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A non-linear finite element model could be a useful tool in the development of a method of predicting soil pressure-sinkage behaviour, and can be used to investigate and analyze soil compaction. This study was undertaken to emphasize that the finite element method (FEM) is a proper technique to model soil pressure-sinkage behaviour. For this purpose, the finite element method was used to model soil pressure-sinkage behaviour and a two-dimensional finite element program was developed to perform the required numerical calculations. This program was written in FORTRAN. The soil material was considered as an elastoplastic material and the Mohr-Coulomb elastoplastic material model was adopted with the flow rule of associated plasticity. In order to deal with material non-linearity, incremental method was adopted to gradually load the soil and a total Lagran-gian formulation was used to allow for the geometric non-linear behaviour in this study. The FEM model was verified against previously developed models for one circular footing problem and one strip footing problem and the finite element program was used to pre-dict the pressure-sinkage behaviour of the footing surfaces. Statistical analysis of the veri-fication confirmed the validity of the finite element model and demonstrated the potential use of the FEM in predicting soil pressure-sinkage behaviour. However, experimental verification of the model is necessary before the method can be recommended for exten-sive use.

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In this paper elastoplastic buckling of thin rectangular plates are analyzed with deformation theory (DT) and incremental theory (IT) and the results are investigated under different loads and boundary conditions. Load is applied in plane and in uniform tension and compression form. The used material is AL7075T6 and the plate geometry is . The Generalize Differential Quadrature method is employed as numerical method to analyze the problem. The influences of loading ratio, plate thickness and various boundary conditions on buckling factor were investigated in the analysis using both incremental and deformation theories. In thin plates the results obtained from both plasticity theories are close to each other, however, with increasing the thickness of plates a considerable difference between the buckling loads obtained from two theories of plasticity is observed. The results are compared with those of others published reports. Moreover, for some different situations new results are presented. Some new consequences are achieved regarding the range of validation of two theories.

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Nowadays, availability, durability, reliability, weight and strength, as the most important factors in optimum engineering design, are responsible for the widespread application of plates in the industry. Buckling in the elastic or elastoplastic regim is one of the phenomena that can be occurred in the axial compressive loading. Using Galerkin method on the basis of trigonometric shape functions, the elastoplastic dynamic buckling of a thin rectangular plate with different boundary conditions subjected to compression exponetiail pulse functions is investigated in this paper. Based on two theories of plasticity: deformation theory of plasticity (DT) with Hencky constitutive relations and incremental theory of plasticity (IT) with Prandtl-Reuss constitutive relations the equilibrium, stability and dynamic elastoplastic buckling equations are derived. Ramberg-Osgood stress-strain model is used to describe the elastoplastic material property of plate. The effects of symmetrical and asymmetrical boundary conditions, geometrical parameters of plate, force pulse amplitude, and type of plasticity theory on the velocity and deflection histories of plate are investigated. According to the dynamic response of plate the results obtained from DT are lower than those predicted through IT. The resistance against deformation for plate with clamped boundary condition is more than plate with simply supported boundary condition. Consequently, the adjacent points to clamped boundary condition have a lower velocity field than adjacent points to simply supported boundary condition.

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When a dynamic load passes a control volume of material as a shock wave, passing this wave through the control volume could cause different phases such as elastic and plastic. From the microscopic view, during phase change, material flow would be taken in control volume which includes mass, heat, energy, and momentum transport. Phase change in material causes a material discontinuity in the control volume. During the phase change process, mass, heat, energy, momentum transport and etc will occur and the equations governing these phenomena are called transport equations. In this article, for the first time, the governing equations of elastoplastic behavior of beam under dynamic load are extracted by using mass, energy and momentum transport equations. Using transport equations with non-physical variables in integral form will cause in employing discontinuity conditions in governing equations and eliminates the discontinuity condition. These equations are also used in continuously modeling of beam elastoplastic behavior under dynamic loading and a continuous model is presented. Finite element method is used to solve the transport equation with non-physical variable. Finally, the time history of stress, strain and velocity wave propagation along beam are presented in elastic and elastoplastic phases

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Engineering analyses of beams are based on the proper guesstimate of deformation fields. Up until now, the analyses of beams are widely proposed and experienced in elastic region of materials behavior. This paper considers the elastoplastic engineering analysis of beams. In this regard, following the definition of a proper deformation pattern known as classical Euler- Bernoulli model and using the variational calculus principals the governing equations are extracted. In this analysis the behavior of material obeys the Romberg-Osgood model and yielding is based on the von Mises criterion. Different numerical solutions are represented for the solution of these complicated equations in the literature. In this paper the exact solution is provided for a thin beam under the action of uniformly distributed load by using the two analytical methods of homotopy and Adomian for the clamped- clamped boundary conditions. In verification phase, the deformation of beam is compared with the results of Abaqus software. Different graphical representations are provided for the results of the analytical solutions and simulations. Using these data, the level of consistency between the simulated solutions in one side and the Adomian and homotopy techniques on the other side, are assessed. At the end, the validity of applying the classical engineering theory of beams in the elastoplastic analyses is discussed.

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One of the most remarkable achievements of finite element method is introducing isoparametric elements. Although these elements are able to use in numerous applications, the lower order isoparametric elements make some difficulties such as shear locking, volumetric locking and hourglass. These issues may improve with an increase in the number of the elements or by increasing the order of the elements, which increases the computational time. Therefore for solving these problems, using the lower order elements with incompatible modes, which enhances accuracy and reduces the computational time, could be considered as an alternative solution option. The aim of this paper is to study the effect of using the incompatible elements on the elastoplastic behavior of isotropic plates and beams under uniform axial and bending loadings. For this purpose, 3D standard elements with eight and twenty nodes and incompatible eight-node elements are used in modeling the 3-D case studies. Besides, the 2D standard elements with four and eight nodes and incompatible ones with four nodes are employed to analyze the 2-D plane stress problems. The obtained results show that using 3D incompatible elements achieves the faster rate of convergence in the solution procedure for obtaining the displacement components and also makes significant run-time reduction. However, there are not any remarkable differences between the obtained plastic Von-Mises stresses using 2D standard and incompatible elements.

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In this paper, the elastoplastic buckling of rectangular plates over the Pasternak foundation has been analyzed with the fixed and simply supported boundary conditions. Associated with the uniform loading conditions on the plate by the in- plane compression and tension, the influence of the elastic foundation is investigated in terms of two stiffness parameters; including the Winkler spring and the Pasternak shear coefficients. In order to extract governing equations, two theories are used from the plasticity: deformation theory (DT) with the Hencky constitutive relations and the incremental theory (IT) based on the Prandtl-Reuss constitutive relations. By implementing the generalized differential quadrature method to discrete the differential equations, influences of loading ratio, length to width ratio, plate thickness, and the elastic foundation characters are studied. By comparing the obtained results with the data reported in references, the accuracy of the model is verified. Consideration of results shows that applying the elastic foundation causes to increase critical buckling load. In addition, enhancing the elastic foundation parameters leads to amplifying the difference between buckling loads obtained from two theories, especially in the larger thicknesses. Moreover, according to increasing the plate thickness in the tensile state of the loading, application of the elastic foundation causes to reach plate stress to a value more than the ultimate stress of the specimen.

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In this work, an elastoplastic constitutive model is planned to analyze the effects of adding silica nanoparticles on the overall elastic-plastic stress-strain curves of the polymer matrix nanocomposites. The elastic modulus of the nanocomposites are evaluated by the combination of the Mori-Tanaka and Eshelby micromechanical models considering interphase region formed due to the interaction between silica nanoparticles and the polymer matrix. Then, the elastic-plastic stress-strain curves of nanocomposites are extracted by employing a micromechanics-based ensemble-volume averaged homogenization procedure. To prove the validity of the developed method, the predictions are compared to the experimental data existing in the literature. The effects of volume fraction and diameter of silica nanoparticles, thickness and adhesion exponent of the interphase on the polymeric nanocomposite elastic-plastic stress-strain curves are extensively examined. Stiffer elastoplastic behavior is found in the presence of interphase region. The results clearly indicate that the strengthening of the silica nanoparticle-reinforced polymer nanocomposites is improved with (1) increasing nanoparticle volume fraction, (2), decreasing the nanoparticle diameter, (3) increasing the interphase thickness and (4) decreasing the interphase adhesion exponent. Finally, the elastic-plastic stress-strain curves of silica nanoparticle/polymer nanocomposites under biaxial loading is achieved.