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- Andersson, Lars-Erik, 1942-, et al.
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A Survey of Basic Mathematical Results for Frictional Contact Problems
- 2001
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In: From Convexity to Nonconvexity. - Dordrecht/Boston/London : Kluwer. - 0792371445 - 9780792371441 ; , s. -392
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Book chapter (other academic/artistic)abstract
- Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.
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- Andersson, Lars-Erik, 1942-, et al.
(author)
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Conditions for use of a non-selfintersection conjecture
- 2006
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In: Computer Aided Geometric Design. - : Elsevier BV. - 0167-8396 .- 1879-2332. ; 23:7, s. 599-611
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Journal article (peer-reviewed)abstract
- Volino and Thalmann have published a conjecture proposing sufficient conditions for non-selfintersection of surfaces. Such conditions may be used in solid modeling, computer graphics, and other application areas, as a basis for collision-detection algorithms. In this paper we clarify certain of the hypotheses of the proposed theorem, and give a proof. A brief summary of possible pitfalls related to using the conditions, when the hypotheses of the formal theorem given here are not satisfied, is also given. We also give examples, and show that the theorem can be extended to domains that are not simply connected. © 2006 Elsevier B.V. All rights reserved.
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- Andersson, Lars-Erik, 1942-, et al.
(author)
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Equivalence of topological form for curvilinear geometric objects
- 2000
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In: International journal of computational geometry and applications. - 0218-1959. ; 10:6, s. 609-622
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Journal article (peer-reviewed)abstract
- Given a curvilinear geometric object in R3, made up of properly-joined parametric patches defined in terms of control points, it is of interest to know under what conditions the object will retain its original topological form when the control points are perturbed. For example, the patches might be triangular BΘzier surface patches, and the geometric object may represent the boundary of a solid in a solid-modeling application. In this paper we give sufficient conditions guaranteeing that topological form is preserved by an ambient isotopy. The main conditions to be satisfied are that the original object should be continuously perturbed in a way that introduces no self-intersections of any patch, and such that the patches remain properly joined. The patches need only have C0 continuity along the boundaries joining adjacent patches. The results apply directly to most surface modeling schemes, and they are of interest in several areas of application.
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- Andersson, Lars-Erik, 1942-, et al.
(author)
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Error analysis for operations in solid modeling in the presence of uncertainty
- 2008
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In: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 29:2, s. 811-826
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Journal article (peer-reviewed)abstract
- The problem of maintaining consistent representations of solids in computer-aided design and of giving rigorous proofs of error bounds for operations such as regularized Boolean intersection has been widely studied for at least two decades. One of the major difficulties is that the representations used in practice not only are in error but are fundamentally inconsistent. Such inconsistency is one of the main bottlenecks in downstream applications. This paper provides a framework for error analysis in the context of solid modeling, in the case where the data is represented using the standard representational method, and where the data may be uncertain. Included are discussions of ill-condition, error measurement, stability of algorithms, inconsistency of defining data, and the question of when we should invoke methods outside the scope of numerical analysis. A solution to the inconsistency problem is proposed and supported by theorems: it is based on the use of Whitney extension to define sets, called Quasi-NURBS sets, which are viewed as realizations of the inconsistent data provided to the numerical method. A detailed example illustrating the problem of regularized Boolean intersection is also given.
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- Andersson, Lars-Erik, 1942-, et al.
(author)
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Existence theorems for noncoercive incremental contact problems with Coulomb friction
- 2006
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In: Analysis and Simulation of Contact Problems. - Berlin/Heidelberg : Springer Berlin/Heidelberg. - 9783540317609 - 9783540317616 - 3540317600 ; , s. 121-128
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Book chapter (other academic/artistic)abstract
- For static or incremental contact problems with Coulomb friction there are satisfactory and well known existence results for the coercive case, i.e., when the elastic body is anchored so that rigid body motions are not possible, see [3, 1, 6, 7, 2]. The articles by Jaruusek and Cocu, [7, 2] indeed contain results for the noncoercive case, i.e., when rigid body motions are possible. However, the compatibility conditions which are used to ensure the existence of a solution, are the same that guarantee that the corresponding contact problem without friction has a solution. The condition is essentially that the applied force field should push the elastic body towards the obstacle. One of few previous articles containing friction-dependent compatibility conditions is.
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