By Jutta Blobner, Günther Kuhn (auth.), Tadeusz Burczynski (eds.)
During the final twenty years the boundary point process has skilled a amazing evolution. modern ideas and methods resulting in the developments of functions and realizing of the mathematical and computational features of the strategy in mechanics are awarded. The specified emphasis on theoretical and numerical concerns, in addition to new formulations and ways for distinct and significant fields of strong and fluid mechanics are thought of. a number of very important and new mathematical points are awarded: singularity and hypersingular formulations, regularity, mistakes and blunder estimators, adaptive tools, Galerkin formulations, coupling of BEM-FEM and non-deterministic (stochastic and fuzzy) BEM formulations. Novel advancements and purposes of the boundary point procedure in numerous fields of mechanics of solids and fluids are thought of: warmth conduction, diffusion and radiation, non-linear difficulties, dynamics and time-depending difficulties, fracture mechanics, thermoelasticity and poroelasticity, aerodynamics and acoustics, touch difficulties, biomechanics, optimization and sensitivity research difficulties, sick posed and inverse difficulties, and id problems.
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Additional resources for IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method: held in Cracow, Poland, 31 May-3 June 1999
Sample text
Cose-] esin +0(1) (33) A NUMERICAL TEST A MATLAB program has been written to test the present direct integration method. To demonstrate its accuracy, we present a comparison 22 MARC BONNET, MASSIMO GUIGGIANI between numerical and exact (analytical) values of double singular integrals of the form: r _r _ } E+E } E+E-e€ W(x ,y)'ljJ(x)cp(y)dsydsx (34) where E , E are straight boundary elements meeting at their common endpoint with an angle 0 (figure 2) and'ljJ and ip are taken as the same piecewise linear 'hat function' : ('ljJ , cp)(~) = 1 ;~ (on E) and ('ljJ , cp)(~) 1-~ = -2- (on E) Integral (34) is scale-independent (this stems from the fact that the kernel W(x, y) is homogeneous of degree -2 with respect to the position vector y - x) , and hence depends only on 0 and the element length ratio 'TJ = lEI/lEI) .
Moreover , expansion (30) is considered and all singular integrals are performed analytically. The final result is f~2) = 1{[~ 1 Q(u,v) : Q(u, 0) dv + Q(u, 0) In 12s(u)1 }dU -In lEI [11 Q(u, O)du + O(E). (32) As in equation (24), the divergent term is of s-type. Singularity at (1],~) = (-1 ,1). , E following E on ,). The integral over region (2) is then nonsingular, and essentially the same treatment as above is applied to the integral over region (1). 6. EVALUATION OF THE SINGULAR FREE TERM Let us go back to the starting identity (4) for the direct SGBEM.
O)-q]dV+ - roO': reP - ln ln i; lnr e~ - >. [-o + On - >. e. of the form OUk(Y) = r oti(X)Ut(x-y) as, - 1sr ~7j(x-y)nj(x)oui(X) dS 1s; t x (7) 54 BERTRAND BURGARDT, MARC BONNET, ANH LE VAN (with Ju E iI 1/ 2 (Sd and Jt E H- 1 / 2(Su)) , stress variations J(J' E L 2(O), plastic strain variations Jc p E L 2(O) and variations 150. E L 2(O), Jq E L 2(O), 15>' E h' E L 2(O), I ~ O}. From eq. ) are implicitly taken at t = tn+l and the index n + 1 is omitted for brevity. n on S involve non-integrable kernels .