X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

“…( 15) and, for static hp-AMR schemes, the interpolation operator given in Eq. (18). Then, the computational cost of the proposed scheme is in general linear in the number of mesh elements and linear in the number of time steps.…”

“…Various modifications of and/or alternatives to the FEM have been proposed in the literature to reduce the meshing effort. A few examples are the extended FEM [16,17] and the extended Ritz method [18], whereby the space of basis functions is enriched to automatically account for the presence of embedded boundaries or interfaces, the Virtual Element Method (VEM) [19], which allows the use of general (also non-convex) polygonal elements, or the Boundary Element Method (BEM) [20,21], which is based on an integral formulation and allows solving the equations of elastodynamics by discretizing the domain's boundaries only.…”

Modelling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

“…A clearer view of the wave structure generated by the concentrated force is displayed in Fig. (18), where the distribution of the velocity component v 2 is displayed at the time instants t = 0.3 s, 0.6 s and 1.0 s. The left column of the figure shows the results computed with the finest uniform grid, whereas the right column shows the results computed with the hp-AMR strategy; the same results are obtained with the two numerical setups. Moreover, in either case, it is possible to distinguish the larger semicircle of the P-waves, which at t = 1.0 s have almost left the domain of analysis, the smaller semicircle of the S-waves, which are travelling slower than the P-waves but have a similar spatial distribution, and the Rayleigh waves, which are travelling attached to the free surface at a speed that is slightly slower than that of the S-waves.…”

“…Various modifications of and/or alternatives to the FEM have been proposed in the literature to reduce the meshing effort. A few examples are the extended FEM [16,17] and the extended Ritz method [18], whereby the space of basis functions is enriched to automatically account for the presence of embedded boundaries or interfaces, the Virtual Element Method (VEM) [19], which allows the use of general (also non-convex) polygonal elements, or the Boundary Element Method (BEM) [20,21], which is based on an integral formulation and allows solving the equations of elastodynamics by discretizing the domain's boundaries only.…”

Pre-buckling and Buckling Analysis of Variable-Stiffness, Curvilinearly Stiffened Panels

“…In this context, semi-analytical procedures have been successfully applied in the past years for analyzing composite structures (see, e.g. [25][26][27][28][29][30]).…”