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Analytical approach for resolving stress states around elliptical cavities

Author(s): Lukić Dragan | Anagnosti Petar

Journal: Facta Universitatis - series : Architecture and Civil Engineering
ISSN 0354-4605

Volume: 3;
Issue: 2;
Start page: 145;
Date: 2005;
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Keywords: coordinates | biharmonic differential equation | stress state | stress function | harmonic functions | recurrent formulas

The determination of stress states around cavities in the stressed elastic body, regardless of cavity shapes, that may be spherical, cylindrical elliptical etc. in its analytical approach has to be based on selection of a stress function that will satisfy biharmonic equation, under given boundary conditions. This paper is concerned with formulation and solution of the cited differential equation using elliptical coordinates in conformity with the cavity shape of oblong ellipsoid [1]. It is therefore considered that the formulation of the stress tensor will be done in conformity to the cited coordinates. The paper describes basic statements and definitions in connection to harmonic functions used for determination of stress states around cavities formed in the stressed homogeneous space. The particular attention has been paid to the use of Legendre`s functions, with definitions and derivation of recurrent formulas, that have been used for determination of stress states around an oblong ellipsoidal cavity, [1]. The paper also includes the description of procedures used in forming series based on Legendre`s functions of the first order.

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