Impact force and moment problems on random mass density fields with fractal and Hurst effects

This paper reports the application of cellular automata to study the dynamic responses of Lamb-type problems for a tangential point load and a concentrated moment applied on the free surface of a half-plane. The medium is homogeneous, isotropic and linear elastic while having a random mass density field with fractal and Hurst characteristics. Both Cauchy and Dagum random field models are used to capture these effects. First, the cellular automata approach is tested on progressively finer meshes to verify the code against the continuum elastodynamic solution in a homogeneous continuum. Then, the sensitivity of wave propagation on random fields is assessed for a wide range of fractal and Hurst parameters. Overall, the mean response amplitude is lowered by the mass density field’s randomness, while the Hurst parameter (especially, for β < 0.2) is found to have a stronger influence than the fractal dimension on the response. The resulting Rayleigh wave is modified more than the pressure wave for the same random field parameters. Additionally, comparisons with previously studied Lamb-type problems under normal in-plane and anti-plane loadings are given. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

2D Elastodynamic Solution for the Impact Response of Laminated Composites

This paper presents a general, exact, two-dimensional (2D) elastodynamic analysis of the response of laminated composite panels subjected to transverse impact loading under conditions of planar deformation. The natural frequencies and mode shapes of free vibration are first extracted. Inspired by a transformation technique for solving a special class of partial differential equations, the forced vibration problem of an impacted laminated panel is solved using an eigenfunction expansion technique. Several examples are studied by varying the laminate lay-up and length-to-thickness ratio. The distributions of transverse stresses in the through-the-thickness direction are further compared with two one-dimensional theories, classical lamination theory (CLT) and first-order shear deformation theory (FSDT), showing the inadequacy of these theories and the necessity to establish a benchmark solution for 2D elastodynamics. The 2D elastodynamic theory that is formulated is also applicable for studying other multilayered structures subjected to arbitrary loading profiles.

Axisymmetric Body-Force Fields in Elastodynamics of Transversely Isotropic Media

In this paper, a complete elastodynamic solution for axisymmetric problems under axial body-forces in terms of two retarded potential functions in transversely isotropic media is extended to the case of general torsionless axisymmetry. Allowing for both axial and radial distributed internal loads through the use of an extra potential, the new solution retains its completeness via the theory of repeated wave equations. By virtue of its analytical design, the formulation can be reduced to the corresponding elastostatic case by simply suppressing the time-dependence of its potentials as well as the case of isotropy. In the limiting case of the latter material condition, the proposed representation for elastostatic problem degenerates to a recent extension of Love’s potential function.