Stress intensity factor computation using the method of fundamental solutions: mixed‐mode problems

Abstract

The method of fundamental solutions is applied to the computation of stress intensity factors in linear elastic fracture mechanics. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy-Navier equations of elasticity and the leading terms for the displacement near the crack tip. Two algorithms are developed, one using a single domain and one using domain decomposition. Numerical results are given.

Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear elastostatics

“…Strictly speaking, however, Table 5 without c j in cases (2), the accuracy of d 1 and the solutions are slightly higher, but the instability is slightly worse. An important consequence is that we may choose only the principal FS in computation, as done in [3,30,31]. Note that the true errors in Tables 3-6 can be evaluated, based on the highly accurate solutions in Table 2 by the CTM for Model C. This displays a significance of the singularity models in evaluations and developments of new and efficient numerical solutions (also see [38]).…”

“…Note that we do not need the smooth particular solution in (5.5) and (5.6), because the FS can approximate very well the smooth part of the solutions. In computation, we choose N and L r4 with the following singular particular solutions: A similar combined method with L¼ 1 was used in Karageorghis et al [3,30]. ffiffiffi h In computation, we will use the method of particular solutions (MPS) in Section 5, the method of fundamental solutions (MFS) and the combined Trefftz method for Models C and D. When L¼0 in (7.1) and (7.2), Eq.…”

Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

“…In [23], inverse problems in planar elasticity were considered whereas axisymmetric elastostatics problems are studied in [13,28]. Recently, the MFS has been applied to the computation of stress intensity factors in linear elastic fracture mechanics [5,14]. Also, Matrix Decomposition Algorithms (MDAs) for the MFS have been developed for two-and three-dimensional boundary value problems in elastostatics and thermoelastostatics in domains with radial symmetry [15,16].…”

A coupled FEM–Bernstein approach for computing the J k integrals

“…Examples of coupling of element-free Galerkin method (EFGM) with FEM can be found in the works by Sukumar et al [26] and Rao and Rahman [27]. Other latest trends in the analysis of cracks by MM-type methods are the application of the method of fundamental solutions (MFS) [28] or the use of level-sets for the description of the discontinuity surface evolution [29].…”