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In a structural analysis, dynamic response of a crack is of significant importance as well as the impacts of elastic waves on stress intensity factors (SIF). In this paper, dynamic analyses of multiple cracks on a half-plane subjected to anti-plane shear stresses are presented. Stress intensity factors are calculated and the interaction of elastic waves with the boundary of plane and the cracks' tips is investigated at different locations. The distribution discontinuous displacement techniques are used, enabling us to solve the crack problems in dynamic fracture mechanics. Integral transformations (Laplace and Fourier) are applied to elastodynamics equations and by using a set of appropriate boundary conditions solved discontinuous displacement and the crack problem is solved through discontinuous displacement method. As a result, the stress equations with hypersingularity terms are obtained. Using Chebyshev series expansion and collocation points in Laplace domain, the crack solution is achieved. Finally, different algorithms of numerical Laplace inversion are presented and the stress intensity factors (SIF) are obtained. The presented results are compared with published data and a good agreement is observed. Moreover, it is also demonstrated that the present theoretical study is capable of modelling multiple cracks with different arrangements.

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Thin revolved shells are intersetted in many engineering applications, in particular dubbly curved shells. In this research, linear and nonlinear buckling analyses (with consideration of geometrical non-linearity) are performed on two different types of elliptical shells known as Oblate and Prolate which are under external hydrostatic pressure. These shells are made of homogeneous steel. ABAQUS (a well-known finite element software) is used for performing the simulations. Several important parameters affecting the buckling behaviour of these revolved elliptical shells are investigated in detail such as the ratio between minor and major radii, the percentage of nonlinear buckling value and the shell thickness magnitude on buckling load capacity. The results show the significant effect of shell geometrical dimensions, the magnitude of nonlinear buckling value as an initial imperfection and the shell thickness variations on the buckling load capacity. Finally, it is also observed that the Oblate shell results in a remarkable reduction in the load capacity compared to the other shell type used in this study. To verify the validity of the results, a comparison is made between the present FEM results and the available theoretical studies and a good agreement is observed.