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Elastic Body (elastic + body)
Selected AbstractsDirectable animation of elastic bodies with point-constraintsCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2008Ryo Kondo Abstract We propose a simple framework for making elastic body animation with point constraints. In general, a physics-based approach for constraint animation offers a variety of animations with physically correct realism, which are achieved by solving the equations of motion. However, in the digital animation industry, solving the equations of motion is an indirect path to creating more art-directed animations that maintain a plausible realism. Our algorithms provide animators a practical way to make elastic body animation with plausible realism, while effectively using point-constraints to offer directatorial control. The animation examples illustrate that our framework creates a wide variety of point-constraint animations of elastic objects with greater directability than existing methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Computation of the J -integral for large strainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Ágnes Horváth Abstract The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J -integral can also be applied to characterize the cracks in elastic or elastic,plastic bodies. This paper describes the computation of the two-dimensional J -integral for large strains to elastic and elastic,plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] Steady-state 3D rolling-contact using boundary elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007R. Abascal Abstract This work presents a new approach to the steady-state rolling contact problem for 3D elastic bodies. The problem solution is achieved by minimizing a general function representing the equilibrium equation and the rolling-contact restrictions. The boundary element method is used to compute the elastic influence coefficients of the surface points involved in the contact (equilibrium equations); while the contact conditions are represented with the help of projection functions. Finally, the minimization problem is solved by the generalized Newton's method with line search. Classic rolling problems are also solved and commented. Copyright © 2006 John Wiley & Sons, Ltd. [source] On computing the forces from the noisy displacement data of an elastic bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2008A. Narayana Reddy Abstract This study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise. Vision-based minimally intrusive force-sensing using elastically deformable grasping tools is the motivation for undertaking this problem. Since this problem involves incomplete and inconsistent displacement/force of an elastic body, it leads to an ill-posed problem known as Cauchy's problem in elasticity. Vision-based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy. Therefore, we use geometrically non-linear modelling of the elastic body, which was not considered by others who attempted to solve Cauchy's elasticity problem before. We present two methods to solve the problem. The first method uses the pseudo-inverse of an over-constrained system of equations. This method is shown to be not effective when the noise in the measured displacement data is high. We attribute this to the appearance of spurious forces at regions where there should not be any forces. The second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique. Both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples. The performance of the two methods is compared using seven numerical examples, all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements. An experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces. Copyright © 2008 John Wiley & Sons, Ltd. [source] A variational r -adaption and shape-optimization method for finite-deformation elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Thoutireddy Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Elasticity of Single Poly(amido amine) DendrimersMACROMOLECULAR RAPID COMMUNICATIONS, Issue 16 2007Nikodem Tomczak Abstract An atomic force microscope in the compression mode was used to probe the nanomechanical response of single dendrimeric molecules, as well as dendrimer aggregates adsorbed on silicon surface. The force-compression behaviour of individual, generation 5 poly(amido amine) (PAMAM) dendrimers was described by a Hertzian model for the deformation of elastic bodies. The modulus values obtained ranged between 700 MPa (single dendrimers) and 150 MPa (dendrimer aggregates). [source] Modeling and numerical analysis of masonry structuresNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2007Mark Ainsworth Abstract We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone-blocks) in unilateral, frictional contact. The problem is formulated as a quasi-variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time-step, the quasi-variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal-dual active-set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch-ring made of bricks, deformed due to body forces and surface tractions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 798,816, 2007 [source] An effective strategy for the multibody simulation of jointed FE models in the framework of the floating frame of reference formulation.PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Wolfgang Witteveen In multibody systems (MBS), where elastic bodies are represented in the frame work of the ,floating frame of reference formulation' (FFRF), structural deformation is usually computed by the superposition of time invariant trial vectors (commonly called ,modes'). However, the mode bases, which are discussed in the literature, do not take joints into special account at the stage of mode generation. In the presented paper we propose a problem,oriented extension of classical mode bases in order to consider the presence of joints. In the novel extension which we call ,Joint Interface Modes' (JIMs), Newton's 3rd law across the joint is taken into account at the stage of mode generation, which leads to a superior convergence at the stage of mode based computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Static self-gravitating elastic bodies in Einstein gravityCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2008Lars Andersson We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries. © 2007 Wiley Periodicals, Inc. [source] Physics-based GPS data inversion to estimate three-dimensional elastic and inelastic strain fieldsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2010Akemi Noda SUMMARY The Earth's crust is macroscopically treated as a linear elastic body, but it includes a number of defects. The occurrence of inelastic deformation such as brittle fracture at the defects brings about elastic deformation in the surrounding regions. The crustal deformation observed through geodetic measurements is the sum of the inelastic deformation as source and the elastic deformation as effect. On such a basic idea, we created a theory of physics-based strain analysis with general source representation by moment tensor, and developed an inversion method to separately estimate 3-D elastic and inelastic strain fields from GPS data. In this method, first, the optimum distribution of moment density tensor is determined from observed GPS data by using Akaike's information criterion. Then, the elastic and inelastic strain fields are obtained from the optimum moment tensor distribution by theoretical computation and direct conversion with elastic compliance tensor, respectively. We applied the inversion method to GPS horizontal velocity data, and succeeded in separately estimating 3-D elastic and inelastic strain rate fields in the Niigata,Kobe transformation zone, central Japan. As for the surface patterns of total strain, the present results of 3-D physics-based inversion analysis accord with the previous results of 2-D geometric inversion analysis. From the 3-D patterns of the inverted elastic and inelastic strain fields, we revealed that the remarkable horizontal contraction in the Niigata,Kobe transformation zone is elastic and restricted near the surface, but the remarkable shear deformation is inelastic and extends over the upper crust. [source] An adaptive multigrid iterative approach for frictional contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006S. A. Mohamed Abstract The objective of this paper is the construction of a robust strategy towards adaptively solving Signorini's frictional contact problems. The frictional contact problem between a linearly elastic body and rigid foundation is formulated as a classical boundary value problem of the elastic body but associated with special inequality conditions on the contact surface. A new iterative approach is presented to solve the problem on a given mesh. In the first iteration the candidate nodes are assumed to be in micro-slip contact and then proceeding to update the contact status according to the actual displacements and stresses obtained at the end of each increment. An efficient multigrid method is developed to solve the discrete problems of different iterations. The proposed iterative procedure is integrated with an error indicator and automatic grid generator to construct an adaptive multigrid method. Numerical results of the convergence rates, automatically generated grid sequence, contact stresses and strains as well as two parametric studies are presented to prove the efficiency of the proposal. Copyright © 2005 John Wiley & Sons, Ltd. [source] A control analysis of interaction problem by fluid forceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001Shoichiro Kato Abstract This paper presents a control analysis of displacement for a building. To control the vertical displacement of the building, control device of multi-balloons with water inside is introduced on the friction piles. Coupling through the water, soil, balloon and pile, the interaction problem is numerically solved. The soil is assumed to be a linear elastic body. The balloon and pile are also modelled as linear elastic truss and rigid-frame components. The water is assumed to be the two-dimensional incompressible Navier,Stokes flow. All components are discretized by the finite element method in space. The control analysis of vertical displacement by fluid force is performed for the purpose of keeping the building horizontal. One of the optimal control theory, the so-called Sakawa,Shindo method, is applied for the control analysis. Using this method, control flux of the water is determined so that position at the top of the balloon comes to be close to the objective position. Copyright © 2001 John Wiley & Sons, Ltd. [source] On computing the forces from the noisy displacement data of an elastic bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2008A. Narayana Reddy Abstract This study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise. Vision-based minimally intrusive force-sensing using elastically deformable grasping tools is the motivation for undertaking this problem. Since this problem involves incomplete and inconsistent displacement/force of an elastic body, it leads to an ill-posed problem known as Cauchy's problem in elasticity. Vision-based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy. Therefore, we use geometrically non-linear modelling of the elastic body, which was not considered by others who attempted to solve Cauchy's elasticity problem before. We present two methods to solve the problem. The first method uses the pseudo-inverse of an over-constrained system of equations. This method is shown to be not effective when the noise in the measured displacement data is high. We attribute this to the appearance of spurious forces at regions where there should not be any forces. The second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique. Both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples. The performance of the two methods is compared using seven numerical examples, all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements. An experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces. Copyright © 2008 John Wiley & Sons, Ltd. [source] A numerical,analytical combined method for vibration of a beam excited by a moving flexible bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2007Huajiang Ouyang Abstract The vibration of a beam excited by a moving simple oscillator has been extensively studied. However, the vibration of a beam excited by an elastic body with conformal contact has attracted much less attention. This is the subject of the present paper. The established model is more complicated but has a much wider range of applications than the moving-oscillator model. Because the moving body is flexible, the moving loads at the contact interface are not known a priori and must be determined together with the dynamics of the whole system. In this paper, the equation of motion of the beam and the moving body are established separately using a numerical,analytical combined approach. It is found from the numerical results of the simulated example that the vibrations of the moving body and the beam excited by the moving body are significantly influenced by the travelling speed. At very low or very high speeds the dynamic effect is small and the beam deforms to take the shape of its static deflection. Vibrations tend to be greater in the intermediate speed range and the total moving force at the interface of the beam and the moving body can be compressive and tensile. Copyright © 2007 John Wiley & Sons, Ltd. [source] A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Daisuke Ishihara Abstract This paper describes a new monolithic approach based on the fluid pressure Poisson equation (PPE) to solve an interaction problem of incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equation system for the fluid-structure interaction (FSI). Based on this approach, we develop two kinds of efficient monolithic methods. In both methods, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint, and all other unknown variables are derived fully explicitly or partially explicitly. The coefficient matrix of the PPE for the FSI becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties. The arbitrary Lagrangian,Eulerian (ALE) method is employed for the fluid part in order to take into account the deformable fluid-structure interface. To demonstrate fundamental performances of the proposed approach, the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd. [source] Elastic Potential Grids: Accurate and Efficient Representation of Intermolecular Interactions for Fully Flexible DockingCHEMMEDCHEM, Issue 8 2009Sina Kazemi Potential fields represented by irregular, deformable 3D grids provide an accurate and efficient lookup table function for evaluating intermolecular interactions in docking algorithms that consider target flexibility. Target movements can be translated into appropriate displacements of grid intersection points in a binding site region if the irregular deformable 3D grid is modeled as a homogeneous linear elastic body. [source] Static self-gravitating elastic bodies in Einstein gravityCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2008Lars Andersson We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries. © 2007 Wiley Periodicals, Inc. [source] | ||||||||||||||||