Three-Dimensional Non-Axisymmetric Anisotropic Stress Concentrations

摘要

Unified explicit analytical solutions for the (non-axisymmetric) first and second boundary value problems of elasticity theory for a spheroidal cavity embedded in a transversely isotropic medium are presented. The analysis is based upon solutions of the homogeneous displacement equations of equilibrium in terms of three quasi-harmonic potential functions, each of which is harmonic in a space different from the physical space. Thus, three spheroidal coordinate systems with different metric scales (one for each potential) are introduced such that the three coordinate systems coincide on the spheroidal cavity. These potential functions are taken in a unique combination of the associated Legendre functions of the first and second kind. Extensive numerical data are obtained for the stress concentration factors associated with axisymmetric and non-axisymmetric problems for a variety of materials. The effect of anisotropy on the stress concentration factor is discussed in much greater detail than has been previously available in the literature.