Elastic waves in compressible materials with initial stresses and a nondestructive ultrasonic method for the determination of biaxial residual stresses

Concise information is given on the theory of the propagation of elastic waves in bodies with initial stresses. This information provides the basis of a nondestructive ultrasonic method for the determination of biaxial residual stresses in isotropic and quasiisotropic materials. The basic acoustoelasticity relation for biaxial stresses is analyzed, and an instrument for the determination of biaxial residual stresses in electric welding is described, along with examples of its application.Adapted from the complete text of a paper submitted to the 18th International Congress on Theoretical and Applied Mechanics, Haifa, Israel, August 22–28, 1992, Session B-A2: Waves in Solids (August 24, 1992).S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 3–17, January, 1994.     

Elastic stresses in bodies with elliptic,parabolic, and tunnel cracks

The paper gives explicit expressions of the elastic T-stress components T _I, T _II, and T _III for an elliptic crack in an unbounded body under uniform pressure and bending and expressions of all the T-stress components for parabolic and tunnel cracks under uniform loading. These formulas are derived by analyzing the asymptotic behavior of the stress components near the crack front using special harmonic functions. The dependence of the T-stresses on Poisson’s ratio, semiaxes and parametric angle of the elliptic crack is studied. The expressions of T _I, T _II, and T _III for a penny-shaped crack under arbitrary uniform pressure and bending follow as a special case from the respective expressions for an elliptic crack __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 57–70, August 2007.     

On the relations governing rayleigh wave propagation in bodies with initial stresses

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Institute of Electrowelding, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 47–52, November, 1993.     

Elastic waves in prestressed bodies interacting with a fluid (survey)

Conclusion The above survey of different studies and analysis of results obtained widiin the framework of linearized three-dimensional theory show that use of the given model makes it possible to account for fluid viscosity and initial stresses in elastic bodies. Both of these factors play a significant role in actual media. The model also permits determination of the effect of fluid viscosity and initial stresses on the wave processes in hydroelastic systems. The use of an approach based on representations of general solutions of linearized problems of aerohydroelasticity for bodies with uniform initial strains and a compressible viscous fluid makes it possible to obtain dispersion relations in a general form diat is invariant relative to different types of elastic potential and valid for arbitrary compressible and incompressible materials. The approach also allows researchers to study the main classes of problems encountered in practice, conduct numerical experiments, and use the results to find new properties, laws, and mechanical effects that are characteristic of the investigated wave processes and reflect the mutual effects of the fields of initial and dynamic stresses, as well as the interaction of elastic bodies with viscous fluids. Translated from Prikladnaya Mekhanika, Vol. 33, No. 6, pp. 3–39, June, 1997.