Conclusions
The numerical results demonstrate the accuracy and efficiency of the studies performed on the basis of the presented strategy of combining the finite-element method and the boundary-element method. Especially interesting is the use of this approach in solving problems in domains with zones of great gradients of stresses, in particular, problems of the theory of cracks. Further progress of the proposed scheme of combining the finite-element method and the boundary-element method seems to consist of the development of software appropriate for the analysis of problems with regard for a local nonlinear behavior of structures.
References
M. Costable. “Symmetric methods of the coupling of finite elements and boundary elements”. in:Boundary Elements IX, Berlin (1987), Vol. 1, pp. 411–420.
G. C. Hsiao and W. L. Wendland, “Domain decomposition via boundary element methods”, in:Numerical Methods in Engineering and Applied Sciences, Barcelona (1992), Part I, pp. 198–207.
E. Schnack and K. Türke, “Domain decomposition with the boundary element method and finite-element method”,Int. J. Num. Meth. Eng.,40, No. 14, 2593–2610 (1997).
J. L. Wearing and M. A. Sheikn, “A combined finite element boundary element technique for stress analysis”,Devel. Boundary Elem. Meth.,1, 493–507 (1988).
W. L. Wendland, “On asymptotic error estimates for the combined boundary element method and finite-element method”, in:Finite Elements and Boundary Element Techniques from Mathematical and Engineering Points of View, CISM Courses and Lectures. New York (1988), pp. 273–333.
O. C. Zienkiewicz, D. W. Kelly, and P. Battess, “Mariage a la mode—the best of both worlds (finite elements and boundary integrals)”, in:Energy Methods in Finite Element Analysis, New York (1979), pp. 81–107.
I. I. Dyyak and A. Yu. Chernukha. “Numerical investigation of a problem of elasticity theory based on a combination of methods of boundary and finite elements”,Visnyk L'viv. Derzh. Univ., Ser. Mekh.-Math., Issue 39, 41–46 (1979).
C. A. Brebbia and S. Walker,Boundary Element Techniques in Engineering, Newnes-Butterworths, London (1980).
G. I. Marchuk,Methods of Calculational Mathematics [in Russian], Nauka, Moscow (1989).
Ya. G. Savula and V. V. Krevs, “Application of the method of decomposition of a region to the heat-conduction problem for a body with a thin coating”,Visnyk L'viv. Derzh. Univ., Ser. Mekh.-Math., Issue 44, 3–10 (1996).
N. P. Golovach and I. I. Dyyak, “Direct boundary-element method for numerically solving thermoelasticity problems”,Visnyk L'viv. Derzh. Univ., Ser. Mekh.-Math., Issue 44, 57–62 (1996).
Additional information
Franko L'viv State Univeristy, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 1, pp. 115–117, January–February, 2000.
Rights and permissions
About this article
Cite this article
Golovach, N.P., Dyyak, I.I. Method of domain decomposition and combined finite-boundary-element analysis of problems of elasticity. Mater Sci 36, 138–141 (2000). https://doi.org/10.1007/BF02805132
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02805132