Showing papers on "Virtual work published in 2001"
21 May 2001
TL;DR: A simple yet comprehensive approach that enables the stiffness of a tripod-based parallel kinematic machine to be quickly estimated and the contributions of different component rigidities to the machine stiffness are discussed.
Abstract: Presents a simple yet comprehensive approach that enables the stiffness of a tripod-based parallel kinematic machine to be quickly estimated. The approach arises from the basic idea for the determination of the equivalent stiffness of a group of serially connected linear springs and can be implemented in two steps. In the first step, the machine structure is decomposed into two substructures associated with the machine frame and parallel mechanism. The stiffness models of these two substructures are formulated by means of the virtual work principle. This is followed by the second step that enables the stiffness model of the machine structure as a whole to be achieved via linear superposition. The three-dimensional representations of the machine stiffness within the usable workspace are depicted and the contributions of different component rigidities to the machine stiffness are discussed. The results are compared with those obtained through experiments.
156 citations
TL;DR: In this article, the authors derived the governing equations for linear vibration of a rotating Timoshenko beam by the d&Alembert principle and the virtual work principle and used the consistent linearization of the fully geometrically non-linear beam theory to solve the natural frequency of the rotating beam.
139 citations
TL;DR: In this paper, a framework for the mechanics of solids, deformable over fractal subsets, is outlined, and an extension of the Gauss-Green theorem to fractional operators is proposed to demonstrate the duality principle for fractal media.
122 citations
Abstract: The behaviour of porous material under dynamic conditions is assessed by a micromechanical approach. By averaging, a general form for the dynamic macrostress is proposed which recovers the static definition when inertia effects are neglected. In this work, a representative volume element for the porous material is defined as a hollow sphere. Using an approximation of the velocity field and the principle of virtual work, an explicit relationship is found between the macroscopic stress and strain rate. The macrostress tensor is proved to be symmetric, in the present formulation proposed for porous materials. Illustrations are shown for hydrostatic tension or compression and also for axisymmetric loading. In the latter case, the effect of stress triaxiality is captured.
99 citations
TL;DR: In this paper, a new derivation of the Green-Naghdi (GN) equations for ''sheet-like'' flows is made by use of the principle of virtual work Divergence-free virtual displacements are used to formulate the momentum equations weakly.
Abstract: A new derivation of the Green-Naghdi (GN) equations for `sheet-like' flows is made by use of the principle of virtual work Divergence-free virtual displacements are used to formulate the momentum equations weakly This results in the elimination of the internal pressure from the GN equations As is well-known in particle dynamics, the principle of virtual work can be integrated to obtain Hamilton's principle These integrations can be performed in a straightforward manner when the Lagrangian description of fluid motion is adopted When Hamilton's principle is written in an Eulerian reference frame, terms must be added to the Lagrangian to impose the Lin constraint to account for the difference between the Lagrangian and Eulerian variables (Lin) If, however, the Lin constraint is omitted, the scope of Hamilton's principle is confined to irrotational flows (Bretherton) This restricted Hamilton's principle is used to derive the new GN equations for irrotational flows with the same kinematic approximation as in the original derivation of the GN equations The resulting new hierarchy of governing equations for irrotational flows (referred to herein as the IGN equations) has a considerably simpler structure than the corresponding hierarchy of the original GN governing equations that were not limited to irrotational flows Finally, it will be shown that the conservation of both the in-sheet and cross-sheet circulation is satisfied more strongly by the IGN equations than by the original GN equations
97 citations
TL;DR: In this paper, a model for analyzing the shear-lag effect in composite beams with flexible shear connection is proposed, which is based on the virtual work theorem for three-dimensional bodies.
Abstract: Taking into account the long-term behavior of the concrete, this paper proposes a model for analyzing the shear-lag effect in composite beams with flexible shear connection. By assuming the slab loss of planarity described by a fixed warping function, the linear kinematics of the composite beam is expressed by means of four unknown functions: the vertical displacement of the whole cross section, the axial displacements of the concrete slab and of the steel beam, and the intensity of the warping (shear-lag function). A variational balance condition is imposed by the virtual work theorem for three-dimensional bodies, from which the local formulation of the problem, which involves four equilibrium equations with the relevant boundary conditions, is achieved. The assumptions of linear elastic behavior for the steel beam and the shear connection and of linear viscoelastic behavior for the concrete slab lead to an integral-differential type system, which is numerically integrated. The numerical procedure, based on the step-by-step general method and the finite-difference method, is illustrated and applied to a composite beam to get information on the complex time-dependent behavior, including shear-lag and connection deformability effects.
82 citations
TL;DR: In this article, an efficient coupled electromechanical model is developed for multilayered composite beams with embedded or surface bonded piezoelectric laminae subjected to static EMG excitation.
82 citations
TL;DR: In this article, the authors re-evaluated the known velocity relationships expressed in the form of a velocity diagram in orthogonal metal cutting, arguing that the metal cutting process be considered as cyclic and consisting of three distinctive stages.
Abstract: This paper re-evaluates the known velocity relationships expressed in the form of a velocity diagram in orthogonal metal cutting, arguing that the metal cutting process be considered as cyclic and consisting of three distinctive stages. The velocity diagrams for the second and third stages of a chip-formation cycle are discussed. The fundamentals of the mechanics of orthogonal cutting, which are the upper-bound theorem applied to orthogonal cutting and the real virtual work equation, are re-evaluated using the proposed velocity diagram and corrected relationships are proposed. To prove the theoretical results, the equation for displacements in the deformation zone is derived using the proposed velocity relationships. To prove that the displacements in the deformation zone follow the derived equation and that this zone consists of two unequal parts, a metallographical study of chip structures has been carried out. To estimate the variation of stress and strain in the deformation zone quantitatively, a microhardness scanning test was conducted. Because it is proved that the chip formation process is cyclic, its frequency is studied. It is shown that when the noise due to various inaccuracies in the machining system is eliminated from the system response and thus from the measuring signal, and when this signal is then properly processed, the amplitude of the peak at the frequency of chip formation is the largest in the corresponding autospectra.
38 citations
TL;DR: In this paper, an 18-node degenerate element with nine nodes located on the base shell structure and nine nodes on the constraining layer is presented for constrained layer damping treatments. But, the element is not suitable for either plate or shell structures.
Abstract: An isoparametric, degenerate element for constrained layer damping treatments is presented The element is valid for either plate or shell structures The element is an 18-node degenerate element with nine nodes located on the base shell (or plate) structure and nine nodes on the constraining layer Each node has five degrees of freedom: translations in x,y, and z and bending rotations α and β about the midsurface where the node is located The displacement field of the viscoelastic layer is interpolated linearly from the nodal displacements; therefore, the viscoelastic layer allows both shear and normal deformations The base shell (or plate) structure and the constraining layer can be linearly elastic or piezoelectric for passive or active applications The viscoelastic layer is assumed to be linearly viscoelastic The equation of motion is derived through use of the principle of virtual work For thin plate structures, numerical results show that the isoparametric element can predict natural frequencies, loss factors, and mechanical impedances that are as accurate as NASTRAN with substantially fewer elements For thin shell structures, locking and spurious modes need to be resolved to yield reasonable results
37 citations
TL;DR: In this paper, a dynamic finite element procedure for the simulation of blow molding and thermoforming of thermoplastic hollow parts is presented. But this procedure does not take inertia effects into account.
Abstract: This paper reports on the development of a dynamic finite element procedure for the simulation of blow molding and thermoforming of thermoplastic hollow parts. The Principle of Virtual Work written herein takes inertia effects into account. The heat-softened parison is assumed to be a nonlinear hyperelastic Mooney-Rivlin membrane and is meshed with classical linear triangular finite elements. We adopt the explicit central differences time integration scheme with the special lumping technique. The mold is divided Into triangular elements and the contact between the parison and the mold is assumed to be sticky. Therefore, contacted degrees of freedom of the parison are fixed on the solid boundary until the end of the simulation. Performances are highly improved by the use of an adaptive mesh refinement procedure based on a geometric criterion for detection and on the simple addition of a node at the mid-side of the longest edge for subdivision. The method is illustrated through some examples of thermoformed and blow-molded parts. Our results are compared with both experimental and numerical results from Literature to validate the present theory.
35 citations
TL;DR: In this paper, a Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration due to the presence of gyroscopic, or Coriolis forces, is taken into consideration.
Abstract: A Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration, due to the presence of gyroscopic, or Coriolis forces, is taken into consideration. The dynamic trigonometric shape functions of uncoupled bending and axial vibrations of an axially loaded uniform beam element are derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables, based on these dynamic shape functions, leads to a single frequency dependent stiffness matrix which is Hermitian and represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by two illustrative examples of vertical and radial beams where the influence of Coriolis forces on natural frequencies of the clamped-free rotating beams is demonstrated by numerical results.
Book•
12 Sep 2001
TL;DR: In this paper, the authors introduce the concept of solid mechanics and propose the symmetric bending theory of beams and apply it to structural mechanics, including axial loadings and de Saint Venant torsion.
Abstract: Preface. PART A: BASIC CONCEPTS. 1 Introductory Concepts of Solid Mechanics. 2 Internal Forces and Stress. 3 Deformation and Strain. 4 Behaviour of Materials: Constitutive Equations. 5 Summary of Basic Results and Further Idealisations: Solutions using the "Mechanics--of--Materials" Approach. PART B: APPLICATIONS TO SIMPLE ELEMENTS. 6 Axial Loadings. 7 Torsion of Circular Cylindrical Rods: Coulomb Torsion. 8 Symmetric Bending of Beams -- Basic Relations and Stresses. 9 Symmetric Bending of Beams: Deflections, Fundamental Solutions and Superposition. 10 Thin--Wall Pressure Vessels: Thin Shells Under Pressure. 11 Stability and Instability of Rods under Axial Compression: Beam--Columns and Tie--Rods. 12 Torsion of Elastic Members of Arbitrary Cross--Section: de Saint Venant Torsion. 13 General Bending Theory of Beams. PART C: ENERGY METHODS AND VIRTUAL WORK. 14 Basic Energy Theorems, Principles of Virtual Work and their Application to Structural Mechanics. 15 Stability of Mechanical Systems by Energy Considerations: Approximate Methods. Appendix A: Properties of Areas. Appendix B: Some Mathematical Relations. Appendix C: The Membrane Equation. Appendix D: Material Properties. Appendix E: Table of Structural Properties. Appendix F: Reactions, Deflections and Slopes of Selected Beams. Answers to Selected Problems. Index.
TL;DR: Lagrangian mechanics is extended to cover situations in which constraint forces are permitted to do work on a system in virtual displacements.
01 Sep 2001
TL;DR: In this paper, a methodical and comparative survey of magnetic force calculation methods found in literature and their relations is presented, and some remarks on the use of these methods for calculating the deformation of magnetized material are formulated.
Abstract: This paper presents a methodical and comparative survey of magnetic force calculation methods found in literature and their relations. Further, on the basis of their physical background and of the force distributions they produce, some remarks on the use of these methods for calculating the deformation of magnetized material are formulated.
19 Sep 2001
TL;DR: In this article, a new finite element formulation of the geometrically exact finite-strain beam theory is presented, which employs the generalized virtual work principle in which the main role is played by the pseudo-curvature vector.
Abstract: A new finite element formulation of the 'geometrically exact finite-strain beam theory' is presented. The formulation employs the generalized virtual work principle in which the main role is played by the pseudo-curvature vector. The solution of the governing equations is obtained by using a combined Galerkin-collocation algorithm. The collocation assures that the equilibrium and the constitutive internal force and moment vectors are equal at a set of the chosen discrete points. A special update procedure for the pseudo-curvature and rotation vectors is employed in Newton's iteration because of the non-linearity of the configuration space. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples.
TL;DR: In this article, the authors present a method allowing the simultaneous identification of parameters governing an orthotropic law with a nonlinear shear response, where the tested specimen is subjected to boundary conditions similar to those of a Iosipescu setup.
Abstract: This paper presents a method allowing the simultaneous identification of parameters governing an orthotropic law with a nonlinear shear response. Such laws appear for instance through the thickness of thick laminated composites. The tested specimen is subjected to boundary conditions similar to those of a Iosipescu setup. The strain field in the central area is processed with the so-called virtual fields method, which is an application of the principle of virtual work with particular virtual fields. The method is simulated with data obtained from finite element calculations.
10 Dec 2001
TL;DR: In this paper, the authors identify the research-based similarities and differences between traditional and virtual teams and present a conceptual framework specifying virtual team competencies based on virtual team performance research.
Abstract: The increasing focus on global organizations, horizontal organizational structures and inter-organizational cooperation has created the virtual work team. This paper identifies the research-based similarities and differences between traditional and virtual teams and presents a conceptual framework specifying virtual team competencies based on virtual team performance research. Related organizational interventions are presented.
21 May 2001
TL;DR: An efficient algorithm for the forward dynamics of open kinematic chains with O(N) complexity, where N is the number of links in the chain, based on the principle of virtual work and does not use any theory in linear algebra or the concept of articulated body inertia.
Abstract: This paper describes an efficient algorithm for the forward dynamics of open kinematic chains with O(N) complexity, where N is the number of links in the chain. The method is based on the principle of virtual work and does not use any theory in linear algebra or the concept of articulated body inertia. The idea of this method is to add a link one by one from the leaflinks to the root evaluating the constraint force at each new joint. The algorithm consists of two iterative procedures: from the leaflinks to the root to compute the constraint forces, and from the root to the leaf to compute the joint accelerations. Some numerical examples show the efficiency of the proposed algorithm. Similarity and differences with other O(N) algorithms are also discussed.
TL;DR: A heuristic procedure to evaluate the minimum value of normal forces, with regard to the whole set of the statically admissible distributions, is proposed and a safe solution is obtainable with standard limit analysis by assuming the limiting frictional resistance to be that associated with this minimum normal force.
Abstract: Part of this paper refers to a research work developed by Jossa and the writer [1] now awaiting publication. It is well known that the static and kinematic behaviour of ancient dry block masonry structures is predominantly regulated by two parameters: self-weight and friction. And it is also well known that any investigation on the safety levels of these structures implies difficulties of analysis, due to the non-associated flow rules imposed by friction. Possibilities of non-unique solutions are directly consequent. This is, therefore, one of the main problems in every programme for the conservation and repair of such structures. The basic guideline of this research is to provide appropriate requirements to treat frictional materials within the framework of the standard limit analysis. This is possible, as shown in the paper, if a way to limit the space of statically admissible solutions can be defined in favour of safety. Generally, in classic plastic theory, an equilibrated distribution of internal forces gives a safe solution if the relative virtual work done, with reference to the true collapse configuration of the structure, is not greater than the virtual work done by the true force distribution. Therefore, in order to define a safe rigid-plastic model for frictional materials, a heuristic procedure to evaluate the minimum value of normal forces, with regard to the whole set of the statically admissible distributions, is herein proposed. Thus, a safe solution is obtainable with standard limit analysis by assuming the limiting frictional resistance to be that associated with this minimum normal force. The heuristic aspect of this procedure is particularly highlighted in the two case studies herein analysed: the 2D masonry wall subject to in-plane traction forces and the voussoir arch subject to its own weight.
TL;DR: In this article, a beam model that takes into account the other state of stress due to torsion and bending on a plane parallel to the connection is presented, in order to analyze the consequence of a flexible connection in these usual states of deformation.
TL;DR: In this article, a shell element is introduced on the boundary of the object to derive magnetic co-energy (or energy) with the help of edge element basis and the local Jacobian derivative technique.
Abstract: The local application of the principle of virtual work for the computation of magnetic forces requires a layer of elements around the object. It fails to work when the object is touching other objects or when the boundary element method is applied on its boundary. To overcome this difficulty, a shell element is introduced on the boundary of the object. Derivation of magnetic co-energy (or energy) is performed on the shell element with the help of edge element basis and the local Jacobian derivative technique. The force expression derived from this method shows a close similarity to the Maxwell stress tensor. Efficiency of the method is shown through the computation of magnetic force on the moving core of an electromagnet when it touches the fixed yoke.
Book•
19 Nov 2001
TL;DR: In this paper, the authors introduce the principle of virtual work, and propose complementary virtual work and energy-efficient virtual work methods, as well as Static and Dynamic Stability (SDS) concepts.
Abstract: Introduction. Preliminaries. Principle of Virtual Work. Complementary Virtual Work. Some Energy Methods. Some Static and Dynamic Stability Concepts. References. Index.
01 Jan 2001
TL;DR: In this article, the authors compare the microplane model with a discrete particle model of discontinuous nature and derive an elastic and an elasto-plastic material characterization of the micro-plane model and the particle model.
Abstract: This paper aims at comparing the microplane model as a particular representative of the class of continuous material models with a discrete particle model which is of discontinuous nature. Thereby, the constitutive equations of both approaches will be based on Voigt’s hypothesis defining the strain state on the individual microplanes as well as the relative particle displacements. Through an appropriate constitutive assumption, the microplane stresses and the contact forces can be determined. In both cases, the equivalence of microscopic and macroscopic virtual work yields the overall stress strain relation. An elastic and an elasto-plastic material characterization of the microplane model and the particle model are derived and similarities of both approaches are illustrated.
01 Jun 2001-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: In this paper, the application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self-field of the magnet on its edges.
Abstract: The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.
TL;DR: In this article, the dependence of the yield function on a non-local equivalent plastic strain measure is considered, which is defined as a weighted average of the corresponding local measure taken over the neighboring material points of the body.
TL;DR: In this paper, the authors derived the equations governing the geometrically nonlinear elastodynamic behavior of multilayered composite shallow shells by using the virtual work principle.
Abstract: Based on a displacement field which: (i) accounts for an arbitrary distribution of the tangential displacements through the shell thickness; (ii) fulfills a priori the continuity conditions on the transverse shear stresses at the interfaces between the layers; (iii) fulfills the zero transverse shear conditions on the top and bottom surfaces; and (iv) allows for jumps in the tangential displacements when interlayer slips are present, the equations governing the geometrically nonlinear elastodynamic behavior of multilayered composite shallow shells are derived by using the virtual work principle. First-order and third-order shallow shells models are obtained as special cases. The work is an extension of the multilayered composite shallow shells of a recently developed model for multilayered composite plates featuring damaged interfaces [AIAA J, 35(11) (1997) 1753].
01 Jan 2001
01 Jan 2001
TL;DR: The total Lagrangian and corotational schemes are introduced as specific examples of solution schemes and these are combined with a Newton-Raphson iteration scheme for the actual solution of the nonlinear equations.
Abstract: In the general case of thin-walled structures, we can have both large displacements and large strains This renders the governing equations highly nonlinear and therefore they can only be solved using computational methods Furthermore, because of the complicated load history dependence, this suggests a time or load incremental solution We combine these two requirements into an incremental/iterative solution algorithm The total Lagrangian and corotational schemes are introduced as specific examples of solution schemes These are combined with a Newton-Raphson iteration scheme for the actual solution of the nonlinear equations
TL;DR: In this article, a dynamic simulation model for mixed-loop planar robots with flexible joint drive and servo-motor control is developed, where the motion of the links is coupled with the deflection of the drive shaft at the joints.
TL;DR: In this article, a homogenization theory of finite deformation was proposed to analyze the microscopic symmetric bifurcation buckling of cellular solids subjected to macroscopically uniform compression.
Abstract: In this paper, we analyze the microscopic symmetric bifurcation buckling of cellular solids subjected to macroscopically uniform compression. To this end, showing the principle of virtual work for periodic solids in the updated Lagrangian form, we build a homogenization theory of finite deformation, which satisfies the principle of material objectivity. Then, we state the following postulate : At a microscopic symmetric bifurcation point, microscopic displacement rate gets spontaneous, but changing the sign of the spontaneous displacement rate field has no influence on the variation of macroscopic states. By applying this postulate to the homogenization theory, we derive the conditions to be satisfied at the bifurcation point. The resulting conditions are discretized using a finite element method in order to employ the present theory in computational analysis. The finite element discretization also deals with a general case, which includes microscopic non-symmetric bifurcation as well as symmetric one.