An extended meshless method that relying upon Galerkin formulation is applied on the crack analysis of orthotropic functionally graded Brazilian disc. Weak form is involved to solve the governing equation in the numerical method. In addition, enrichment terms and sub-triangle techniques are applied to improve the accuracy of relevant results. This paper depicts the influence of variation in the crack stretch and non-homogeneity parameters on the values of stress intensity factors using a developed MATLAB program. In the isotropic case, it is clear that when the length of crack increases, SIF increases. Graduation in has more effect in increasing the values of SIF in corresponding increased crack length. The verification has been checked by changing the range of the J-integral domain and variation of the support domain.

This paper presents an efficient meshless method in the formulation of the weak form of local Petrov-Galerkin method MLPG. The formulation is carried out by using an elliptic domain rather than conventional isotropic domain of influence. Therefore, the method involves an MLPG formulation in conjunction with an anisotropic weight function. In the elliptic weight function, each node has three characteristic indicated that were major radius, inner radius, and the direction of the local domain. Furthermore, the space that will be covered by the elliptical domain will be less than the area of the circle (isotropic) at the same main diameter. This means leaving many points of integration are not necessary. Therefore, the computational cost will be decreased. MLPG method with the elliptical domain is used in solving problems of linear elastic fracture mechanism LEFM. MATLAB and Fortran codes are used for obtaining the results of this research .The results were compared with those presented in the literature which shows a reduction in the computational cost up to 15%, and an error criteria enhancement up to 25%.

In this study, the extended element free Galerkin method (XEFG) is used for crack analysis an edge crack parallel to the material variation in a rectangular functionally graded material (FGM) plate under traction loading. For the first time, the effective parameters of XEFGM are employed such as the sub-triangulation term for numerical integration, suitable influence domain, and enrichment functions for discontinues locations in the fracture analysis of different crack positions of an edge cracked FGM plate. In addition, the incompatible formulation is adopted to extract the stress intensity factors (SIFs). Good data and results are observed about the relationship between the crack lengths and SIFs with good verification during changing XEFG parameters. There is good agreement and stability in the results of SIFs through the sizes of J-integral rJ equal to 0.4 -0.8. In addition, the acceptance results for the size of the support domain are bound between dmax=1.52 to 2.

In this study, glass-filled epoxy functionally graded material (FGM) was prepared by adopting the hand lay-up method. The vertical gravity casting was used to produce a continuous variation in elastic properties. A 30 % volume fraction of glass ingredients that have mean diameter 90 μm was spread in epoxy resin (ρ = 1050 kg/m3). The mechanical properties of FGM were evaluated according to ASTM D638. Experimental results showed that a gradually relationship between Young’s modulus and volume fraction of glass particles, where the value of Young’s modulus at high concentration of glass particles was greater than that at low concentration, while the value of Poisson’s ratio at high concentration of glass particles was lower than that at low concentration. The manufacture of this FG beam is particularly important and useful in order to benefit from it in the field of various fracture tests under dynamic or cyclic loads.

The extended-finite element method (X-FEM) is usedfor crack analysis of orthotropic and isotropic functionally graded composite material (FGCM) plate with a slanted crackunder thermal loadings. The enrichments functions ofdiscontinuity are implemented. Mixed-mode SIFs arecalculated in isotropic and orthotropic FGMs. Gaussiantechnique (Q4) has been applied in the numerical calculation ofinteraction of solution. Thermal effects, fundamentalequations, the interaction integral of non-homogeneous cases(M-integral), and proposal numerical integration rule is set tosimulate and to debate the accuracy of the present work resultsin comparing with the results of the references available inthe literature. In addition, the effect of the size of crack is studiedto discuss the values of energy release rate and stress intensityfactors with different crack angles. The present study isimplemented by using MATLAB program to present steady-state thermo XFEM fracture analysis of isotropic and anisotropic FG plate with inclined center crack.