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References
J.F.Ahner and G.C.Hsiao, On the two-dimensional boundary-value problems of elasticity, SIAM J. Appl. Math. 31 (4) (1976) 677–685.
J.E.Ashton and J.M.Whitney, Theory of Laminated Plates, Progress in Materials Science Series, IV, Technomic, Stanford (1970).
D.Arnold and W.L.Wendland, Collation versus Galerkin procedures for boundary integral methods. In C.A.Brebbia (ed.) Boundary Element Methods in Engineering, pp. 18–13. Berlin Heridelberg New York: Springer-Verlag (1982).
D.Caillerie, Thin elastic periodic plates, Math. Meth. in Appl. Sci. 6 (1984) 159–191.
P.G.Ciarlet, The Finite Element Method for Elliptic Problems, Amsterdam New York Oxford: North Holland (1978).
P.G.Ciarlet and P.Destuynder, A justification of the two-dimensional linear plate model, Journal de Mécanique 18 (2) (1979) 315–344.
M. Costabal and W.L. Wendland, Strong ellipticity of boundary integral operators, Preprint No. 889, Technische Hochschule, Darmstadt.
G.Fichera, Existence theorems in elasticity. Unilateral constraints in elasticity. In: S.Flugge (ed.) Handbuch der Physik, Vol. VIa, pp. 2, 347–424. Berlin Heidelberg New York: Springer-Verlag (1972).
G.Fichera, Linear elliptic equations of higher order in two independent variables and singular integral equations, Proc. Conference on Partial Differential Equations and Continuum Mechanics (Madison, WI), Univ. of Wisconsin Press, Madison (1961).
G. Fichera and P. Ricci, The single layer potential approach in the theory of boundary value problems for elliptic equations, in Lecture Notes in Mathematics 561 (1976) 39–56.
D.Gilbarg and N.S.Trudinger, Elliptic Partial Differential Equations for Second Order. Berlin Heidelberg New York: Springer-Verlag (1977).
R.P.Gilbert, G.C.Hsiao and M.Schneider, The two-dimensional, linear orthotropic plate, Applicable Analysis 15 (1983) 147–169.
R.P.Gilbert and M.Schneider, The linear anisotropic plate, J. Compos. Materials 15 (1981) 71–78.
L.Hormander, Pseudo-differential operators and non-elliptic boundary problems, Annals Math. 83 (1966) 129–209.
G.C. Hsiao, On the stability of integral equations of the first kind with logarithmic kernels, Archive Rat. Mech. Analysis, in print.
G.C.Hsiao, P.Kopp and W.L.Wendland, A Galerkin collocation method for some integral equations of the first kind, Computing 25 (1980) 89–130.
G.C.Hsiao, P.Kopp and W.L.Wendland, Some applications of a Galerkin-collocation method for integral equations of the first kind, Math. Meth. in Appl. Sci. 6 (1984) 280–325.
G.C.Hsiao and R.C.McCamy, Solutions of boundary value problems by integral equations of the first kind, SIAM Review 15 (1973) 687–705.
G.C. Hsiao and W.L. Wendland, On a boundary integral method for some exterior problems in elasticity, Preprint No. 769, Technische Hochschule Darmstadt (1983).
G.C.Hsiao and W.L.Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3 (1981) 299–315.
G.C.Hsiao and W.L.Wendland, A finite element method for some integral equations of the first kind, SLAM Review 15 (1973) 687–705.
J.J.Kohn and L.Nirenberg, On the algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965) 269–305.
V.D.Kupradze, Potential Methods in the Theory of Elasticity, Jerusalem, Isreal Program Scientific Transl. (1965).
V.D.Kupradze, T.G.Gegelia, M.O.Basheleishvili and T.V.Burchuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity, Amsterdam: North-Holland (1979).
P.D.Lax and L.Nirenberg, On stability for difference schemes; a sharp form of Garding's inequality, Comm. Pure Appl. Math. 19 (1966) 473–492.
S.G.Lekhnitskii, Anisotropic Plates, 2nd edn. New York: Gordon and Breach (1968).
E.Martensen, Potentialtheorie. Stuttgart: B.G. Teubner (1968).
R.C.MacCamy, On singular integral equations with logarithms or Cauchy kernels Potentialtheorie. Stuttgart: B.G. Teubner 7 (1958) 355–376.
S.G.Michlin and S.Prössdorf, Singuläre Integraloperatoren. Berlin: Akademie-Verlag (1980).
N.I.Muskhelishvili, Singular Integral Equations. Groningen: Noordhoff (1953).
N.I.Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity. Groningen: Noordhoff (1953).
S.Prössdorf, Some Classes of Singular Equations. Amsterdam: North-Holland (1978).
S. Prössdorf and G. Schmidt, A finite element collocation method for systems of singular integral equations. Preprint P., Math., 26/81, Akademie d. Wiss. DDR, Inst. Math., (1981).
R.Seeley, Topics in psueod-differential operators. In: L.Nirenberg (ed.) Pseudo-Differential Operators, pp. 168–305. Roma: C.I.M.E., Cremonese (1969).
E.Stephan and W.L.Wendland, Remarks to Galerkin and least squares method with finite elements for general elliptic problems, Manuscripta Geodaetica 1 (1976) 93–123.
M.Taylor, Pseudo-differential Operators, Princeton: University Press (1981).
F.Treves, Introduction to Pseudo-differential and Fourier Integral Operators I. New York London: Plenum Press (1980).
W.L.Wendland, E.Stephan and G.C.Hsiao, On the integral equation method for the plane mixed boundary value problem of the Laplacian, Math. Methods in the Appl. Sciences I (1979) 265–321.
U.Zastrow, Solution of the anisotropic elastostatical boundary value problems by singular integral equations, Acta Mechanica 44 (1982) 59–71.
U.Zastrow, Numerical plane stress analysis by integral equations based on the singularity method, Solid Mechanics Archives 10 (1985) 113–128.
U.Zastrow, On the formulation of the fundamental solution for orthotropic plane elasticity, Acta Mechanica 57 (1985) 113–128.
U.Zastrow, On the complete system of fundamental solutions for anisotropic slices and slabs: a comparison by use of the slab analogy. J. Elasticity 15 (1985) 293–318.
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Gilbert, R.P., Magnanini, R. The boundary integral method for two-dimensional orthotropic materials. J Elasticity 18, 61–82 (1987). https://doi.org/10.1007/BF00155437
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DOI: https://doi.org/10.1007/BF00155437