In Kombination mit einer Aktiven-Mengen-Strategie entsteht ein Algorithmus, der die Elimination der diskreten Knotenwerte der Lagrange-Multiplikatoren erlaubt. The Boundary Elements Method (BEM) is used to compute the influence coefficients of the surface points involved, and contact conditions are imposed us- ing projection functions. Ein Tensor ist eine lineare mathematische Funktion, die eine bestimmte Anzahl von Vektoren auf einen Zahlenwert abbildet. urements. The position of the contact frame and the local coordinate of the contacting node along the contact frame are also treated as the independent variable, which enables the exact satisfaction of the constraint conditions without the deficiency or redundant constraint. The sample results agree well with corresponding exact solutions. Copyright © 2015 John Wiley & Sons, Ltd. Approximation du probl eme de contact unilat eral par la m ethode des el ements nis avec joints. Gleichzeitig erlaubt die Diskretisierung der Multiplikatoren mit dualen Formfunktionen die einfache Kondensation der zusätzlichen Unbekannten aus dem resultierenden Gleichungssystem. Ein Temperaturfeld ist eine skalarwertige Funktion mit einem Wertebereich von 0 bis unendlich (bei Angabe der Temperatur in Kelvin, von etwa -273 bis unendlich bei Angabe in Grad Celsius), die auf dem gesamten dreidimensionalen Raum bzw. Die algorithmische Erhaltung zentraler Eigenschaften wie der Gesamtenergie und der Impulsabbildungen führen in der Praxis zu einer herausragenden numerischen Stabilität; insbesondere bei Kontakt-Vorgängen ist dies von qualitativ ho- hem Interesse. The work deals with the numerical solution of contact problems by the finite element method. Many techniques for evaluating thermo-elasto-plasticity and damage analysis have been proposed9101112. Here we intent to introduce such a test for the 3D case and demonstrate that the localised Lagrange multiplier approach can be used successfully to pass the 3D Patch test for nonconforming grids. The mortar element uses the mixed formulation of boundary element formulations. Regarding time, a “parallel” property is also described. The proposed algorithm is portable between dynamic and quasi-static codes and can efficiently model contact between a variety of finite element types including shells, bricks, beams, and particles. Delta ist intuitiv eine unendlich hohe, unendlich schmale Verteilung, ein nadelförmiger Impuls. The motivation in essence is: the importance of the unifying associative algebra of function composition (viz. Durch die Verwendung der Methode der Lagrange’schen Multiplikatoren erfüllt diese Formulierung die Nichtdurchdringungsbedingung exakt. Die vorliegende Arbeit befasst sich mit verschiedenen Aspekten der Diskretisierung von Kontaktvorgängen in Raum und Zeit. Particular interest in this paper is the development of an efficient solution methodology for prediction of gaps at block interfaces in pressure die casting. For statically indeterminate systems, the correction due to flexibility and compatibility is orthogonal to the principal solution. All rights reserved. Im Bereich der mathematischen Darstellungstheorie ist eine projektive Darstellung einer Gruppe G auf einem Vektorraum V über einem Körper K ein Homomorphismus von G in die projektive lineare Gruppe:: → Definition. In der Mathematik ist eine Volumenform auf einer differenzierbaren Mannigfaltigkeit eine top-dimensionale Form (dh eine Differentialform von höchstem Grad). In order to assure proper communication, energy formulations of the fluid and structure models are in terms of displacements and associated time derivatives. It is seen that Drucker–Prager model in the representing elasto-plastic behaviour of arch dams and in estimating location of cracks in dam body is a fast tool. straight GFEM. Ein Tensor ist eine lineare mathematische Funktion, die eine bestimmte Anzahl von Vektoren auf einen Zahlenwert abbildet. For the case of frictional impact, the linear momentum is exactly conserved and the angular momentum is approximately conserved with negligible error. 2(a)). Numerische Untersuchungen dokumentieren die Leistungsfähigkeit beider FE-Formulierungen. The potential advantages of the new formulation are demonstrated. Kikuchi N, Oden JT. The HITA contact searching algorithm and the DENA interface algorithm are reviewed. Converted file can differ from the original. J f den Real-, bzw. Definition: (Taylor-Polynom p-ten Grades im IR n) Sei f : D —+ IR, D c IRTb eine (p+l)-mal stetig diff 'bare Funktion und [a, a-eh] C D eine im Inneren von D liegende Strecke. A. (1999) energetisch stabil. DEFINITION 1.1. This paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. In der Mathematik ist eine Volumenform auf einer differenzierbaren Mannigfaltigkeit eine top-dimensionale Form (dh eine Differentialform von höchstem Grad). Imaginärteil von /. Sometimes it can be even impossible to make such meshes conforming like for instance in contact analysis with sliding. On the stress distribution of cylindrical elastic bodies in contact. The time-stepping computations are organized in a way that eliminates the traditional prediction step characteristic of staggered solution procedures. Graphisch stellt man solche Felder durch 2-dimensionale Schnitte dar, in denen die Flächen (Äquipotentialfläche) als Höhenlinien erscheinen. This thesis presents a new coupling method for treating the interaction of an acoustic fluid with a flexible structure, with emphasis on handling spatially non-matching meshes. Die Fourier-Zahl \mathit (nach Jean Baptiste Joseph Fourier) ist eine dimensionslose Kennzahl zur Beschreibung von Problemen der instationären Wärmeleitung oder allgemeinen Stoffaustauschprozessen. Bei der Definition von Funktionen sollte man keine belegten Variablen verwenden. The present formulation is applicable to both linearized vibration analysis and nonlinear FSI transient analysis provided that a convected kinematics is adopted for updating the mesh geometry in a finite element discretization. Herein, both contacting bodies are calculated serially. Mal abgesehen davon, dass ich keinen Zusammenhang zur Feldstärke in der Physik sehe: Wie will man denn das Differential einer skalarwertigen Funktion wiederum als skalarwertige Funktion auffassen? An elastic-plastic analysis of contact problems is presented. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. ... : Einfluß der lagrangeschen Multiplikatoren auf die künstliche Oberfläche Die Knotenpunkte der diskreten künstlichen Oberfläche werden an den Stellenx, unter der Bedingung M(x) = 0, positioniert. Und wie. Then, we realize a numerical analysis of the algorithm and, using a bootstrapping argument, we give an upper bound of the convergence rate similar to that already obtained for compatible grids. Dissertation, Chalmers Tekniska Special attention is paid to the influence of the mass matrix lumping on the oscillations of the contact pressure. Im Gegensatz zu dieser gibt das Energie-Korrekturkraft-Verfahren die dissipierte Energie jedoch nicht ausschließlich in kinetischer Form zurück. Slide surface and contact boundary conditions can be implemented via Lagrange multipliers in the algebraic equations in implicit structural analysis. Ein Schätzer von wird in der Regel durch das Symbol bezeichnet ist . We present a finite element method for a class of contact-impact problems. Copyright © 2000 John Wiley & Sons, Ltd. Copyright © 2008 John Wiley & Sons, Ltd. A family of gap elements are developed for treating non-matching interfaces occurring in partitioned analysis of mechanical systems. This paper proposes a new finite element method of frictional impact of elastic bodies. Anhand von numerischen Experimenten werden abschließend die untersuchten Verfahren bewertet. Somit wird der übliche Nachteil der Methode der Lagrange’schen Multiplikatoren vermieden. Coupling is done through a displacement frame interposed between the interface meshes. Whereas the bulk of the results were obtained via the ‘classical’ Galerkin finite element method (GFEM) and the trapezoidal (TR) time integrator, we also tested several alternative options: flux-conservative formulation, energy-conservative formulation, streamline upwinding, mass lumping, In this paper, a proper orthogonal decomposition (POD) method is applied to reducing a classical stabilized mixed finite element (SMFE) formulation for the non-stationary Navier–Stokes equations. This solution is independent of the stress–strain constitutive properties as well as of the compatibility equations. Numerical experiments show that the errors between the reduced SMFE solutions and the classical SMFE solutions are consistent with theoretical results. Mit anderen Worten: Die Funktion f wird in einer Umgebung von ξ gut durch die lineare Funktion g(x) = f0(ξ)(x−ξ)+f(ξ) approxi-miert, d.h. lim x→ξ Eine vektorwertige Funktion ist in der Mathematik eine Funktion, deren Zielmenge ein mehrdimensionaler Vektorraum ist. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes. Iteration is limited in general to very few cycles and, as small matrices are handled, can be very economical. The formulation introduces a contact frame that is placed in between contacting bodies and represents the contact surface. A mixed penalty formulation is employed in approximating the resulting variational inequalities. Oden JT. Und wie. The coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure, and using node-collocated Lagrange multipliers to connect the frame to each subsystem. Copyright © 2006 John Wiley & Sons, Ltd. They thereby facilitate an efficient analysis, maintaining node-to-node contact during the contact deformation. Der Rückschluss ist nun, wenn eine Funktion nicht stetig war, dann ist sie auch nicht (total) differenzierbar. Firstly, the stability and robustness of the BFGS algorithm for constrained systems are increased. In all illustrations, wear coefficients are estimated by self-averaging strategy with available experimental datum reported elsewhere. The paper deals with multiple scales in both space and time. The algorithm is composed of a location strategy that uses a global search to decide which slave nodes are in proximity to a master surface and an accurate detailed contact check that uses the projected motions of both master surface and slave node. The variable-node elements, in which nodes are added freely where they are needed, make it possible to transform the non-matching meshes into matching meshes directly. A smart interfacing method based on domain/boundary decomposition is presented for the non-linear analysis of thermo-elastoviscoplastic damage and contact. Teilmengen von ihm definiert ist.Ein Temperaturfeld ordnet jedem Raumpunkt seines Definitionsbereiches eine Temperatur zu. Four specializations of the present framework are discussed. Then the proposed algorithm and how it addresses these problems is described. Since the surface of the hexahedron element is quadrilateral, the gap element is pyramidal. Interior displacements are decomposed into rigid-body and deformational components to handle floating subdomains. Das heißt, dass man zu ... Wenn eine Funktion differenzierbar ist, dann muss sie auch stetig sein. On the mortar surface, contact kinematics are easily evaluated on a single discretized space. Furthermore, the results also show that the central processing unit time required by the proposed method is nearly half that of the previous methods without loss of accuracy. The method is general and could be extended to solve other than elastic problems. This approach is taken to satisfy the momentum and energy conservation. A particular difficulty however is the decrease in convergence rate associated with the increase in number of solution domains. In this study, a new method of allocating the frame nodes for effective and accurate treatment of nonmatching interface meshes is introduced. The current approach can be widely applied easily to fields such as the study of the wear behaviors on ante-version, impingement, and time-dependent behaviors of prostheses etc. The traditional approach of defining master and slave contact surfaces will not work because we do not know a priori how to partition the surface of the structure. lim f(x) so ist die Funktion f an x partiell differenzierbar nach xj. 34 Beziehungen. In this last method, the discretized normal and tangential stresses on the contact surface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. In the first calculation step one of the contacting bodies represents a rigid obstacle for the other elastic one. The connection between the solids is done using a displacement frame inter- calated between the interfaces meshes, and the LLM are collocated at the interface nodes. For efficiency, static condensation is employed to condense a large model down to a smaller one which involves nodes within the potential contact surfaces only. The test is also applied to mixed displacement—strain formulations of elasticity, and limiting formulations are noted. Es handelt sich um einen linearen Differentialoperator innerhalb der mehrdimensionalen Analysis.. Der Laplace-Operator spielt in vielen physikalischen Theorien, insbesondere bei der Beschreibung elektrischer und gravitativer Felder, eine zentrale Rolle und bildet z.