A Method for Stress Determination in Plane Anisotropic Elastic Bodies

Abstract

Using a fundamental solution to the appropriate field equations of linear anisotropic elasticity, a real variable integral formula of the Somigliana type is derived. The formula relates an elastic displace ment field to boundary traction and displacement vectors; all refer to an arbitrary equilibrated stress state present in an orthotropic body of arbitrary shape and connectivity. A fundamental relation between boundary traction and displacement is then derived which is a mechanism for determining (numerically in practice) that part of such boundary data not initially given from a knowledge of that part which is given. Once all boundary quantities are known, the field solution is given by the integral formula and its first derivatives. Finally, the body may be composite; i.e., it may contain inclusions or inhomogeneities which may be isotropic or rigid as special cases. Numerical techniques are indicated and several problems are solved for illustration.