Within the framework of the two-dimensional theory of elastodynamics a closed-form, quasi-stationary, solution is given to the problem of continuous failure of bond between an elastic half space and a rigid body. The bond failure is due to a line force moving at the interface.

The redistribution of dynamic stresses due to the presence of a circular cylindrical discontinuity in an unbounded isotropic homogeneous elastic plate is studied. The source of excitation is a time-harmonic line force located at a finite distance from the discontinuity. In particular, the effects of source location on the concentration of energy around a rigid insert or a cavity is explored.

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

Closed-form solution is constructed to plane state of strain generated in a semi-infinite elastic medium when a portion of its boundary is heated. The heated region is assumed to be moving with uniform velocity. It is shown that stresses are bounded everywhere and are identically zero when the velocity of the moving temperature discontinuity vanishes. The study is based on uncoupled quasi-static thermoelastic theory.

Singular solutions are constructed which generate the singularities for great many types of concentrated action on shallow spherical and cylindrical shells. Subsequently a technique is introduced to construct the Green’s functions for closed circular cylindrical shells. Also, the deformation of thin plates subjected to moving hot spots is discussed briefly.

The paper gives the singularity for a concentrated lateral load on a unidirectionally compressed plate. The method of images is used to treat the infinite strip. For suitable initial conditions, the results derived for the unidirectionally compressed plate under static loads may also be interpreted as a solution for the plate subjected to moving loads.

Using Lagrange’s equation of motion for thin plates, the equations of plane stress, and the equations for shallow cylindrical shells, the deformations of thin plates and cylindrical shells subjected to bending and plane hot spots are studied. The interrelation between different singular functions associated with these problems has been indicated also.

Singularities for uniformly moving and static concentrated forces on shallow circular cylindrical shells are obtained in terms of the integrals of the products of cylindrical and circular functions. Some relations between the solutions of Helmholtz’s equation and the solutions of bi-Helmholtz’s equation are also given.