In this paper, following a critical assessment of earlier work of Green and Sneddon, Segedin, Kassir, and Sih (who obtained solutions for specific cases of normal loading on the crack face and the cases of constant and linear shear distribution on the crack face), Shah and Kobayashi (whose work is limited to the case of third-order polynomial distribution of normal loading on the crack face), and Smith and Sorensen (whose work is limited to the case of a third-order polynomial variation of shear loading on the crack face), a general solution is presented for the case of arbitrary normal as well as shear loading on the faces of an embedded elliptical crack in an infinite solid. The present solution is based on a generalization of the potential function representation used by Shah and Kobayashi. Expressions for stress-intensity factors near the flaw border, as well as for stresses in the far-field, for the foregoing general loadings, are given.

No abstract

No abstract

After formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [ 14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.