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Abstract The element free Galerkin (EFG) method, which is based on the moving least square (MLS) approximation, requires only nodal data and no element connectivity. These features make the method more flexible than the conventional FEM. Nevertheless, direct imposition of the essential boundary conditions in the EFG method is always difficult because the shape functions obtained from the MLS approximation do not have the Kronocker-delta property. A new method named "the complementary integral method" is proposed here to overcome this difficulty. The presented method is more consistent with the variational basis of the EFG method. Several numerical examples are used to illustrate the implementation and performance of the method. The numerical examples including the Poisson's equation and 2D static and dynamic elasticity problems show that the method converges fast with reasonably accurate result for both the unknown variables and its derivatives.

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In this research, the effects of different parameters on simulation of Young’s modulus of a Graphene sheet are studied. In simulation of Young’s modulus of Graphene sheet, different parameters such as the thickness of a single layer of Graphene, type of loading and boundary conditions, effects of interactions non-neighbor atoms, type of element for carbon-carbon bond, mechanical properties of carbon-carbon bond and the size of the Graphene sheet influence the results. It was found that the thickness of a single layer Graphene and the type of element are effective parameters. Moreover, the type of loading and boundary conditions did not influence the Young’s modulus of the Graphene sheet. Therefore, the Graphene sheet can be considered as an isotropic material. Considering the effects of interactions of non-neighbor atoms increases the run-time and improves the accuracy of calculations. Mechanical properties of carbon-carbon bond are important parameters and must be chosen carefully. Also, it has been observed that when the length and width of the Graphene sheet are smaller than one nanometer, the size of Graphene sheet has a great influence on the Young’s modulus.

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In this paper, the dynamic characteristics of two highway bridges have been extracted via performing several operational modal tests. The tests have been performed during the normal traffic passage and ambient condition. The first bridge studied here, the "Ziar-1" Bridge built in 2003s in the road between the cities of Isfahan and Ziar, is a two span reinforced concrete with cast in place slab-on-rectangular girder superstructure system with the total length of 33 m. The deck is simply supported over a wall type middle pier and two side abutments with closed type. The superstructure is supported by the piers and abutments through elastomeric bearings. The second bridge, the "Ziar-2" Bridge built in 2012s as the new line of that road, is a two span reinforced concrete with in-site slab-on-precast girder superstructure system with similar length of the first bridge. The deck of this bridge is continuous without middle or side expansion joints and is supported over a pier bent consisting of a bent cap and three circular columns. The bridges, which pass over the "Zayandeh-Rood" river, are structurally separate and a 50cm distance has been provided between them. Both the bridges have similar geometry but different boundary conditions. The results of the modal tests have been also compared with the results of supporting finite element models of the bridges and the effects of boundary conditions on the dynamic characteristics of the bridges have been investigated. At the time of the first phase experiments, the river was dry due to drought in recent years and the level of underground water was sufficiently deep. It is predicted that presence of water current around bridge piers, in which the superstructure have monolithic connection with piers and side abutments, may change the dynamic properties of superstructure. In order to investigate to what extent the presence of water current in the river may affect the dynamic characteristics of the bridges; additional modal test has been performed on the second bridge, in which its deck is continuously connected to the supporting elements. On the other hand, the seasonal effects of the water current in the river on the dynamic characteristics of one of the bridges, as representative of reinforced concrete slab-on-girder integral bridges, have been also studied. In order to realize to what extent the pier-superstructure connection in this bridge is monolithic, the actual displacement pattern of the measurement points on the superstructure at the pier location has been closely measured and compared with corresponding results of the finite element model of the bridge. The results show that, as far as the boundary conditions of the deck is concerned, it has significant effect on the dynamic behavior and corresponding natural frequencies of the superstructure, especially in the first bending and the first torsional modes. Also, it was found that the presence of water current around the piers of the bridge leads to slightly increase in the natural frequency and the associated damping values of the bridge.

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Due to their accuracy and reliability, atomistic-based methods such as molecular dynamics (MD) simulations have played an essential role in the field of predictive modeling of single layered graphene sheets (SLGSs(. However, due to the computational costs, applications of these methods are limited to small systems. Additionally, according to the discrete nature of SLGSs, conventional continuum-based methods cannot be utilized to study the mechanical characteristics of them. To overcome these issues, here, a new Atomic-scale Finite Element Method (AFEM) based on the Tersoff-Brenner potential has been developed. Efficiency of the proposed method is evaluated through a numerical example analyzed by both of the proposed method and MD simulation. The results show that the computational cost is much reduced (~100 times), while the accuracy of MD simulation is kept. Furthermore, the effects of initial C-C bond length and number of atoms on the speed of the proposed method is investigated. To mimic the MD simulation completely, periodic boundary conditions have been implemented in the extended AFEM. It is demonstrated that there is a noticeable deviation from MD results without considering this type of boundary conditions.

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Thin sheets stiffened with lattice structures are used widely in many engineering industries. Investigation of stability behavior for the grid structures and determination of the buckling load under compressive loads is an issue that has attracted the attention of many researchers; and extensive studies have been done in this field. In this paper, a new grid called Diacube is introduced and its buckling load is examined. For this aim, first, the buckling behavior of 5 common types of stiffened flat lattice panels containing hexagonal, triangular, square, diamond and kagome grid are investigated under compressive axial load; and the results are compared with Diacube grid. The effect of network density used in each structure on the buckling of these structures will be studied under different boundary conditions. In addition to common grids,. Regarding to the mass difference of samples, specific critical load parameter (the buckling load to mass ratio) is used for comparison between the structures. Using the finite element modeling and numerical analysis, the grid that has the highest buckling load in each boundary condition is determined It is found that if unloaded edges in lattice panels are simply supported, this new Diacube grid will have the highest buckling load among all structures. Finally, validity of the numerical result obtained for two samples of the structures including hexagonal and Diacube grid is evaluated experimentally; and the numerical results are confirmed.

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In this article, the ghost fluid-lattice Boltzmann method, used to simulate the curved boundaries is combined with an extrapolation based refilling method to cope with the moving curved boundaries, where in each iteration some of the solid nodes step into the fluid domain. The refilling method is used to approximate the unknown density and internal energy distribution functions of such solid nodes. To examine the accuracy of the presented method, several case studies are considered. From those case studies, natural convection problem between to concentric and eccentric cylinders as well as heat transfer from a cylinder in a cross flow are considered to validate the ghost-fluid lattice Boltzmann method used to simulate the hydrodynamic and thermal conditions at the curved boundaries. To test the accuracy of the employed refilling method, sedimentation of a single isothermal cold particle in a vertical channel investigated. The results show that the presented ghost fluid-lattice Boltzmann method with refilling is capable of simulating the moving thermal curved boundaries with excellent accuracy.