The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Jaroslav Haslinger - One of the best experts on this subject based on the ideXlab platform.
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Applications of Mathematics
2020Co-Authors: Jaroslav HaslingerAbstract:The paper presents the analysis, approximation and Numerical Realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction F which depends on a solution. It is shown that a solution exists for a large class of F and is unique provided that F is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for Numerical Realization are described and several model examples illustrate the efficiency of the proposed approach.
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Discretization and Numerical Realization of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coeffi cients of friction
2020Co-Authors: Jaroslav HaslingerAbstract:This paper analyzes a discrete form of 3D contact problems with local orthotropic Coulomb friction and coeffi cients of friction which may depend on the solution itself. The discrete model and its Numerical Realization are based on the fixed-point refor mulation of the original problem. Conditions guaranteeing the existence and uniqueness of discrete solutions are established. Finally, Numerical results of a model example are presented.
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Discretization and Numerical Realization of contact problems for elastic-perfectly plastic bodies. PART II - Numerical Realization, limit analysis: Numerical Realization of contact problems for elastic-perfectly plastic bodies and limit analysis
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2015Co-Authors: Martin Cermak, Jaroslav Haslinger, Tomáš Kozubek, Stanislav SysalaAbstract:The paper deals with Numerical Realization of discretized, frictionless static contact problems for elastic-perfectly plastic materials and the computational limit analysis. Two Numerical methods based on the variational formulation in terms of stresses are analyzed: the semi-smooth Newton method with damping and the alternating direction method of multipliers. These methods are used for tracking the loadings path to determine the discretized limit loading parameter and for solving elastic-perfectly plastic problems.Web of Science95121371134
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approximation and Numerical Realization of 3d quasistatic contact problems with coulomb friction
Mathematics and Computers in Simulation, 2012Co-Authors: Jaroslav Haslinger, Radek Kucera, Oldřich Vlach, Charalambos C BaniotopoulosAbstract:AbstractThis paper deals with the full discretization of quasistatic 3D Signorini problems with local Coulomb friction and a coefficient of friction which may depend on the solution. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is solved by the T-FETI domain decomposition method used in auxiliary contact problems with Tresca friction. Numerical experiments show the efficiency of the proposed method.
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Approximation and Numerical Realization of 3D contact problems with given friction and a coefficient of friction depending on the solution
Applications of Mathematics, 2009Co-Authors: Jaroslav Haslinger, Tomáš LigurskýAbstract:The paper presents the analysis, approximation and Numerical Realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction $$ \mathcal{F} $$ which depends on a solution. It is shown that a solution exists for a large class of $$ \mathcal{F} $$ and is unique provided that $$ \mathcal{F} $$ is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for Numerical Realization are described and several model examples illustrate the efficiency of the proposed approach.
Michael Gorelik - One of the best experts on this subject based on the ideXlab platform.
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Statistical Fracture Mechanics — Basic Concepts and Numerical Realization
Probabilities and Materials, 1994Co-Authors: A Chudnovsky, Michael GorelikAbstract:The apparent randomness of brittle fracture is closely associated with the distribution of defects on various scales within a solid. The presence of microdefects is modeled by a random field of specific fracture energy γ following the framework of Statistical Fracture Mechanics (SFM). A brief summary of SFM is presented. SFM is the only model which explicitly incorporates the fractographic information, e.g. fractal characterization of fracture surfaces in the probabilistic description of brittle fracture. At the same time, the model has limitations in engineering applications, mainly due to its mathematical complexity. In this paper the Monte Carlo technique is employed to overcome these limitations. It allows one to combine the physical insight and modeling of the fracture mechanisms in SFM with the flexibility of the Monte Carlo method. Probability distributions of the fracture parameters such as a critical load, critical crack length, and fracture toughness are simulated and compared with experimental observations. Dependency of the conventional measure of fracture toughness on roughness of crack profiles, specimen and grain size, as well as load level is discussed. The ambiguity of the concept of fracture toughness in a probabilistic setting is addressed.
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statistical fracture mechanics basic concepts and Numerical Realization
1994Co-Authors: A Chudnovsky, Michael GorelikAbstract:The apparent randomness of brittle fracture is closely associated with the distribution of defects on various scales within a solid. The presence of microdefects is modeled by a random field of specific fracture energy γ following the framework of Statistical Fracture Mechanics (SFM). A brief summary of SFM is presented. SFM is the only model which explicitly incorporates the fractographic information, e.g. fractal characterization of fracture surfaces in the probabilistic description of brittle fracture. At the same time, the model has limitations in engineering applications, mainly due to its mathematical complexity. In this paper the Monte Carlo technique is employed to overcome these limitations. It allows one to combine the physical insight and modeling of the fracture mechanisms in SFM with the flexibility of the Monte Carlo method. Probability distributions of the fracture parameters such as a critical load, critical crack length, and fracture toughness are simulated and compared with experimental observations. Dependency of the conventional measure of fracture toughness on roughness of crack profiles, specimen and grain size, as well as load level is discussed. The ambiguity of the concept of fracture toughness in a probabilistic setting is addressed.
Jie-lin Zhang - One of the best experts on this subject based on the ideXlab platform.
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Numerical Realization of the conditions of Max Nöther’s residual intersection theorem
Applied Mathematics-a Journal of Chinese Universities Series B, 2014Co-Authors: Er-bao Feng, Jie-lin ZhangAbstract:The aim of this paper is to study Numerical Realization of the conditions of Max Nother’s residual intersection theorem. The Numerical Realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The Numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the Numerical Realization is polynomial time.
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Numerical Realization of the conditions of max nother s residual intersection theorem
Applied Mathematics-a Journal of Chinese Universities Series B, 2014Co-Authors: Er-bao Feng, Jie-lin ZhangAbstract:The aim of this paper is to study Numerical Realization of the conditions of Max Nother’s residual intersection theorem. The Numerical Realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The Numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the Numerical Realization is polynomial time.
Dan S. Henningson - One of the best experts on this subject based on the ideXlab platform.
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Numerical Realization of helical vortices: application to vortex instability
Theoretical and Computational Fluid Dynamics, 2019Co-Authors: Mattias Brynjell-rahkola, Dan S. HenningsonAbstract:The need to Numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier–Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to the case of two helices, which is of renewed interest due to its relevance for wind turbines and helicopters. Three-dimensional stability analysis is performed in both a rotating and a translating frame of reference, which yield eigenvalue spectra that feature both mutual inductance and elliptic instabilities. Comparison of these spectra with available theoretical predictions is used to validate the proposed baseflow model, and new insights into the elliptic instability of curved Batchelor vortices are presented. Furthermore, it is shown that the instabilities in the rotating and the translating reference frames have the same structure and growth rate, but different frequency. A relation between these frequencies is provided.
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a note on the Numerical Realization of helical vortices application to vortex instability
2017Co-Authors: Mattias Brynjellrahkola, Dan S. HenningsonAbstract:The need to Numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to priori ...
Michael Hintermuller - One of the best experts on this subject based on the ideXlab platform.
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inverse coefficient problems for variational inequalities optimality conditions and Numerical Realization
Mathematical Modelling and Numerical Analysis, 2001Co-Authors: Michael HintermullerAbstract:We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the Numerical Realization we utilize a complementarity function, which allows us to rewrite the optimality conditions as a set of equalities. Finally, Numerical results obtained from a least squares type algorithm emphasize the feasibility of our approach.
