Semi‐analytical computation of 3D stress singularities in linear elasticity

Abstract

SUMMARYThe boundary ÿnite element method (BFEM (Finite-Element Modelling of Unbounded Structures. Wiley: Chichester, England, 1996, The Scaled Boundary Finite Element Method. Wiley: Chichester, England, 2003) is employed for the investigation of the order of stress singularities for several classes of three-dimensional singular stress concentration problems, namely notch, crack and laminate freeedge situations. In all cases, the BFEM results agree excellently with reference results. The required computational e ort is considerably lower compared to e.g. standard ÿnite element computations and thus establishes the BFEM as a powerful tool for the semi-analytical modelling of linear elastic solids. KEY WORDS: stress singularities; boundary ÿnite element method; cracks; notches; free-edge e ects THE BOUNDARY FINITE ELEMENT METHOD (BFEM)The purely numerical analysis of singular elasticity problems-e.g. three-dimensional crack [1][2][3] or notch [4] situations as well as stress ÿelds in the vicinity of free edges [5] and corners [6-8] of layered structures-by means of standard ÿnite element method (FEM) analyses is computationally quite involved. Thus, there is a particular interest in introducing new and e cient analysis methods like e.g. the boundary ÿnite element method (BFEM) (BFEM, see e.g. References [9, 10], also known as scaled BFEM or consistent inÿnitesimal ÿnite element cell method), especially when detailed information on the asymptotic behaviour of the state variables-displacements, strains and stresses-in the vicinity of the singularity is desired. The BFEM combines the advantages of the FEM and the boundary element method (BEM) to a new and e cient procedure. The BFEM applies for the investigation of unbounded as well as bounded structures and as a prerequisite assumes a certain scalability of the given

A high‐order generalized FEM for through‐the‐thickness branched cracks

“…In the following, we assume = 0.5 as the order of the singularity (smoothness parameter) in the estimates for the convergence rates of the error norm reported in [33]. The smallest eigenvalue of the asymptotic expansion of the elasticity solution in the neighbourhood of the crack vertices is larger than 0.5 [31]. Far from the vertices, the smallest eigenvalue is equal to 0.5, the classical two-dimensional case.…”

“…The stress state in the neighbourhood of a crack front is not well known in three dimensions, and analytical expansions are available only for particular crack geometries [30,31]. Complex crack front geometries, curved crack surfaces or the intersection of the crack surface with the boundary, create complex stress distributions that are, in general, not amenable to closed form expansions.…”

Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons

“…Local enrichment with analytical asymptotic expansion is also not required. Furthermore, the SIFs can be computed directly from their definitions, as has been demonstrated in various studies on fracture in isotropic-, anisotropic-and bi-materials [33,35,37,[39][40][41][42][43][44][45].…”

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

“…These advantages are also preserved when applied to three-dimensional fracture problems. Recent published literature on the three-dimensional fracture analysis with the scaled boundary finite element method include homogeneous and interface cracks [60,61,62], composite laminates [63,64,65] and piezoelectric materials [66].…”