IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v269y2015icp1007-1021.html
   My bibliography  Save this article

Combined symmetric BEM and semi-smooth Newton method for the contact problems in linear elasticity of Yukawa type

Author

Listed:
  • Tchoualag, L.

Abstract

The semi-smooth Newton method and the boundary element method are developed and analyzed for the solution of 2-D Signorini contact problems in linear elasticity of Yukawa type. First we consider the contact problem with Tresca friction. This leads to a constrained non-differentiable minimization problem where the solvability is in general problematic. But, by utilizing the Fenchel duality theory, the dual formulation in terms of contact stresses turns out to be a quadratic optimization problem with a smooth functional. The regularization of the dual problem motivated by the augmented Lagrangian is suitable for the application of the generalized Newton method. Applying the boundary integral equation method, the problem is reduced to the boundary curve. The corresponding boundary integral equations are approximated by using a Galerkin method with the help of B-splines on the boundary curve (BEM). This yields an algebraic system of linear equations with dense stiffness matrix but which is symmetric. The symmetry property of the stiffness matrix enables the application of efficient iterative solution strategies for the linear systems at each Newton step. Second, the methods are carried over to the Coulomb friction problem by means of a fixed point approach. In particular, the analysis of the algorithm is presented and some numerical examples, which show a remarkable efficiency and reliability of the semi-smooth Newton method, are given.

Suggested Citation

  • Tchoualag, L., 2015. "Combined symmetric BEM and semi-smooth Newton method for the contact problems in linear elasticity of Yukawa type," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1007-1021.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:1007-1021
    DOI: 10.1016/j.amc.2015.08.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315010838
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eck, C. & Steinbach, O. & Wendland, W.L., 1999. "A symmetric boundary element method for contact problems with friction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 43-61.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:1007-1021. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.