Diffraction of horizontally polarized shear waves by normal edge cracks in a plate

A combined finite element and analytical method is presented here for analyzing scattering of time harmonic horizontally polarized shear (SH) waves by material and geometric irregularities in an isotropic linearly elastic infinite plate. All the irregularities are assumed to be contained in a bounded region. The problem of scattering is solved by replacing this region with a finite element mesh. A nodal force-displacement relation is developed to satisfy the continuity conditions along the boundaries separating the inner finite-element region from the exterior regular region. The method is illustrated by solving the problem of scattering of SH waves by a surface breaking crack. The crack is taken to be normal to the surface of the plate. The reflection and transmission coefficients are computed for zeroth, first, and second incident wave modes. The validity and accuracy of the results are checked by satisfaction of the energy conservation principle and the reciprocity relations.

[1]  Forman S. Acton,et al.  Numerical methods that work , 1970 .

[2]  C. M. Fortunko.  Ultrasonic Detection and Sizing of Two-Dimensional Weld Defects in the Long-Wavelength Limit , 1980 .

[3]  R. Barsoum.  Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements , 1977 .

[4]  A. H. Shah,et al.  Diffraction of plane sh waves in a half‐space , 1982 .

[5]  A. Mal,et al.  Diffraction of Antiplane Shear Waves by an Edge Crack , 1980 .

[6]  Subhendu K. Datta,et al.  Diffraction of SH-Waves by an Edge Crack , 1979 .

[7]  Anthony R. Ingraffea,et al.  Transition elements to be used with quarter-point crack-tip elements , 1978 .

[8]  A. H. Shah,et al.  Scattering of SH waves by embedded cavities , 1982 .

[9]  C. Fortunko,et al.  Nondestructive evaluation of planar defects in plates using low‐frequency shear horizontal waves , 1982 .

[10]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[11]  Subhendu K. Datta,et al.  DIFFRACTION OF MEDIUM AND LONG WAVELENGTH HORIZONTALLY POLARIZED SHEAR WAVES BY EDGE CRACKS , 1982 .

[12]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[13]  J. Achenbach,et al.  Scattering of longitudinal and transverse waves by a sub-surface crack , 1981 .

[14]  Jan Drewes Achenbach,et al.  Scattering of surface waves by a sub-surface crack , 1981 .

[15]  Leon M Keer,et al.  Scattering of elastic waves by a surface-breaking crack , 1980 .