Wave Propagation Analysis using High-Order Finite Element Methods: Spurious Oscillations excited by Internal Element Eigenfrequencies

From a computational point of view, the numerical analysis of ultrasonic guided waves is still a very demanding task. Because of the high-frequency regime both a fine spatial and temporal discretization is required. To minimize the numerical costs, efficient and robust algorithms ought to be developed. One promising idea is therefore to focus on high-order finite element methods (ho-FEM).The current article investigates the behavior of the p-version of the finite element method (p-FEM) and the spectral element method (SEM) with respect to the existence of spurious oscillations in the solution. Convergence studies have shown that it is possible to observe non-physical oscillations under certain conditions. These parasitic vibrations, however, significantly deteriorate the accuracy of the simulation. For this reason, we analyse this phenomenon in detail and propose solutions to avoid its occurrence.Without loss of generality, we employ a two-dimensional plane strain model to derive a guideline as to how to avoid these spurious oscillations, placing a special emphasis on the relation between the element size, the polynomial degree of the high-order shape functions and the excitation frequency.Our results show that accurate simulations are possible if the model is generated according to the proposed methodology. Moreover, the implementation of the guideline into an existing finite element software is straightforward; these properties turn the method into a useful tool for practical wave propagation analyses

Discrete modeling of fiber reinforced composites using the scaled boundary finite element method

A numerical method for the discrete modeling of fiber reinforced composites based on the scaled boundary finite element method (SBFEM) is proposed. A unique feature of this method is that the meshes of the matrix, aggregates, in general volumetric entities can be generated independently of the fibers which are treated as truss elements. To this end, a novel embedding method is developed which connects the mesh of the matrix consisting of scaled boundary polytopes to the fibers. This approach ensures that conforming matrix and fiber meshes are achieved. The computed stiffness matrices for both components are then simply superimposed using the nodal connectivity data. Since volume elements can be intersected by fibers at arbitrary locations, it is of paramount importance to be able to generate polytopal elements which is one unique feature of the chosen SBFEM implementation. An advantage of this procedure is that no interface constraints or special elements are required for the coupling. Furthermore, it is possible to account for random fiber distributions in the numerical analysis. In this contribution, a perfect bonding between the matrix and fibers is assumed. By means of several numerical examples, the versatility and robustness of the proposed method are demonstrated