A semi‐analytical curved element for linear elasticity based on the scaled boundary finite element method

Abstract

This work introduces a semi-analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis.

Guided waves for damage identification in pipeline structures: A review

“…The wave FE method treats the homogenous waveguide as a periodic system, and it can be an alternative to the SAFE method when combined with FE method. Furthermore, the scaled boundary FE method, taking advantages of both boundary element and FE methods, has been utilised to study wave propagation in straight or bent pipes …”

“…Furthermore, the scaled boundary FE method, taking advantages of both boundary element and FE methods, has been utilised to study wave propagation in straight or bent pipes. [54,55] 3.3 | Experimental approaches for damage detection in pipes…”

The family of multilayered finite elements for the analysis of plates and shells of variable thickness

“…The division into layers, which was adopted during the formation of element characteristics, is shown in Fig.1. The stiffness matrix of an element is calculated by the formula (see, for example, [16]);…”

“…where Bis the geometric matrix, connecting the components of the deformations and displacements, andC is the physical matrix, connecting the stress components with the components of the strains. When using the Kirchhoff hypothesis and adopted approximating functions of displacements, the matrixB is reduced to the form [16]:…”

“…However, variable thickness elements are available not in all finite element programs. Therefore, calculators and designers using such programs are forced to simplify design schemes and present slabs of varying thickness as stepped slabs [11][12][13][14][15][16][17][18]. This leads to a distortion of the stress-strain state of the structures being calculated.…”