Singularity methods for elastostatics

Abstract

By distributing the concentrated singularities such as a Kelvin doublet along the axis of symmetry we describe the displacement field, in an elastic medium, for various modes of rotation and translation for a rigid prolate and oblate spheroid. The limiting cases of a sphere, a slender body and a thin circular disk are also discussed. All the solutions are presented in a closed form. RESUMt~En distribuant les singularit6es concentr6es, comme par exemple un doublet de Kelvin, le long des axes de symetrie, nous d6crivons le champs de d6placement en milieu 61astique, pour divers modes de rotation et de translation d'un ellipsoide rigide, oblong ou prolong. Les cas limites d'une sph6re, d'.une aiguille et d'un disque circulaire mince sont aussi discut6s. Toutes les solutions sont present6es sous une forme ferm6e,

Rectilinear oscillations of a rigid spheroid in an elastic medium

“…is the static force evaluated in [1], Relation (24) agrees with the value obtained earlier [1,2] except that now the value of P0 is given explicitly. In outer variables the prolate spheroid reduces to a needle of zero radius and finite length when Ma is arbitrary.…”

“…A method of singularities has recently been developed to solvevarious displacement-type boundary value problems in elastostatics [1], Our aim is toextend this method to elastodynamics. Specifically, we study the dynamical displacements set up in an infinite elastic space when a rigid spheroid, embedded in this space, is subjected to a transverse periodic displacement.…”

“…The solution. We use the singularity method in [1] and solve Eqs. (7) subject to a zero displacement condition.…”

Dynamic Propagation Problems of Mode Iii Semi-Infinite Crack

“…All meeting this function relationship are resolved by Equation 6, 7 and 8 according to the format of homogeneous functions relative to variable τ. This method is utilized not only in elastodynamics (Cherepanov, 1979;Kostrov, 1964;Freund, 1998;Nian-Chun et al, 2004;2005;2006;Atkinson, 1965;Hoskins, 1979;Lu et al, 2010a;2010b;2010c), but also in elastostatics (Muskhelishvili, 1977;Sih, 1977b;Kanwal and Sharma, 1976;Sneddon, 1951), so much as in the else region (Muskhelishvili, 1977;Galin, 1953).…”

“…Considering dissymmetry and the conditions of the infinite point of the plane corresponding to the origin of coordinates of the physical plane as well as singularities of the stress at the crack tip (Gahov, 1966;Sih, 1977b;Kanwal and Sharma, 1976), the rudimental solution of the above problems can be obtained as follows Equation 13:…”