PSI - Issue 52

626 2

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

J.C. Wen et al. / Procedia Structural Integrity 52 (2024) 625–646

Nomenclature FGMs

functionally graded materials

FBM XFEM SOPT

finite block method

extended finite element method second order perturbation technique

SIFs FEM BEM

stress intensity factors finite element method boundary element method

MDDM XWGM GFBM

hybrid meshless/displacement discontinuity method

extended wavelet Galerkin method Galerkin finite block method Singular Value Decomposition crack opening displacement

SVD COD

2-D 3-D

two dimensional three dimensional

E 

Young’s modulus Poisson’s ratio

normal stress shear stress





, x y n n , x y b b

outer normal vectors of x -direction and y -direction

body force mass density



physical domain mapping domain integral contour Laplace parameter shape functions time



' 



t

s

i M

Jacobian

J

( ) k T z ( ) k U z

the k -th order Chebyshev polynomial of the first kind the k -th order Chebyshev polynomial of the second kind

coefficient of Chebyshev polynomials Chebyshev polynomial terms

mn 

, M N

h

height of the plane width of the plane

w 1 c

the velocity of longitudinal waves

,  

angle



crack opening displacement stress intensity factor for mode I stress intensity factor for mode II

I K

II K

radial distance crack increment

A r

a 