In the present paper we apply the real boundary integral equation method to solve interior and exterior mixed boundary value problems arising in a linear theory of anti-plane elasticity which includes the effects of material microstructure.
[1] Eringen, A.C.: Linear theory of micropolar elasticity. J. Math. Mech., 15, 909-923 (1966).
2.
[2] Nowacki, W.: Theory of Asymmetric Elasticity, Polish Scientific Publishers, Warszawa (1986).
3.
[3] Potapenko, S., Schiavone, P., and Mioduchowski, A.: Anti-plane Shear Deformations in a Linear Theory of Elasticity with Microstructure. J. Appl. Math. Phys. (in press).
4.
[4] Fichera, G.: Sul problema della derivata obliqua e sul problema misto per l’equazione di Laplace. Boll. Un. Mat. Ital. Ser. III, 7, 367-377 (1952).
5.
[5] Wendland, W.L., Stephan, E., and Hsiao, G.C.: On the integral equation method for the plane mixed boundary value problem of the Laplacian. Math. Mech. Appl. Sci., 1, 265-321 (1979).
6.
[6] Constanda, C.: Some comments on the integration of certain systems of partial differential equations in continuum mechanics. J. Appl. Math. Phys., 29, 835-839 (1978).
7.
[7] Kupradze, V.D.et al.: Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam (1979).
8.
[8] Kupradze, V.D.: Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem (1965).
9.
[9] Vekua, N.P.: Systems of Singular Integral Equations, Noordhoff, Groningen (1967).
10.
[10] Schiavone, P. and Ru, C.Q.: On the exterior mixed problem in plane elasticity. Math. Mech. Solids, 1, 335-341 (1996).
