Four crack problems are considered in classical two-dimensional elastostatics. Each problem is equivalent to a mixed boundary-value problem for a quarter-plane. A governing functional relation of the Wiener–Hopf type is obtained for each problem by the application of various Mellin transforms. It is shown that values for the stress intensity factor, and the crack energy, in corresponding ‘interior’ arid ‘exterior’ problems are identical for certain distributions of crack pressure.

A two (spatial) dimensional initially strained elastic body is excited by a point impulse. Expressions are found for the various displacement components in a form which is readily evaluated by residues. The solid itself is characterized by three parameters which depend on the material properties and the initial deformation. For the case when two of these parameters are equated, explicit expressions for the displacements are given along the Cartesian axes passing through the origin of the point impulse. Wave front singularities and lacunas are identified and discussed. Some typical numerical results are given.