3D FEM Analysis of the Buckling Delamination of a Rectangular Viscoelastic Composite Plate with an Embedded Rectangular Crack Under Two-Axial Compression

In Akbarov, Yahnioglu and Karatas (2010) a buckling delamination problem for a rectangular viscoelastic composite plate with a band and edge cracks was investigated under uniaxial compression of the plate. In the present study this investigation is developed for the case where the mentioned rectangular plate contains an embedded rectangular crack and in addition it is assumed that the plate is subjected to two-axial compression.
It is supposed that all end surfaces of the considered plate are simply supported and that these ends are subjected to uniformly distributed normal compressive forces with intensity p₁ and p₃ which act along the O_x1 and O_x3 axes, respectively. Moreover, we assume that the plate contains a rectangular embedded crack, the edge-surfaces of which have initial infinitesimal imperfections before the loading.
The evolution of these initial imperfections with time under two-axial compression of the plate is studied within the framework of the three-dimensional geometrically nonlinear field equations of the theory of viscoelasticity for anisotropic bodies.
For determination of the values of the critical force or of the critical time, as well as those of the buckling delamination mode of the considered plate, the initial imperfection criterion is used.
For the solution to the corresponding boundary-value problems, boundary form perturbation techniques; the Laplace transform; the Schapery method for obtaining the numerical inverse Laplace transform of the sought values; and the 3D FEM are used.
The numerical results of the critical force and critical time, as well as of the buckling delamination modes are presented and discussed.     

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials. The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics. The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution. Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators. The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials. Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed. As a result of the numerical investigations, in particular, it is established that in the case where the rheological parameters of the components of the compound cylinder are the same, the viscosity of the layers' materials causes the axisymmetric wave propagation velocity to decrease.