters and solution convergence aspects.
TL;DR: Recursive matrix relations in kinematics and dynamics of a Delta parallel robot having three revolute actuators are established and the inverse dynamic problem is solved using an approach based on the fundamental principle of virtual work.
Abstract: Recursive matrix relations in kinematics and dynamics of a Delta parallel robot having three revolute actuators are established in this paper. The prototype of the manipulator is a three degrees-of-freedom space mechanism, which consists of a system of parallel closed kinematical chains connecting to the moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot's element. Further, the inverse dynamic problem is solved using an approach based on the fundamental principle of virtual work. Finally, a comparative study on time-history evolution of the torques of the three actuators is analysed.
TL;DR: An updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed and a new possible galloping mode is discovered under the condition that the lowest order of vertical natural frequency of the transmissionline is approximately two times of the horizontal one.
Abstract: Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a threenode isoparametric cable element with three translational and one torsional degrees-offreedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.
TL;DR: In this article, the Star parallel manipulator is used to determine the position, velocity and acceleration of each robot's link, and the inverse dynamics problem is solved using an approach based on the principle of virtual work.
01 Jan 2009
TL;DR: In this paper, the authors explore the associated concepts of work and energy for the solution of specific elasticity problems and explore some new energy methods or principles that provide additional techniques to solve elasticity problem.
Abstract: Before proceeding to the solution of specific elasticity problems we wish to explore the associated concepts of work and energy. Boundary tractions and body forces will do work on an elastic solid and this work will be stored inside the material in the form of strain energy. For the elastic case, removal of these loadings will result in complete recovery of the stored energy within the body. Development of strain energy concepts will yield new and useful information not found by other methods. This study will also lead to some new energy methods or principles that provide additional techniques to solve elasticity problems. In some sense these methods may be thought of as replacements of particular field equations that have been derived previously. For problems in structural mechanics involving rods, beams, plates, and shells, energy methods have proven to be very useful in developing the governing equations and associated boundary conditions. These schemes have also provided a method to generate approximate solutions to elasticity problems. More recently, particular energy and variational techniques have been used extensively in the development of finite and boundary element analysis. Our presentation here will only be a brief study on this extensive subject.
TL;DR: In this article, a 3D Timoshenko's beam with a homogeneous orthotropic fabric was proposed and the analytical equilibrium equations were performed using the total Lagrangian form of the virtual work principle.
Abstract: A theoretical analysis of inflatable beam was performed. These circular cross-section beams are made from fabric of polyester fibers coated with PVC. Such fabric may be tailored to form an arch when inflated. In many analyses, the Saint Venant Kirchhoff hypothesis was used and the authors assumed that the beams are made from an isotropic fabric. In this paper, a 3D Timoshenko's beam with a homogeneous orthotropic fabric was proposed. The model took into account the geometric nonlinearities and the inflation pressure follower force effect. The analytical equilibrium equations were performed using the total Lagrangian form of the virtual work principle. As these equations were nonlinear, a linearization was performed at the prestressed reference configuration to obtain the equations devoted to linearized problems. As an example, the bending problem was investigated. Four cases of boundary conditions were treated and the deflection and rotation's results improved the existing models in the case of an isotropic fabric. The wrinkling load in every case was also presented.
TL;DR: In this paper, the inverse kinematics and dynamics of a symmetric spherical 3-DOF mechanism with three prismatic actuators are established using the principle of virtual work.
Abstract: Recursive relations in kinematics and dynamics of the symmetric spherical 3-
$\mathit{U\underline{P}S}/S$
parallel mechanism having three prismatic actuators are established in this paper. Controlled by three forces, the parallel manipulator is a 3-DOF mechanical system with three parallel legs connecting to the moving platform. Knowing the position and the rotation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity, and acceleration of each manipulator’s link. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, but it has been verified using the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input forces and powers are obtained.
TL;DR: In this article, the virtual work principle is used for the dynamic formulation of redundant and non-redundant parallel manipulators for dynamic parameter identification, and the selection of pivotal point and the computation of inertia force and moment about the pivotal point are studied.
TL;DR: In this article, a finite element model for the stress analysis of circular arches strengthened with composite materials is developed, which uses the principle of virtual work, the Bernoulli-Euler curved beam theory for the arch and the composite reinforcement, and a high-order kinematic assumption that satisfies the compatibility and tangential equilibrium conditions of the adhesive.
TL;DR: In this paper, a nonlinear finite element model is provided to predict the static aero-thermal deflection and the vibration behavior of geometrically imperfect shape memory alloy hybrid composite panels under the combined effect of thermal and aerodynamic loads.
TL;DR: In this article, the free vibration and mode shapes of straight Euler-Bernoulli-Vlasov beams were analyzed by using the virtual work principle which includes the second order terms of finite beam rotations.
TL;DR: In this paper, Opoka and Pietraszkiewicz presented a non-linear theory of thin shells expressed in terms of displacements of the shell reference surface as the only independent field variables.
TL;DR: The simulation results verify the efficiency of the contact force and deformation model with reasonable realism, and relations between the virtual force and nodal displacements are analyzed to obtain elastic deformations.
Abstract: This article addresses a largely open problem in haptic simulation and rendering: contact force and deformation modeling for haptic simulation of a discrete globe mass-spring model, especially for global deformation The mass-spring system is composed of nodes connected with radially distributed springs We tackle the problem using the theory of virtual work, and relations between the virtual force and nodal displacements are analyzed to obtain elastic deformations The global deformation is controlled by the total nodal deformations based on a force equation at each node The simulation results verify the efficiency of the contact force and deformation model with reasonable realism
TL;DR: In this paper, the authors analyzed the kinematics and dynamics of a wheeled mobile robot, consisting of a platform, two conventional wheels and a crank that controls the motion of a free rolling caster wheel.
Abstract: Kinematics and dynamics of a mobile robot, consisting of a platform, two conventional wheels and a crank that controls the motion of a free rolling caster wheel, are analyzed in the paper. Based on several matrix relations of connectivity, the characteristic velocities and accelerations of this non-holonomic mechanical system are derived. Using the principle of virtual work, expressions and graphs for the torques and the powers of the two driving wheels are established. It has been verified the results in the framework of the second-order Lagrange equations with their multipliers. The study of the dynamics problems of the wheeled mobile robots is done mainly to solve successfully the control of the motion of such systems.
TL;DR: In this article, a new 3D geometric stiffness matrix based on the principle of virtual work is proposed for linear buckling analysis of 3D layered continua using the Cosserat approach.