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In this work, the buckling behavior for edge cracked plates under compression loading is studied considering the influence of the crack parameters (i.e. size, location and orientation), plate aspect ratio and plate boundary conditions. The problem was solved numerically using finite element method utilizing ANSYS software version11 .The obtained results show that the crack parameters as well as plate aspect ratio and plate boundary conditions are efficient factors on the buckling coefficient and corresponding nodal patterns of such plates. The useful numerical results for buckling coefficients and corresponding nodal patterns are displayed in figures. According to the author's knowledge about the published literature on the buckling field, there is no specific report on the nodal patterns results of such edge cracked plates.

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This research describes crack analysis in the functionally graded materials (FGMs) by adopting the extended element free Galerkin method (XEFGM) under mixed mode and asymmetric loading. These loads are somewhat similar to fatigue loads because, numerically, they are load values from zero and then directly to the critical load. The meshfree method can be easily simulated the fracture problems against the traditional numerical method because it is not dependent on mesh. Triangles technique in the process of numerical integration at regions of discontinuity, functions of enrichment, and as well as the appropriate support field to contain numerical points and nodes to from the shape functions are used in this study. In addition, incompatible interaction integration technique has used to determine the stress intensity factors (SIFs). Two study cases with different crack positions were studied and compared with the experimental works of the relevant reference literature, where accurate and identical results were obtained.

We prove the stability of maximum preserving functional equation by substituting the addition with the maximum operation in Cauchy functional equation in multi-Banach lattice by fixed point method.