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Andersson, Lars-Erik
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Publications (10 of 28) Show all publications
Andersson, L.-E., Pinto da Costa, A. & Agwa, M. A. (2016). Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds. Zeitschrift für angewandte Mathematik und Mechanik, 96(1), 78-105
Open this publication in new window or tab >>Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds
2016 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, p. 78-105Article in journal (Refereed) Published
Abstract [en]

We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH, 2016
Keywords
Coulomb friction; quasistatic and rate problems; existence/uniqueness; sharp critical bounds; finite elements
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-124481 (URN)10.1002/zamm.201400143 (DOI)000367732000007 ()
Available from: 2016-02-02 Created: 2016-02-01 Last updated: 2017-11-30
Andersson, L.-E., Barber, J. R. & Ponter, A. R. (2014). Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions. International Journal of Solids and Structures, 51(21-22), 3710-3714
Open this publication in new window or tab >>Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions
2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 21-22, p. 3710-3714Article in journal (Refereed) Published
Abstract [en]

We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Contact problems; Shakedown; Melans theorem; Coulomb friction; Attractors
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-111594 (URN)10.1016/j.ijsolstr.2014.07.004 (DOI)000342254800019 ()
Available from: 2014-10-27 Created: 2014-10-27 Last updated: 2017-12-05
Andersson, L.-E., Barber, J. R. & Ahn, Y.-J. (2013). Attractors in Frictional Systems Subjected to Periodic Loads. SIAM Journal on Applied Mathematics, 73(3), 1097-1116
Open this publication in new window or tab >>Attractors in Frictional Systems Subjected to Periodic Loads
2013 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 73, no 3, p. 1097-1116Article in journal (Refereed) Published
Abstract [en]

This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2013
Keywords
contact problems, shakedown, Melans theorem, Coulomb friction, attractors, uniqueness
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-95982 (URN)10.1137/120885024 (DOI)000321040600001 ()
Available from: 2013-08-12 Created: 2013-08-12 Last updated: 2017-12-06
Andersson, L.-E. (2013). Existence and uniqueness for thermoelastic contact. In: Hetnarski, Richard B. (Ed.), Encyclopedia of Thermal Stresses: . Springer
Open this publication in new window or tab >>Existence and uniqueness for thermoelastic contact
2013 (English)In: Encyclopedia of Thermal Stresses / [ed] Hetnarski, Richard B., Springer, 2013, p. -6643Chapter in book (Other academic)
Abstract [en]

The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work.  In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared  by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses

Place, publisher, year, edition, pages
Springer, 2013
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-96920 (URN)978-94-007-2738-0 (ISBN)
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2014-03-19Bibliographically approved
Agwa, M., Andersson, L.-E. & Pinto da Costa, A. (2012). Critical bounds for discrete frictional incremental problems, rateproblems and wedging problems. In: : . Paper presented at Euromech Colloquium 514, Corse, France, March, 2012.
Open this publication in new window or tab >>Critical bounds for discrete frictional incremental problems, rateproblems and wedging problems
2012 (English)Conference paper, Published paper (Other academic)
Abstract [en]

Summary. Questions of existence and uniqueness for discrete frictional quasi-static incremental problems, rate problems and wedging problems are discussed. Various methods to compute critical bounds for the coefficient of friction which guarantee existence and uniqueness are described, as well as the sharpness of the bounds and their interdependence.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-96918 (URN)
Conference
Euromech Colloquium 514, Corse, France, March, 2012
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2013-08-29
Andersson, L.-E. (2010). Critical bounds for frictional rate- and wedging problems. In: : . Paper presented at Laboratoire de Mecanique et d'Acoustique, Centre National de Recherche Scientific (LMA, CNRS), Marseille in June 2010. (pp. 1-51).
Open this publication in new window or tab >>Critical bounds for frictional rate- and wedging problems
2010 (English)Conference paper, Published paper (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-96915 (URN)
Conference
Laboratoire de Mecanique et d'Acoustique, Centre National de Recherche Scientific (LMA, CNRS), Marseille in June 2010.
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2014-04-03
Andersson, L.-E. & Stewart, N. F. (2010). Introduction to the Mathematics of Subdivision Surfaces. Society for Industrial and Applied Mathematics
Open this publication in new window or tab >>Introduction to the Mathematics of Subdivision Surfaces
2010 (English)Book (Other academic)
Abstract [en]

Subdivision surfaces permit a designer to specify the approximate form of a surface defining an object and to refine and smooth the form to obtain a more useful or attractive version of the surface.

A considerable amount of mathematical theory is required to understand the characteristics of the resulting surfaces, and this book

• provides a careful and rigorous presentation of the mathematics underlying subdivision surfaces as used in computer graphics and animation, explaining the concepts necessary to easily read the subdivision literature;

• organizes subdivision methods into a unique and unambiguous hierarchy to facilitate insight and understanding;

• gives a broad discussion of the various methods and is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points.

Introduction to the Mathematics of Subdivision Surfaces is excellent preparation for reading more advanced texts that delve more deeply into special questions of regularity. The authors provide exercises and projects at the end of each chapter. Course material, including solutions to the exercises, is available on an associated Web page.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2010. p. 356
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-96917 (URN)10.1137/1.9780898717617 (DOI)978-0-89871-697-9 (ISBN)
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2013-09-06Bibliographically approved
Lars-Erik, A. (2009). Existence results for quasistatic frictional contact problems and frictional wedging problems. In: : . Paper presented at European Solid Mechanics Conference 2009 Lisbon 7-11 September 2009 (pp. 1-14).
Open this publication in new window or tab >>Existence results for quasistatic frictional contact problems and frictional wedging problems
2009 (English)Conference paper, Published paper (Other academic)
Abstract [en]

We consider first quasistatic evolution problems with Coulomb friction in elasticity and then so called wedging problems and their relation to the evolution problems.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-96913 (URN)
Conference
European Solid Mechanics Conference 2009 Lisbon 7-11 September 2009
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2013-08-29
Andersson, L.-E., Stewart, N. F. & Zidani, M. (2008). Error analysis for operations in solid modeling in the presence of uncertainty. SIAM Journal on Scientific Computing, 29(2), 811-826
Open this publication in new window or tab >>Error analysis for operations in solid modeling in the presence of uncertainty
2008 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 29, no 2, p. 811-826Article in journal (Refereed) Published
Abstract [en]

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.    

Keywords
solid modeling, NURBS, regularized Boolean operations, Whitney extension
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-42088 (URN)10.1137/040604303 (DOI)60297 (Local ID)60297 (Archive number)60297 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
Andersson, L.-E. & Khludnev, A. (2008). On crack crossing a contact boundary. Fictitious domain method and invariant integrals (Russian) .. Siberian journal of industrial mathematics, 11(3), 15-29
Open this publication in new window or tab >>On crack crossing a contact boundary. Fictitious domain method and invariant integrals (Russian) .
2008 (English)In: Siberian journal of industrial mathematics, ISSN 1560-7518, Vol. 11, no 3, p. 15-29Article in journal (Refereed) Published
Abstract [en]

    

Keywords
cracks, boundary. Fictitious domain, invariant integrals
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-43915 (URN)75077 (Local ID)75077 (Archive number)75077 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-10
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