Computational Methods in Engineering

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The spline finite strip method (S.F.S.M.) for buckling analysis of plates and plate assemblies subjected to longitudinal compression and bending, transverse compression as well as shear is described. The method allows for the boundary conditions. Local buckling coefficients of plates with different boundary conditions under compression, bending and shear are calculated. Convergence studies with increasing number of section knots are described. The method is also applied to study the elastic local buckling interaction of bending and shear for plates with different aspect ratios.

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Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange interpolation functions. The spectral method is, in fact, the solution of motion equation for an axially moving plate. Although this method has some limitations concerning boundary condition of plate and in-plane forces, it leads to an exact solution of free vibration and stability of plates travelling on parallel rollers. The method can be used as a benchmark of accuracy of other numerical methods.

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This paper is concerned with elastic local buckling of rectangular plates subjected to intermediate and end inplane loads. Since closed form solution for buckling analysis of plates with different end conditions and subjected to intermediate loads is complicated, numerical methods are more useful. Because of restrictions on the two finite strip methods, the longitudinal B3 spline expressions combined with conventional transverse shape functions are used as displacement functions. This method is computationally more efficient than the finite element method, more flexible in boundary treatment, and more accurate in dealing with point forces and axial loads than the conventional finite strip method. Local buckling coefficients are presented for plates under intermediate and end inplane loads which are useful for design of steel walls or plates that support intermediate floors/loads.

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Graphene is one of the nanostructured materials that has recently attracted the attention of many researchers. This is due to the increasing expansion of nanotechnology and the application of this nanostructure in technology and industry owing to its mechanical, electrical and thermal properties. Thermal buckling behavior of single-layered graphene sheets is studied in this paper. Given the failure of classical theories to consider the scale effects and the limitations of the nano-sized experimental investigations of nano-materials, the small-scale effect is taken into account in this study, by employing the modified couple stress theory which has only one scale parameter. On the other hand, the two-variable refined plate theory, which considers the shear deformations in addition to bending deformations, is used to define the displacement field and to formulate the problem. The developed finite strip method formulation is used to evaluate the critical buckling temperature of the nanoplates. The validity of the proposed method is confirmed by comparing the results of this study with the those in the literature. The effects of different boundary conditions, temperature changing patterns, aspect ratio, and the ratio of length parameter to thickness on the critical buckling temperature are considered and the results are presented in the form of Tables and Figures

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Dynamic stability and liquefaction of tailings dams are great concerns for geotechnical engineers. In this study, the seismic response of the Esphordi mine tailing dam located in Bafgh seismic region of Yazd province is investigated. A finite-difference code (FLAC2D) is used to model the seismic liquefaction applying two constitutive criteria, namely Mohr-Coulomb and Finn-Byrne. For this purpose, a fish function is implemented into the code to simulate the non-linear elasto-plastic Finn-Byrne constitutive model. Horizontal and vertical displacements (subsidence) in the dam body, additional pore pressure, failure zones, and liquefaction due to seismic load were determined using the two selected criteria under the seismic load of the 6.4 magnitude earthquake occurred in 2005. Considering the type of behavioral model, Mohr-Coulomb and Finn-Byrne, the maximum horizontal displacement of 5 and 35 cm in the dam body and downstream, and subsidence of 4 and 23 cm at the dam crest and upstream are observed, respectively. Also, the calculated ratio of excess pore pressure (R_u), for both criteria, was less than the liquefaction limit (0.9), the maximum value of which was 0.7 for the Finn-Byrne criterion and 0.2 for the Mohr-Coulomb criterion. In general, the results show that considering the cumulative effect of the seismic load cycles in the Finn- Byrne model, this criterion provides a better understanding of the liquefaction phenomenon.