Showing papers on "Virtual work published in 1992"
TL;DR: In this article, a Rayleigh-Ritz procedure was used to discretize the problem and the resultant non-linear equations were solved iteratively using Newton's method, and the predicted response was found to be in very good agreement with the experimental result.
194 citations
TL;DR: Different methods are presented for the calculation of torque as a function of rotation angle in an electrical machine, using Maxwell stress tensor, coenergy derivation, Coulomb's virtual work, and the magnetizing current method.
Abstract: Different methods are presented for the calculation of torque as a function of rotation angle in an electrical machine. These methods are integrated in a calculation code by using the finite element method. The movement is taken into account by means of the moving band technique, involving quadrilateral finite elements in the airgap. The torque is calculated during the displacement of the moving part by using the following methods: Maxwell stress tensor, coenergy derivation, Coulomb's virtual work, A. Arkkio's method (1988), and the magnetizing current method. The results obtained by the different methods are compared with experimental data and make it possible to obtain practical information concerning the advantages and limitations of each method. >
142 citations
07 Jul 1992
TL;DR: A new interface device SPIDAR (Space Interface Device for Artificial Reality) is proposed that can measure the position of a finger and give force feed- back to a finger when it touches the virtual object.
Abstract: To develop a human interface for three- dimensional modeling it is necessary to construct a vir- tual work space where we can manipulate object models directly, just as in real space. In this paper, we propose a new interface device SPIDAR (Space Interface Device for Artificial Reality) for this virtual work space. SPIDAR can measure the position of a finger and give force feed- back to a finger when it touches the virtual object. We
121 citations
TL;DR: A space interface device called SPIDAR is proposed, as the I/O device needed in composing the virtual work space for generation and manipulation of the three-dimensional shape, and the usefulness of the method is verified.
Abstract: To realize the human interface which efficiently models a three-dimensional shape on a computer, it is necessary to provide an environment in which the shape model can be manipulated directly as the actual three-dimensional object. Such an environment is called the virtual work space. In the human manipulation of an object by hand, such sensations as visual, tactile (touch), and force are utilized unconsciously.
To compose the virtual work space, it is important that the human be given such sensory information in an integrated way. Such information must totally be generated artificially by computer processing. Based on such an idea, this paper proposes anew a space interface device called SPIDAR, as the I/O device needed in composing the virtual work space. The device functions to derive the information concerning the finger position and to provide the force sense information to the finger tip.
The virtual work space for generation and manipulation of the three-dimensional shape is composed using SPIDAR. An experiment is conducted to examine the effect of the force sense on the direct manipulation of the three-dimensional shape in the virtual work space, and the usefulness of the method is verified.
66 citations
TL;DR: In this article, the authors present a consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load.
Abstract: The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.
59 citations
TL;DR: In this paper, an edge-element method was proposed for the computation of force fields in full generality: deformable bodies, nonlinear b-h laws, and the presence of magnets.
Abstract: The author presents an edge-element method (h-formulation) for the computation of force fields in full generality: deformable bodies, nonlinear b-h laws, and the presence of magnets. It gives not only integrated quantities such as resultant or torque, but also local force. The main ingredients are: (1) a Langrangian approach ('co-moving' mesh and Maxwell equations expressed in 'material' form); (2) the virtual work principle (force as the derivative of coenergy with respect to configurations), and (3) edge-based degrees of freedom, which can be interpreted as magnetomotive forces along the edges. >
54 citations
TL;DR: In this paper, a geometrically nonlinear model for elastic adhesive joints is derived, starting from a three-dimensional problem, a linearly varying displacement through the thickness of the adhesive is assumed and a geometric two-dimensional theory for the adhesive layer is obtained.
Abstract: In this paper a geometrically nonlinear model for elastic adhesive joints is derived. Starting from a three-dimensional problem, a linearly varying displacement through the thickness of the adhesive is assumed and a geometrically two-dimensional theory for the adhesive layer is obtained. The introduction of generalized stress and strain measures is discussed. The model obtained is further simplified in the case of a thin adhesive made from a flexible material. Aiming at a Newton type solution scheme, the virtual work equation and the constitutive equations are linearized. A finite element discretization is performed and associated matrix equations are given. Finally, as applications of the theory a single-lap joint and a cantilever beam are studied.
51 citations
TL;DR: In this paper, a corotational total Lagrangian formulation of beam elements is presented for the nonlinear analysis of three-dimensional beam structures with large rotations but small strains.
Abstract: A corotational total Lagrangian formulation of beam element is presented for the nonlinear analysis of three-dimensional beam structures with large rotations but small strains. The nonlinear coupling among the bending, twisting, and stretching deformations is considered. All of the element deformations and equations are defined in body-attached element coordinates. Three rotation parameters are proposed to determine the orientation of the element cross section. Two sets of element nodal parameters termed explicit nodal parameters and implicit nodal parameters are introduced. The explicit nodal parameters are used in the assembly of the system equations from the element equations and chosen to be three components of the incremental translation vector and three components of the incremental rotation vector. The implicit nodal parameters are used to determine the deformations of the beam element and chosen to be three components of the total displacement vector and nodal values of the three rotation parameters. The element internal nodal forces corresponding to the implicit nodal parameters are obtained from the virtual work principle. Numerical examples are presented and compared with the numerical and experimental results reported in the literature to demonstrate the accuracy and efficiency of the proposed method. HREE-DIMENSIONAL beams are very important structural elements in all types of engineering systems. In many applications, these beam elements undergo finite rotations that require a nonlinear formulation to their structural analysis. The development of new and efficient formulations for nonlinear analysis of beam structures has attracted the study of many researchers in recent years. Based on different kinematic assumptions, different alternative formulation strategies and procedures to accommodate large rotation capability during the large deformation process have been presented.1"20 The kinematic assumptions used in Refs. 4, 5, 7, 11, and 17-19 are based on Timoshenko's hypothesis: the effect of stretching, bending, torsion, and transverse shear are taken into account.
45 citations
TL;DR: In this article, a flexural theory of elastic sandwich beams is derived which renders quite precise results within a wide range of ratios of dimensions, mass densities, and elastic constants of the core and faces.
Abstract: A flexural theory of elastic sandwich beams is derived which renders quite precise results within a wide range of ratios of dimensions, mass densities, and elastic constants of the core and faces. The assumptions of the Timoshenko theory of shear-deformable beams are applied to each of the homogeneous, linear elastic, transversely isotropic layers individually. Core and faces are perfectly bonded. The principle of virtual work is applied to derive the equations of motion of a symmetrically designed three-layer beam and its boundary conditions. By definition of an effective cross-sectional rotation the complex problem is reduced to a problem of a homogeneous beam with effective stiffnesses and with corresponding boundary conditions. Thus, methods of classical mechanics become directly applicable to the higher-order problem. Excellent agreement of the results of illustrative examples is observed when compared to solutions of other higher-order laminate theories as well as to exact solutions of the theory of elasticity.
44 citations
TL;DR: In this article, the mechanics of drilling tool-rock interfaces under shear are studied by means of consistent second-grade generalization of the flow theory of plasticity for frictional, cohesion-softening material.
38 citations
TL;DR: This paper presents a constraint method for physically based computer graphics models, based on the constraint stabilization method of Baumgarte and on the dynamic constraints of Barzel and Barr, called generalized dynamic constraints (GDCs).
TL;DR: In this paper, a geometrically nonlinear theory for sandwich shells with seven kinematic degrees of freedom is presented, which is capable of describing the global as well as the local structural behaviour.
Abstract: This paper presents (on the base of the classical and some additional sandwich assumptions) a geometrically nonlinear theory for sandwich shells with seven kinematic degrees of freedom which is capable to describe the global as well as the local (load singularities, wrinkling) structural behaviour. For the kinematic specification a position vector is used to describe a point of the geometrical middle surface and a corresponding director (no unit vector) as well as a further scalar degree of freedom which could be explained as the linear part of the transversal strain. According to the definition of Green-Lagrangian strains and second Piola-Kirchhoff stress resultants, the nonlinear field equation of force equilibrium with pertinent boundary conditions will be gained from the principal of virtual work. Finally, the equation according to the first order theory for plane structures will be mentioned as a simple special case.
TL;DR: In this article, a unified variational theory for design sensitivity analysis of nonlinear dynamic response of structural and mechanical systems for shape, nonshape, material and mechanical properties selection, as well as control problems is described.
Abstract: This paper describes a unified variational theory for design sensitivity analysis of nonlinear dynamic response of structural and mechanical systems for shape, nonshape, material and mechanical properties selection, as well as control problems. The concept of an adjoint system, the principle of virtual work and a Lagrangian-Eulerian formulation to describe the deformations and the design variations are used to develop a unified view point. A general formula for design sensitivity analysis is derived and interpreted for usual performance functionals. Analytical examples are utilized to demonstrate the use of the theory and give insights for application to more complex problems that must be treated numerically.
TL;DR: In this paper, the authors describe an approach to parameter estimation of complex linear structures called the mutual residual energy approach, which is based on the assumption that the topology and geometry of the structure are known, and that the system matrices can be linearly parameterized in terms of kernel matrices that have a solid physical basis and are easy to assemble.
Abstract: In this work we describe an approach to parameter estimation of complex linear structures that we call the mutual residual energy approach. We have endeavored to develop a unified approach to the discrete inverse problems describing static equilibrium and free, undamped vibration, with a particular view toward evolving methods that are amenable to large-scale computation. The mutual residual energy method is based on the assumption that the topology and geometry of the structure are known, and that the system matrices can be linearly parameterized in terms of kernel matrices that have a solid physical basis and are easy to assemble. Measured motions of the structure are used (in conjunction with measured loads for the static case) to make estimates of the constitutive parameters. The method is based on a particular statement of the principle of virtual work and yields equations for estimating stiffness and mass parameters of linear structures. A condensation procedure is presented to deal with the case of incompletely measured systems. The quantity and quality of response measurements required, the consequences of noisy data, and the choice of load form are among the issues important to the success of our parameter estimation scheme. A numerical simulation is presented to demonstrate the features of the method.
TL;DR: In this article, it is demonstrated that the lack of equilibrium for rotated angled joints is not a physical reality, but a result of overlooking compatibility conditions for interconnected elements in the deformed position.
Abstract: Previous buckling analyses for three-dimensional frames based on discrete element formulations have been criticized for the lack of equilibrium at angled joints in the buckling state. While this problem can be overcome through the introduction of the so-called semitangential rotations and moments, this approach suffers from the drawback that the semitangential definitions are rather artificial. In this paper, it is demonstrated that the so-called lack of equilibrium for rotated angled joints is not a physical reality, but a result of overlooking compatibility conditions for interconnected elements in the deformed position. One feature of such compatibility conditions is that they are irrelevant to any elastic deformations. In a finite element formulation, they can only be included through the external virtual work terms. In this paper, the procedure for calculating the element forces in a step-by-step nonlinear analysis is also discussed. The adequacy of the present approach is confirmed in the numerical study.
TL;DR: In this article, the authors used complementary virtual work to evaluate the flexibility matrix of a tapered I-beam finite element with different slopes, and compared the results to full-blown shell finite element models, and stepped beam models constituted by a series of uniform beam elements.
Abstract: The principle of complementary virtual work is used to evaluate numerically the flexibility matrix of tapered I-beams accounting for shear deformations. Equilibrium considerations of the top and bottom fibres reveal that the shear stress is not equal to zero at these locations. To correct for this non-vanishing shear, a statically admissible shear stress field is considered by assuming a parabolic distribution of shear stress which takes non-zero values at the top and bottom fibres such that the global equilibrium is satisfied within the assumed stress profile. The flexibility matrices of the proposed tapered I-beam finite element with different slopes are generated using numerical integration based on Gauss quadrature. The results are compared to full-blown shell finite element models, and stepped beam models constituted by a series of uniform beam elements, to illustrate the effectiveness of the proposed method.
TL;DR: In this paper, the authors presented the application of approximate equations of a two-dimensional theory for the analysis of stress and displacement distributions of a thick elastic plate with fixed boundaries, by using the method of power series expansion of displacement components.
TL;DR: In this article, a two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate-dependent viscoplastic constitutive models in large deformation problems.
Abstract: A two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate-dependent viscoplastic constitutive models in large deformation problems. A similar scheme can be applied to rate-independent solids as well. These algorithms are a generalization of the mid-point integration rule. Full linearization of the principle of virtual work is performed in an updated Lagrangian framework together with a calculation of the consistent linearized moduli. Some details of the finite element implementation are given for plane strain and axisymmetric problems. The method is compared with other objective integration schemes and is tested with several examples where large strains and rotations occur.
TL;DR: In this paper, full linearization of the virtual work equation is performed in an updated Lagrangian framework together with a calculation of the consistent linearized material moduli, where the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration.
Abstract: An important step in the solution of non-linear deformation problems using a Newton-Raphson type of iterative scheme is the calculation of a tangent operator (the so-called Jacobian) by linearizing the involved field equations. In this paper, full linearization of the virtual work equation is performed in an updated Lagrangian framework together with a calculation of the consistent linearized material moduli. To update the material state, a material frame indifferent two parameter integration scheme introduced earlier by the authors is used. In general, the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration. Another approach is to use the previous equilibrium state (at the beginning of a time step) as the reference configuration until the new equilibrium configuration at the end of the time step is found. The present paper explores the performance of two different Jacobians based on the above two approaches, with emphasis on their accuracy and convergence characteristics when large incremental steps are used. Finally, some details of their finite element implementation are given and results for several numerical tests including upset forging and extrusion of an axisymmetric billet are presented and discussed.
01 Jan 1992
TL;DR: In this article, a finite-element based method for the computation of force fields, using the language and concepts of differential geometry, in the familiar "eddy-currents" context (displacement currents ignored).
Abstract: We present a finite-element based method for the computation of force fields, using the language and concepts of differential geometry, in the familiar "eddy-currents" context (displacement currents ignored). The approach is Lagrangian (comoving mesh) and the degrees of freedom are magnetomotive forces along material lines which coincide with the edges of the mesh. The essential result is: the edge-element implementation of the h-formulation of the eddy-currents problem can serve without any modification when conductors are mobile and deformable, provided the assembly of finite-element matrices is done at each time step. A simple formula gives the virtual work of electromagnetic forces, hence a notion of "nodal forces" from which an interpolation of the force field can be derived if needed.
TL;DR: In this paper, a p-version geometrically non-linear formulation based on the total Lagrangian approach for a nine node three dimensional curved shell element is presented, where the element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element.
Abstract: This paper presents a p-version geometrically non-linear formulation based on the total Lagrangian approach for a nine node three dimensional curved shell element. The element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction. The element approximation functions and the corresponding nodal variables are derived from the Lagrange family of interpolation functions. The resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures C° continuity.
The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete three dimensional stresses and strains are considered, hence the element is equally effective for very thin as well as extremely thick shells and plates.
Incremental equations of equilibrium are derived and solved using the standard Newton–Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the literature.
TL;DR: In this paper, a general lumped mass finite element structural dynamics model was developed for a three-dimensional elastic beam with an arbitrary and large base movement, which can incorporate either a prescribed arbitrary motion of the base or as coupling of the beam with other substructures.
TL;DR: In this article, a trilinear theory was devised to predict theoretically the moment-load curves of reinforced concrete frames throughout the loading history, as well as the principle of virtual work to express the compatibility condition and to find...
Abstract: The nonlinear behaviour of reinforced concrete frames with sidesway is governed by two efects: first the nonlinearity of materials due to cracking and the plastic behaviour of materials, and second the nonlinearity of geometry caused by the second-order deformation. These two efects may interact, and the whole phenomenon is known as the nonlinearity of geometry and materials. Reinforced concrete frames are frequently used to resist wind or earthquake forces. These forces will accentuate the complexity of the frame behaviour because of the continuous change of the shape of the bending moment diagram. The change of moment diagram will in turn afect the magnitude of the cumulative plastic rotations. A trilinear theory was devised to predict theoretically the moment-load curves of reinforced concrete frames throughout the loading history. This method utilized the trilinear moment-curvature curve for critical sections, as well as the principle of virtual work to express the compatibility condition and to find ...
TL;DR: In this paper, a numerical model of the interaction of highly deformable fluid-filled membranes and ocean waves has been developed and verified using a boundary element model and a finite element model.
TL;DR: In this paper, the authors compared the efficiency of three procedures developed for geometrically nonlinear analysis with a Lagrangian co-ordinate system and leading to the formulation of a symmetric secant stiffness matrix.
Abstract: The efficiency is compared of three procedures developed for geometrically non-linear analysis with a Lagrangian co-ordinate system and leading to the formulation of a symmetric secant stiffness matrix. The first, based upon the principle of total potential energy with a special form of the strain energy expression, is due to Mallett and Marcal.1 The second, due to Wood and Schrefler,2 achieved symmetry of the secant matrix by correlation of a procedure based on the virtual work principle with the Mallett–Marcal procedure. The authors3 have recently developed a new symmetric secant matrix procedure also based on the virtual work principle.
The aim of this paper is to draw attention to the time-consuming operations involved in the Mallett–Marcal procedure and to highlight the new secant and tangential stiffness matrix formulations, which are different from those of Wood and Schrefler and easier to compose. This paper also demonstrates how the Wood–Schrefler procedure can be modified to accommodate the new formulation.
18 Oct 1992
TL;DR: A modification to a linear-time forward dynamics algorithm can express the equations of motion of a manipulator that has either time-varying or impulsive forces applied anywhere on the manipulator, which permits the efficient simulation of accidental contact, and of multiple contacts that arise naturally in dextrous manipulation.
Abstract: The dynamics of robot manipulation with arbitrary forces, torques, and impulses applied to any link in the mechanism are studied. Using the principle of virtual work, and formulating the Lagrangian dynamics with spatial vectors, a modification to a linear-time forward dynamics algorithm can express the equations of motion of a manipulator that has either time-varying or impulsive forces applied anywhere on the manipulator. This permits the efficient simulation of accidental contact, and of multiple contacts that arise naturally in dextrous manipulation. The authors have implemented the equations as part of a computer simulation of robot dynamics, to test the effects of various external loadings. The initial results were derived from the study of free, unpowered planar mechanisms of two and three links subject to gravity. >
TL;DR: In this article, an alternative method of formulating the equations of motion and using a computer-aided symbolic method for modeling of elastic mechanical systems is presented, derived from the principle of virtual work and cast in an expanded and closed form.
Abstract: In this paper an alternative method of formulating the equations of motion and using a computer-aided symbolic method for modeling of elastic mechanical systems is presented. The formalism is derived from the principle of virtual work and cast in an expanded and closed form. Symbolic generation of nonlinear closed-form equations of motion and their linearization are discussed. Symbolic equations for two examples are generated using the above method. Numerical results and comparison between full nonlinear and linearized robot models are presented
01 Sep 1992
TL;DR: In this paper, a new (1, 2)-order theory for the linear elasto-static analysis of laminated composite plates is proposed, which is particularly suited for finite element discretization as it requires simple C(sup 0)- and C( sup -1)-continuous displacement interpolation fields.
Abstract: A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.