Abstract: In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Abstract: When dealing with mechanical constraints, it is usual in continuum mechanics to enforce ideas that stem from the seminal work of Bernoulli and D'Alembert and require that internal constraints do no...

Abstract: Thus far, only the dynamics of multibody systems consisting of interconnected rigid bodies has been discussed. In Chapter 2, methods for the kinematic analysis of the rigid frames of reference were presented and many useful kinematic relationships and identities were developed. These kinematic equations were used in Chapter 3 to develop general formulations for the dynamic differential equations of motion of multi-rigid-body systems. In rigid body dynamics, it is assumed that the distance between two arbitrary points on the body remains constant. This implies that when a force is applied to any point on the rigid body, the resultant stresses set every other point in motion instantaneously, and as shown in the preceding chapter, the force can be considered as producing a linear acceleration for the whole body together with an angular acceleration about its center of mass. The dynamic motion of the body, in this case, can be described using Newton–Euler equations , developed in the preceding chapter. In recent years, greater emphasis has been placed on the design of high-speed, lightweight, precision mechanical systems. These systems, in general, incorporate various types of driving, sensing, and controlling devices working together to achieve specified performance requirements under different loading conditions. In many of these industrial and technological applications, systems cannot be treated as collections of rigid bodies and the rigid body assumption is no longer valid. In such cases, a mechanical system can be modeled as a multibody system that consists of two collections of bodies. One collection consists of bulky compact solids that can be modeled as rigid bodies, while the second collection consists of relatively elastic bodies, such as rods, beams, plates, and shells, that may deform.

Abstract: Using continuum design sensitivity analysis (CDSA), in conjunction with the virtual work principle, equations have been derived for calculating forces without the need to solve the adjoint system. The resultant expressions are similar to the Maxwell stress tensor, but have the important advantage of the integration taking place on the surface of material rather than in the air outside. Implementation of the scheme leads to efficient calculations and improved accuracy.

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.

Abstract: The objective of this paper is to develop a finite element model for multi-body contact analysis of Cosserat materials. Based on the parametric virtual work principle, a quadratic programming method is developed for finite element analysis of contact problems. The contact problem with friction between two Cosserat bodies is treated in the same way as in plastic analysis. The penalty factors, that are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Compared with the conventional work on Cosserat elasticity, the newly developed model is on the contact analysis of the Cosserat materials and is seldom found in the existing literatures. Four examples are computed to illustrate the validity and importance of the model developed.

Abstract: A p-version, hierarchical finite element for moderately thick composite laminated plates is presented, where the effects of the rotary inertia, transverse shear, and geometrical nonlinearity are taken into account. The time-domain free-vibration equations of motion are obtained by applying the principle of virtual work. Those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor-corrector procedure. The linear natural frequencies of vibration of several plates are determined, and the convergence properties of the element are investigated. It is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy. The influences of the plate's thickness, of the width to length ratio, and of the fiber orientation on nonlinear free vibrations are investigated.

Abstract: The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.

Abstract: Mechanical deformation in incompressible linear and nonlinear magnetic materials was evaluated using various conventional electromagnetic volume and surface force density methods. These conventional force density methods are the Maxwell stress tensor method, Korteweg-Helmholtz force density method (KH), magnetic charge method, magnetizing current method, and Kelvin force density method (KV). The total force values obtained using these different force density methods were found to be the same and equal to the total force using the principle of virtual work, but the distribution of force density values calculated using the given force density methods was found to be different from each other. Using the given five force density methods, the mechanical deformations were evaluated and compared to one another. The KH and KV in incompressible material were shown to give the same mechanical deformation by employing the finite element method (FEM), verifying the theoretical equivalence. To implement the KV, the de...

Abstract: We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual non-equilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths.

Abstract: Recently, rare earth giant magnetostrictive materials (GMM) have drawn a lot of attention. Their applications are developing quickly owing to their unique features, especially at room temperature, such as giant strain coefficient, efficient electric(magnetic)-mechanical transformation ability, and so on. In this paper, a design model for magnetic and mechanical energy coupling and transformation, so-called coupled field iteration, is firstly described through the finite element method (FEM), including the calculation of magnetostrictive force, which is analyzed through the local application of the virtual work principle. Then a prototype of single GMM actuator is designed and comparison between the calculated deformations and experiment measurements is exhibited. Based on these results, a new motor is designed and fabricated by combining two single actuators with a metallic annulus. The metallic annulus is vibrated in elliptical motion mode, which is driven by the two actuators with specific input current pattern. Finally the elliptical motion is validated by the experiments.

Abstract: In this paper the formulation of an electric–mechanical beam-to-beam contact element is presented. Beams with circular cross-sections are assumed to get in contact in a point-wise manner and with clean metallic surfaces. The voltage distribution is influenced by the contact mechanics, since the current flow is constricted to small contacting spots. Therefore, the solution is governed by the contacting areas and hence by the contact forces. As a consequence the problem is semi-coupled with the mechanical field influencing the electric one. The electric–mechanical contact constraints are enforced with the penalty method within the finite element technique. The virtual work equations for the mechanical and electric fields are written and consistently linearized to achieve a good level of computational efficiency with the finite element method. The set of equations is solved with a monolithic approach. Copyright © 2005 John Wiley & Sons, Ltd.

Abstract: The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem.

Abstract: Modal coordinate formulation for analysing the dynamic interaction between a moving train and a simply supported bridge is presented in this article. The train is composed of a series of identical vehicles, and each vehicle is modelled as a four-wheelset mass-spring-damper multi-rigid body system with two-stage suspension having ten degrees of freedom (DOFs). A simply supported bridge, together with the track, is modelled as a Bernoulli-Euler beam. The deflection of the beam is described by superimposing modes. The train and the beam are regarded as an entire dynamic system, and then the modal coordinate formulation with time-dependent coefficients for this system is directly derived from the principle of virtual work. The formulation is solved by direct time integration method, to obtain the dynamic responses of this system. The correctness of the proposed formulations is illustrated by a comparison with the existing literature. The formulation helps save computer time using a few beam modes for ...

Abstract: A systematic methodology for solving the inverse dynamics of the Delta robot is presentedFirst,the inverse kinematics is solved based on the vector methodA 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 meaningThen based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developedMeanwhile 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 termsThis 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

Abstract: While it is generally believed that superior-subordinate relationships play a salient role in determining individual work outcomes, given the increasing popularity of virtual work arrangements, we ...

Abstract: 1 Introductory Principles.- 1.1 Review of Mechanics.- 1.2 Idealizations and Mathematical Models.- 1.3 Newton's Laws.- 1.4 Newton's Law of Universal Gravitation.- 1.5 Systems of Units and Conversion Factors.- 1.6 Dimensional Analysis.- 1.7 Problem Solving Techniques.- 1.8 Accuracy of Data and Solutions.- 2 Equilibrium of a Particle in Two Dimensions.- 2.1 Scalar and Vector Quantities.- 2.2 Elementary Vector Operations.- 2.3 Force Expressed in Vector Form.- 2.4 Addition of Forces Using Rectangular Components.- 2.5 Supports and Connections.- 2.6 The Free-Body Diagram.- 2.7 Equilibrium Conditions and Applications.- 3 Equilibrium of Particles in Three Dimensions.- 3.1 Force in Terms of Rectangular Components.- 3.2 Force in Terms of Magnitude and Unit Vector.- 3.3 Dot (Scalar) Product.- 3.4 Addition of Forces Using Rectangular Components.- 3.5 Equilibrium Conditions and Applications.- 4 Equilibrium of Rigid Bodies in Two Dimensions.- 4.1 Concept of the Moment-Scalar Approach.- 4.2 Internal and External Forces-Force Transmissibility Principle.- 4.3 Replacement of a Single Force by a Force and a Couple.- 4.4 Replacement of a Force System by a Force and a Couple.- 4.5 Replacement of a Force System by a Single Force.- 4.6 Replacement of a Distributed Force System by a Single Force.- 4.7 Supports and Connections.- 4.8 The Free-Body Diagram.- 4.9 Equilibrium Conditions and Applications.- 5 Equilibrium of Rigid Bodies in Three Dimensions.- 5.1 Definition of the Cross (Vector) Product.- 5.2 The Cross-Product in Terms of Rectangular Components.- 5.3 Vector Representation of the Moment of a Force.- 5.4 Varignon's Theorem.- 5.5 Moment of a Force About a Specific Axis.- 5.6 Vector Representation of a Couple.- 5.7 Replacement of a Single Force by a Force and a Couple.- 5.8 Replacement of a General Force System by a Force and a Couple.- 5.9 Equilibrium Conditions and Applications.- 5.10 Determinacy and Constraints.- 6 Truss Analysis.- 6.1 Analysis of Simple Trusses.- 6.2 Member Forces Using the Method of Joints.- 6.3 Members Carrying No Forces.- 6.4 Member Forces Using the Method of Sections.- 6.5* Determinacy and Constraints.- 6.6 Compound Trusses.- 6.7* Three-Dimensional Trusses: Member Forces Using the Method of Joints.- 7 Frames and Machines.- 7.1 Multiforce Members.- 7.2 Frame Analysis.- 7.3 Machine Analysis.- 8 Internal Forces in Members.- 8.1 Internal Forces.- 8.2 Sign Conventions.- 8.3 Axial Force and Torque Diagrams.- 8.4 Shear and Moment at Specified Cross-Sections.- 8.5 Shear and Moment Equations.- 8.6 Load, Shear, and Moment Relationships.- 8.7 Shear and Moment Diagrams.- 8.8* Cables Under Concentrated Loads.- 8.9* General Cable Theorem.- 8.10* Cables Under Uniform Loads.- 8.11 Frames-Internal Forces at Specified Sections.- 8.12 Internal Force Diagrams for Two-Dimensional Frames.- 9 Friction.- 9.1 Nature and Characteristics of Dry Friction.- 9.2 Angles of Static and Kinetic Friction.- 9.3 Applications of the Fundamental Equations.- 9.4 The Six Fundamental Machines.- 9.5* Friction on V-Belts and Flat Belts.- 9.6* Friction on Pivot and Collar Bearings and Disks.- 9.7* Friction on Journal Bearings.- 9.8 Problems in Which Motion Is Not Predetermined.- 10 Centers of Gravity, Centers of Mass, and Centroids.- 10.1 Centers of Gravity and of Mass.- 10.2 Centroid of Volume, Area, or Line.- 10.3 Composite Objects.- 10.4 Centroids by Integration.- 10.5* Theorems of Pappus and Guldinus.- 10.6* Fluid Statics.- 11 Moments and Products of Inertia.- 11.1 Concepts and Definitions.- 11.2 Parallel-Axis Theorems.- 11.3 Moments of Inertia by Integration.- 11.4 Moments of Inertia of Composite Areas and Masses.- 11.5* Area Product of Inertia.- 11.6* Area Principal Axes and Principal Moments of Inertia.- 11.7* Mohr's Circle for Area Moments and Products of Inertia.- 11.8* Mass Principal Axes and Principal Moments of Inertia.- 12 Virtual Work and Stationary Potential Energy.- 12.1 Differential Work of a Force.- 12.2 Differential Work of a Couple.- 12.3 The Concept of Finite Work.- 12.4 The Concept of Virtual Work.- 12.5* Work of Conservative Forces.- 12.6* The Concept of Potential Energy.- 12.7* The Principle of Stationary Potential Energy.- 12.8* States of Equilibrium.- Appendix A. Properties of Selected Lines and Areas.- Appendix B. Properties of Selected Masses.- Appendix C. Useful Mathematical Relations.- Appendix D. Selected Derivatives.- Appendix E. Selected Integrals.- Appendix F. Supports and Connections.- Appendices.- Answers.

Abstract: This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures for which dynamical response is mainly governed by plastic deformations so as to be able to provide designers with sufficiently accurate results. The method to be presented is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation are outlined. The procedure is applied to a typical SDOF system and results are compared with NLTH analysis commonly used for design purposes. Secondly, by means of the Virtual Work Principle, the definition of the equation of motion of a desired collapse mechanism of a multi degree of freedom (MDOF) system is presented. This equation is of the same type as in the SDOF case, and therefore the procedure presented in the first part of the paper may be used. The method is applied to a 4-story reinforced concrete frame structure. Results are compared to those derived by a conventional NLTH analysis and found to be encouraging.

Abstract: IntroductIon Globalization is an issue currently affecting many organizations and is one that has profound consequences for the nature of work In the new, networked economy, knowledge is seen as an asset that needs to be managed and is central to the success of organizations (Boersma & Stegwee, 1996). Since the 1980s, many organizations have taken steps to outsource and downsize in an effort to remain competitive as off-shoring, has been happening at a rapid pace in a growing range of activities and sectors. Out-sourcing, off-shoring, downsizing and programs of planned redundancy all mean that, as people leave, they take with them a valuable stock of corporate knowledge. This can be knowledge of how the work is done in practice and domain knowledge (Sachs, 1995). Some knowledge is easy to replace, but the knowledge of how a company operates is built over years and is irreplaceable in the short term. In addition, many organizations now have to cope with the increasing internationalization of business that forces collaboration and knowledge-sharing across geographical boundaries. Working in a more internationalized setting places strains on the way a team operates, as they have to cope not only with geographical distance, but also time, 1967 Effective Virtual Working through Communities of Practice culture and possibly language barriers. For such organizations, there is an urgent need to identify ways to work effectively in such groups.

Abstract: In this paper a Finite strip method is developed to analyze very large deformations of thin plates and folded plates by use of the elastic Cosserat theory. The principle of virtual work is exploited to present the weak form of the governing differential equations. Through a linear mapping, a rectangular strip is transformed into a standard square computational domain in which the deformation and director fields are developed together with the general forms of the uncoupled nonlinear equations. The geometric and material tangential stiffness matrices are formed through linearization, and a step by step procedure is presented to complete the scheme. The validity and the accuracy of the method are illustrated through certain numerical examples and comparison of the results with other researches. The method is shown to be capable of handling numerical analysis of plates experiencing very large deformations.

Abstract: In this paper,based on the geometric nonlinear behavior of cable structures,a finite element method with four-node isoparametric element was presented,the third order polynomial was used as displacement functions and initial curve of the elementBy means of the principle of virtual work and the updated Lagrangian method,the authors derived the finite element equations,and solved them by Newton-Raphson methodThe proposed model leads to high precision and can meet the engineering requirementsThe model presented in this paper can be applied in the analysis of long-span tension structures,such as cable structures,cable domes and so forth