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Least-squares stabilized augmented Lagrangian multiplier method for elastic contact
Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we propose a stabilized augmented Lagrange multiplier method for the finite element solution of small deformation elastic contact problems. We limit ourselves to friction–free contact with a rigid obstacle, but the formulation is readily extendable to more complex situations.

Keyword [en]
Lagrange multiplier, stabilization, contact, augmented Lagrangian
National Category
Vehicle Engineering
Identifiers
URN: urn:nbn:se:liu:diva-124568OAI: oai:DiVA.org:liu-124568DiVA: diva2:900218
Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2016-02-04Bibliographically approved
In thesis
1. Finite Element Modeling of Contact Problems
Open this publication in new window or tab >>Finite Element Modeling of Contact Problems
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Contact is the principal way load is transferred to a body. The study of stresses and deformations arising due to contact interaction of solid bodies is thus of paramount importance in many engineering applications. In this work, problems involving contact interactions are investigated using finite element modeling.

In the first part, a new augmented Lagrangian multiplier method is implemented for the finite element solution of contact problems. In this method, a stabilizing term is added to avoid the instability associated with overconstraining the non-penetration condition. Numerical examples are presented to show the influence of stabilization term. Furthermore, dependence of error on different parameters is investigated.

In the second part, a disc brake is investigated by modeling the disc in an Eulerian framework which requires significantly lower computational time than the more common Lagrangian framework. Thermal stresses in the brake disc are simulated for a single braking operation as well as for repeated braking. The results predict the presence of residual tensile stresses in the circumferential direction which may cause initiation of radial cracks on the disc surface after a few braking cycles. It is also shown that convex bending of the pad is the major cause of the contact pressure concentration in middle of the pad which results in the appearance of a hot band on the disc surface. A multi-objective optimization study is also performed, where the mass of the back plate, the brake energy and the maximum temperature generated on the disc surface during hard braking are optimized. The results indicate that a brake pad with lowest possible stiffness will result in an optimized solution with regards to all three objectives. Finally, an overview of disc brakes and related phenomena is presented in a literature review.

In the third part, a lower limb donned in a prosthetic socket is investigated. The contact problem is solved between the socket and the limb while taking friction into consideration to determine the contact pressure and resultant internal stress-strain in the soft tissues. Internal mechanical conditions and interface stresses for three different socket designs are compared. Skin, fat, fascia, muscles, large blood vessels and bones are represented separately, which is novel in this work.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. 34 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1736
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:liu:diva-124572 (URN)10.3384/diss.diva-124572 (DOI)978-91-7685-847-9 (Print) (ISBN)
Public defence
2016-03-04, E1405, Tekniska Högskolan, Jönköping University, Jönköping, 10:00 (English)
Opponent
Supervisors
Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2016-02-09Bibliographically approved

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