No abstract

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.

This paper is concerned with determining the elastic properties of a composite material composed of hollow spherical inclusions embedded in a matrix. Both inclusions and surrounding material are taken to be isotropic and elastic.As the result of a straightforward extension of Hashin's work, upper and lower bounds have been developed for the gross shear modulus of the composite. In addition, a closed form expression is presented for the gross bulk modulus of the material. Numerical results have been presented illustrating the effect of wall thickness of the inclusion upon the elastic constants of the composite. As illustrated by example, control of the properties and geometry of the inclusions permits "design" of a material with prescribed elastic behavior.

Solutions are presented, within the scope of classical elastostatics, for a class of asymmetric mixed boundary-value problems of the elastic half-space. The boundary conditions considered are prescribed interior and exterior to a circle and are mixed with respect to shears and tangential displacements. Using an established integral-solution form, the problem is reduced to two pairs of simultaneous dual integral equations for which the solution is known. Two illustrative examples, motivated by problems in fracture mechanics, are presented; the resulting stress and displacement fields are given in closed form.

The viscoelastic analysis of tape systems composed of rate-dependent materials is presented. Histories for winding, winding-pause, and winding-pause-unwinding are considered. The winding problem is reduced to determining the appropriate Green’s function by numerical solution of a Volterra integral equation of the second kind. This Green’s function and integral superposition permits the evaluation of the stress and displacement fields in the tape system for any winding history. Viscoelastic unwinding is treated by the superposition of two-states — one determined from the initial condition of the tape when unwinding begins and the second state given in terms of an arbitrary external pressure evaluated by solving an integral equation. Numerical results are presented for several histories and representative material properties.