zbMATH — the first resource for mathematics

A boundary element method for plane anisotropic elastic media. (English) Zbl 0724.73256
Summary: The general problem of plane anisotropic elastostatics is formulated in terms of a system of singular integral equations with Cauchy kernels by means of the classical stress function approach. The integral equations are represented over the image of the boundary in the complex plane and a numerical scheme is developed for their solution. The boundary curve is discretized and suitable polynomial approximations of the unknown functions in terms of the complex variable are introduced. This reduces the equations to a set of complex linear algebraic equations which can be inverted to yield the stresses in a straightforward manner. The major difference between the present technique and the previous ones is the numerical formulation. The integral equations are discretized in the complex plane and not in terms of real variables which depend on arc length, resulting in improved accuracy in presence of strong boundary curvature.

74S15 Boundary element methods applied to problems in solid mechanics
74E10 Anisotropy in solid mechanics
45E05 Integral equations with kernels of Cauchy type
74B10 Linear elasticity with initial stresses
Full Text: DOI