The paper aims to present a novel mathematical formulation for the modelling of damage. In particular, the decay of the mechanical properties of the elastic media is modeled by means of two-dimensional smooth functions, which are the Gaussian and the ellipse shaped ones. Various damaged configurations are obtained as concentrated variations of the elastic properties of the materials by setting properly the parameters that define the distributions at issue. This approach is employed to investigate the dynamic behavior of damaged plates and shells made of composite materials. In particular, a massive set of parametric studies is presented for this purpose. The results are obtained numerically by means of the Generalized Differential Quadrature (GDQ) method and are presented in terms of natural frequencies. Several Higher-order Shear Deformation Theories (HSDTs), which can include also the Murakami’s function to capture the so-called zig-zag effect, are used and compared.
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