Abstract
Steady-state heat conduction is considered for perforated thin plates with non-insulated facial surfaces. The heat conductivities of the materials and the convection coefficients are assumed piecewise constant. Influence functions of point sources are analytically obtained for some such plates of standard shape. Their singular components are derived in a closed form, ensuring accurate straightforward computer implementations. Special integral representations are then used for obtaining influence functions of a point source for perforated plates. Computability of those representations is tested with a number of illustrative examples.
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J.V. Beck, K.D. Cole, A. Haji-Sheikh and B. Litkouhi, Heat Conduction Using Green's Functions. New York: Hemisphere (1992) 550pp.
Yu.A. Melnikov, Influence Functions and Matrices. New York-Basel: Marcel Dekker (1999), 469pp.
J.C.F. Telles and S. Guimaraes, Green's function: a numerical generation for fracture mechanics problems via boundary elements. Comp. Meth. Appl. Mech. Engng. 188 (2000) 847–858.
D. Duffy, Green's Functions with Applications. Boca Raton: CRC Press (2001) 443pp.
J.R. Berger and V.K. Tewary, Green's functions for boundary element analysis of anisotropic materials. Engng. Anal. Bound. Elem. 25 (2001) 279–288.
B. Yang and E. Pan, Efficient evaluation of three-dimensional Green's function in anisotropic eleastostatic multilayered material composite. Engng. Anal. Bound. Elem. 26 (2002) 355–366.
V.I. Smirnov, A Course of Higher Mathematics, Vol. 4. Oxford-New York: Pergamon Press (1964) 812pp.
I.M. Dolgova and Yu.A.Melnikov, Construction of Green's functions and matrices for equations and systems of elliptic type. J. Appl. Math. Mech. 42 (1978) 740–746.
Yu.A. Melnikov, Accuracy of series approximations of Green's functions. In: Int. Symp. Bound. Elem. Meth. Paris (1998) 147–148.
S.L. Marshall, A rapidly convergent modified Green's function for Laplace equation in a rectangular region. Proc. R. Soc. London 455 (1999) 1739–1766.
G.F. Roach, Green's Functions. New York: Cambridge University Press (1982) 325pp.
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Melnikov, Y. Influence functions of a point source for perforated compound plates with facial convection. Journal of Engineering Mathematics 49, 253–270 (2004). https://doi.org/10.1023/B:ENGI.0000031187.96637.ea
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DOI: https://doi.org/10.1023/B:ENGI.0000031187.96637.ea