Chemie und Prozesstechnik
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It can be difficult to efficiently model ultrasonic waves in 3D structures, especially when the computational model needs to account for complex geometries. This contribution presents a solution based on the Scaled Boundary Finite Element Method (SBFEM). It is a numerical tool suitable for elastodynamic problems. A space-tree discretisation, namely quad-trees, is used. This technique allows the decomposition of an image into quadrilaterals or quads, which are extruded to generate the 3D plate geometry. In particular, small quads resolve regions with discontinuities, allowing them to represent fine details in the structure. Moreover, this meshing technique allows for exploiting cell similarities, making the calculation procedure more efficient. The space-tree discretisations are generated from a high-resolution image containing all the information about damaged regions or boundary conditions. The resulting SBFEM polyhedral domains employ transition elements to ensure correct coupling between cells of different sizes. The analytical solution of a cylindrical scatterer serves as a reference to validate the proposed approach. Other examples also demonstrate the validity of the methodology and its flexibility.
This paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity. The enrichment consists of semi-analytical singular modes constructed using the Scaled Boundary Finite Element Method (SBFEM).
In contrast to analytical methods, the SBFEM provides modes for inhomogeneous and anisotropic materials without additional effort. The finite element basis can be of arbitrary order and remains unaltered by the enrichment. The approach requires enrichment in only one layer of elements around a node. Due to the compatibility of SBFEM with FEM, there is no Need for transitional elements, and there are no parasitic terms. The approach is tested for several benchmark problems. The stress intensity factors are computed based on techniques inspired by the SBFEM. The proposed procedure is compared to a Standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses.