liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Finite Element Modeling of Contact Problems
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
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: urn:nbn:se:liu:diva-124572DOI: 10.3384/diss.diva-124572ISBN: 978-91-7685-847-9 (print)OAI: oai:DiVA.org:liu-124572DiVA: diva2:900379
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: 2017-05-15Bibliographically approved
List of papers
1. Least-squares stabilized augmented Lagrangian multiplier method for elastic contact
Open this publication in new window or tab >>Least-squares stabilized augmented Lagrangian multiplier method for elastic contact
(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
Lagrange multiplier, stabilization, contact, augmented Lagrangian
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:liu:diva-124568 (URN)
Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2016-02-04Bibliographically approved
2. An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes
Open this publication in new window or tab >>An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes
2012 (English)Conference paper, Published paper (Other academic)
Abstract [en]

In this paper an ecient approach to simulate thermal stresses due to tem-perature variations in disc brakes is presented. In the approach thermal and stress analysis are performed sequentially. The frictional heat analysis is based on the Eulerian method, which requires signicantly low computational time as compared to the Lagrangian approach. The nodal temperature history is recorded at each time step and is used in a sequentially coupled stress analysis, where a temperature dependent elasto-plastic material model is used to compute the stresses in the disc brake. The results show that during hard braking, high compressive stresses are generated on the disc surface in circumferential direction which cause plastic yielding. But when the disc cools down, the compressive stresses transform to tensile stresses. Such thermoplastic stress history may cause cracks on disc surface after a few braking cycles. These results are in agreement with experimental observations available in the literature.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-94281 (URN)
Conference
15th Nordic Symposium on Trbology, NORDTRIB,Trondheim, Norway, 12-15 June
Available from: 2012-09-17 Created: 2013-06-20 Last updated: 2016-02-16Bibliographically approved
3. Sequential simulation of thermal stresses in disc brakes for repeated braking
Open this publication in new window or tab >>Sequential simulation of thermal stresses in disc brakes for repeated braking
2013 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 227, no 8, 919-929 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.

Place, publisher, year, edition, pages
Sage Publications, 2013
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-94283 (URN)10.1177/1350650113481701 (DOI)
Available from: 2013-04-26 Created: 2013-06-20 Last updated: 2017-12-06Bibliographically approved
4. Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by adopting an Eulerian approach
Open this publication in new window or tab >>Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by adopting an Eulerian approach
2013 (English)In: EuroBrake 2013 Conference Proceedings, FISITA , 2013Conference paper, Published paper (Other academic)
Abstract [en]

In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional geometries of the ventilated disc and pad are used in the simulations. A sequential approach is adopted, where the contact forces are computed at each time step taking the wear and thermal deformations of the mating parts into account. After each brake cycle, the wear profile of the pad is updated and used in subsequent analysis. The results show that when wear is considered, different distributions of the temperature on disc are obtained for each new brake cycle. After a few braking cycles two hot bands appear on the disc surface instead of only one. These results are in agreement with experimental observations.

Place, publisher, year, edition, pages
FISITA, 2013
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-94284 (URN)978-0-9572076-0-8 (ISBN)
Conference
EuroBrake 2013, Chassis Brakes International, Dresden, Germany, June 17-19, 2013
Available from: 2013-06-20 Created: 2013-06-20 Last updated: 2016-03-07Bibliographically approved
5. Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
Open this publication in new window or tab >>Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
2013 (English)Conference paper, Published paper (Other academic)
Abstract [en]

Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objective optimization (EMO) methods based on surrogate modeling is one approach of solving this class of problems. In this paper, multi-objective optimization of a disc brake system to a heavy truck by using EMO and radial basis function networks (RBFN) is presented. Three conflicting objectives are considered. These are: 1) minimizing the maximum temperature of the disc brake, 2) maximizing the brake energy of the system and 3) minimizing the mass of the back plate of the brake pad. An iterative Latin hypercube sampling method is used to construct the design of experiments (DoE) for the design variables. Next, thermo-mechanical finite element analysis of the disc brake, including frictional heating between the pad and the disc, is performed in order to determine the values of the first two objectives for the DoE. Surrogate models for the maximum temperature and the brake energy are created using RBFN with polynomial biases. Different radial basis functions are compared using statistical errors and cross validation errors (PRESS) to evaluate the accuracy of the surrogate models and to select the most accurate radial basis function. The multi-objective optimization problem is then solved by employing EMO using the strength Pareto evolutionary algorithm (SPEA2). Finally, the Pareto fronts generated by the proposed methodology are presented and discussed.

Place, publisher, year, edition, pages
The American Society of Mechanical Engineers, 2013
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-94285 (URN)10.1115/DETC2013-12809 (DOI)978-0-7918-5590-4 (ISBN)
Conference
ASME 2013 International Design Engineering Technical Conferences (IDETC) and Computers and Information in Engineering Conference (CIE), Portland, USA, August 4-7, 2013
Note

Paper No. DETC2013-12809, pp. V03BT03A029; 10 pages.

Available from: 2013-06-20 Created: 2013-06-20 Last updated: 2016-02-04Bibliographically approved
6. Overview of Disc Brakes and Related Phenomena - a review
Open this publication in new window or tab >>Overview of Disc Brakes and Related Phenomena - a review
2014 (English)In: International Journal of Vehicle Noise and Vibration, ISSN 1479-1471, Vol. 10, no 4, 257-301 p.Article in journal (Refereed) Published
Abstract [en]

Disc brakes have evolved over time to be a reliable method of decelerating and stopping a vehicle. There have been different designs of disc brake systems for different applications. This review gives a detailed description of different geometries of the components and the materials used in a disc brake system. In spite of all the improvements, there are still many operational issues related to disc brakes that need to be understood in greater detail and resolved. There has been a lot of research going on about these issues and at the same time different methods are being proposed to eliminate or reduce them. There has also been intensive fundamental research going on about the evolution of the tribological interface of the disc-pad system. One major purpose of the present paper is to give a comprehensive overview of all such developments.

Place, publisher, year, edition, pages
Inderscience Enterprises, UK, 2014
Keyword
Disc brakes; disc geometry; pad geometry; disc pad tribology; brake fade; brake noise; vehicle noise; vehicle braking
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:liu:diva-124566 (URN)10.1504/IJVNV.2014.065634 (DOI)
Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2016-02-16Bibliographically approved
7. Simulation of internal mechanical conditions in the lower limb donned in a transtibial prosthetic socket
Open this publication in new window or tab >>Simulation of internal mechanical conditions in the lower limb donned in a transtibial prosthetic socket
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper investigates the internal mechanical conditions in a transtibial cross-section while in contact with a prosthetic socket. The nite element model considers the nonlinear behaviors of individual soft tissues instead of lumping them together. The contact problem is solved between socket and limb while taking the friction into consideration to determine the contact forces and resultant internal stress-strain in the limb. Simulation results are presented for three dierent socket designs; total contact, total surface-bearing and hydrostatic sockets. Inuence of higher blood pressure on internal mechanical conditions is also explored.

Keyword
Prosthetic socket, internal mechanical conditions, transtibial socket, interface pressure, stress distribution
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:liu:diva-124567 (URN)
Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2016-02-04Bibliographically approved

Open Access in DiVA

fulltext(3150 kB)330 downloads
File information
File name FULLTEXT01.pdfFile size 3150 kBChecksum SHA-512
c972a7b2be7ab988598776c23bfcf98f7ce4844e5d585f355ee612c2ac77f14d9141e1564bd38daa07574fcb732763b138113eae7f3ac351bc284459dec077ce
Type fulltextMimetype application/pdf
omslag(732 kB)34 downloads
File information
File name COVER01.pdfFile size 732 kBChecksum SHA-512
b96b428a8ed25a59e3e98768d49f1dc145060c5217954746fb3acc2db6c1179584e1408b9d7d6fe31536bf3def28ee7c4c89e086886c5ded9da2c206d2d92bac
Type coverMimetype application/pdf

Other links

Publisher's full text
By organisation
Solid MechanicsFaculty of Science & Engineering
Vehicle Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 330 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 2629 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf