Abstract
By making use of a convenient decomposition of the fundamental tractions, a new formula for the C-matrix in the Somigliana identity for a three- or two-dimensional elastic isotropic body is derived. This kind of formula is more advantageous for analytical and computational C-matrix evaluations than the currently well-known formula. A general closed analytical formula of the C-matrix for the case of any finite number of tangent planes to the boundary of the body at a non-smooth boundary point, presented in the final section of this paper, demonstrates the usefulness of the new formula.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
J. Balaš, J. Sládek and V. Sládek, Stress Analysis by Boundary Element Methods, Amsterdam: Elsevier (1989).
M. Berger, Géométrie, Paris: CEDIC/Nathan (1978).
C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques Theory and Application in Engineering, Berlin: Springer-Verlag (1984).
N.M. Chutorianskii, Boundary integral and integro-differential equations of the second kind for mixed boundary value problem of the theory of elasticity (in Russian), Priklaenye problemy prochnosti a plastichnosti, Vsesoiuznyi mezhvuzovskii sbornik, Gorkii (1981), 3–13.
M. Guiggiani and P. Casalini, Direct computation of Cauchy principal value integrals in advanced boundary elements. International Journal for Numerical Methods in Engineering 24 (1987) 1711–1720.
M. Guiggiani and A. Gigante, A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. Transaction of the ASME. Journal of Applied Mechanics 57 (1990) 906–915.
F. Hartmann, Computing C-matrix in non-smooth boundary points. In: C.A. Brebbia (ed.), New Developments in Boundary Element Methods, London: Butterworths (1980) pp. 367–379.
F. Hartmann, The Somigliana identity on piecewise smooth surfaces, Journal of Elasticity 11 (1981) 403–423.
V. Mantič. On computing boundary limiting values of boundary integrals with strongly singular and hypersingular kernels in 3D BEM for elastostatics. Engineering Analysis with Boundary Elements (in press).
P.C. Ricardella, An implementation of the boundary integral technique for planar problems in elasticity and elastoplasticity, Report No. SM-73-10, Dept. Mech. Engng., Carnegie Mellon Univ., Pittsburgh 1973.
F.J. Rizzo, D.J. Shippy and M. Rezayat, A boundary integral equation method for radiation and scattering of elastic waves in three dimensions. International Journal for Numerical Methods in Engineering 21 (1985) 115–129.