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In this study, an analytical solution is presented to calculate interlaminar stresses in long symmetric cross-ply composite laminates subjected to uniform axial strain and thermal loading. At first, the most general form of layerwise-based displacement field is extracted by a successive integration of elastic strain–displacement relations and imposing the physical restrictions based on deformation patterns of these laminates. The equilibrium equations are then derived by using the principle of minimum total potential energy and solved analytically in order to obtain three-dimensional stress field in the laminated plate. Finally, various numerical examples are investigated in order to validate the efficiency and accuracy of the layerwise theory in predicting the interlaminar stresses. For the assessment of the accuracy of the proposed method, the interlaminar stresses are also calculated within the framework of a 3D finite element analysis using the Abaqus software. The corresponding numerical results are in good agreement with those obtained through the layerwise theory. All results indicate that the presented approaches have a good prediction capability of interlaminar stresses in interior regions of the laminate and theirs high stress concentration near its free edges that can cause delamination failure.

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In the present study, in order to evaluate the elastic displacement field and subsequently the fracture parameters within the isotropic homogeneous elastic solids with the edge or interior cracks, the extended finite element method with level set technique was used to avoid the disadvantages associated with the standard finite element method. An overdeterministic least squares method was utilized to determine the crack stress intensity factors as well as the coefficients of the higher order terms in the Williams' asymptotic series solution for structures containing crack in various modes of failure by fitting the series solution of displacement fields around the crack tip to a large number of nodal displacements obtained from the extended finite element method. For validating the results, several cracked specimens subjected to pure mode I, pure mode II, and mixed modes I/II loading were performed. Comparisons with results available from the literature obtained by the other formulations reveal the efficiency and the simplicity of the proposed method and demonstrate the capability of it to capture accurately the crack stress intensity factors and the coefficients of higher order terms.

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This study aims to investigate the transverse vibration of single- and double-layered graphene sheets embedded in an elastic medium based on the third-order shear deformation theory considering the axial force effect within the framework of Eringen’s nonlocal elasticity theory, where the governing equations of motion are obtained using Hamilton’s principle. The superiority of the studied non-local continuum model to its local counterpart is to consider the effect of size on the mechanical behavior of the structure. The results from a natural frequency analysis are obtained for different conditions such as the effect of size and aspect ratio, axial force, nonlocal coefficient, and change in the stiffness properties of the surrounding elastic medium by using the Navier-type solution for simply supported boundary conditions. Given that in a double-layered graphene sheet, the system has an in-phase vibrational mode and anti-phase vibrational mode with 180-degrees phase difference, the effect of van der Waals force on both vibrational modes is attempted to be investigated and it is shown that the van der Waals force has no effect on in-phase vibrational mode and by increasing it, the anti-phase frequency increases. It is also demonstrated that the nonlocal parameter is not a constant parameter but its value depends on the size and atomic structure, like chiral and zigzag configurations, and even on the type of boundary conditions.