Trefftz functions using the fundamental solution with the singularity outside the domain

• Autorzy: Jakubovičová L. , Vaško M. , Kompiš V.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

Two types of Trefftz (T-) functions are often used - fundamental solutions with their singularities outside the given region and general solutions of homogenous differential equations. For elasticity problems the general solution of the homogeneous differential equation (equilibrium equation in displacements known as Lame-Navier equations) can be found in the polynomial form. In this paper we present the first type of T-functions. The paper deals with the investigation of accuracy and stability of the resulting system of discretized equations in relation to the position of the source (singularity) point. In this way non-singular reciprocity based boundary integral equations relate the boundary tractions and the boundary displacements of the searched solution to corresponding quantities of the known solutions. It was found that there exist an optimal relation of the distance of the singularity to the distance of the collocation points where both the integration accuracy and numerical stability are good.

Słowa kluczowe

EN

BEM; FEM; infinitesimal displacements

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 515--521
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Jakubovičová L.

• Department of Mechanics, Faculty of Mechanical Engineering, University of Žilina,Vel'ky Diel, 010 26 Žilina, Slovakia

autor

Vaško M.

• Department of Mechanics, Faculty of Mechanical Engineering, University of Žilina,Vel'ky Diel, 010 26 Žilina, Slovakia

autor

Kompiš V.

• Department of Mechanics, Faculty of Mechanical Engineering, University of Žilina,Vel'ky Diel, 010 26 Žilina, Slovakia

Bibliografia

• [1] P. Eschmann, L. Hasbargen, K. Weigand. Ball and Roller Bearings, Theory, Design and Applications. John Wiley & Sons Ltd., Chichester, England, 1985.
• [2] W. Changsen. Analysis of Rolling Element Bearings. Mech. Eng. Publications Ltd., London, 1987.
• [3] J.O. Smith, C.K. Liu. Stresses due to tangential and normal loads on an elastic solid with application to some contact stress problem. Journal of Applied Mechanics, 21: 157-166, 1953.
• [4] W.D. Pilkey. Formulas for Stress, Strain, and Structural Matrices. John Wiley, New York, 1990.
• [5] D.A. Hills, D. Nowell, A. Sackfield. Mechanics of Elastic Contacts. Butterworth Heinemann Ltd., Oxford, 1993.
• [6] G.A. Castleberry. Analyzing contact stresses more accurately. Machine Design, pages 92-97, 1984.
• [7] B. Schaude. Optimal Profiling of Rolling Elements of Cylinder Rollers (in German). PhD thesis, University Karrlsruhe, 1978.
• [8] K. Knothe, H.L. The. A contribution to the calculation of the contact stress distribution between two elastic bodies of revolution with non-elliptical contact. Computers & Structures, 18: 1025-1033, 1984.
• [9] S. Vijayakar. A combined surface integral and finite element solution for a three-dimensional contact problems. Int. J. Numer. Meth. in Engng., 31: 525-545, 1991.
• [10] J.J. Kalker. An Algorithm for the Computation of the Frictionless Contact Pressure between two Bodies of Revolution. PhD thesis, TH Delft, 1981.
• [11] V. Kompiš, M. Handrik, P. Elesztös, F. Koch. Analysis and design of roller bearings. In: EAEC 2001 Congress, Bratislava, 2001. CD-ROM.
• [12] A.E.H. Love. A Treatice on the Mathematical Theory of Elasticity. Cambridge University Press, Cambridge, 1927.
• [13] N.I. Muskhelishvili. Some Basic Problems of Mathematical Theory of Elasticity (in Russian), Nauka, Moscow, 1966.
• [14] S.P. Timoshenko, J.N. Goodier. Theory of Elasticity. McGraw-Hill, New York, 3rd edition, 1970.
• [15] B.I. Blokh. Theory of Elasticity (in Russian). Univ. Press, Kharkov, 1964.
• [16] V.D. Kupradze. Potential Methods in Theory of Elasticity (in Russian). Nauka, Moscow, 1963.
• [17] G. Kuhn. Boundary element technique in elastostatics and linear fracture mechanics. In: E. Stein and W.L. Wendland, editors, Finite Element and Boundary Element Techniques Form Mathematical and Engineering Point of View, number 301 in CISM Courses and Lectures, pages 109-170. Springer-Verlag, Wien, 1988.
• [18] V. Sládek , J. Balaš, J. Sládek. Stress Analysis by Boundary Element Methods. Elsevier, Amsterdam, 1989.
• [19] V. Kompiš. Selected topics in boundary integral formulations of solids and fluids. Number 433 in CISM Courses and Lectures. Springer-Verlag, Wien, 2002