Integral equations of the second principal problem of elasticity for multiply-connected anisotropic plate (Q2759431)

The problem is reduced to determination of complex potentials \(\varphi(z_1)\), \(\psi(z_2)\) satisfying at the boundary of domain the following conditions: \(2\,{\text{Re}}\,[p_1\varphi(z_1)+p_2\psi(z_2)] =g_1\), \(2\,{\text{Re}}\, [q_1\varphi(z_1)+q_2\psi(z_2)] = g_2\), where \(z_1=x+s_1 y\), \(z_2=x+s_2 y\); \(s_1\) and \(s_2\) are roots of the characteristic equation, \(p_i\) and \(q_i\) are complex constants calculated through mechanical characteristics of material, \(g_1\) and \(g_2\) are prescribed displacement components at the boundary. Derived from these conditions singular boundary integral equations are solved using the method of mechanical quadratures. An example for a plate with two identical elliptic inclusions is considered, numerical results are presented.