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In this paper, elastic-plastic deformation of a rotating hollow FGM cylinder is analytically studied based on small strain theory and for plane-strain state. Variation of elasticity modulus, density and yield stress are assumed to obey power-law functions of radial coordinate. Material was assumed to obey Tresca yield criterion and its associated flow rule. To evaluate and validate the presented analysis, numerical results were compared with previously published results for homogeneous and also FGM cylinder with constant density and yield stress, as two special cases. Then the effect of density and yield stress variation, which was not considered in the previous researches, was investigated on the elastic-plastic deformation of the FGM rotating cylinder. The results show that when the variation of density and yield stress is ignored, considerable differences may arise not only in the magnitude of computed radial displacement and stress and strain components, but also in predicting the pattern of yield initiation and also plastic zone development.

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Flexible roll forming is a modern process for producing profiles with changing cross section. One of the important defects in this process is the web warping of product that causes failure to obtain dimensional and geometrical tolerances. In this paper, mechanism of web warping occurrence was investigated by finite element simulation in ABAQUS/CAE software. Results of simulation indicated that inadequate longitudinal strain in the edge of profile’s flange in transition zone is the reason of profile’s web warping. Furthermore, the effect of geometric parameters of product such as flange length, bend angle, radius of transition zone and thickness on the web warping were determined. Analysis of variance showed flange length and bend angle are recognized as the most effective factors on warping of profiles with specific thickness. An equation for prediction of warping was proposed in terms of geometrical parameters of product. In order to verify the finite element model, the longitudinal strain of deformed strip edge was obtained from simulations and compared with the experimental results of other researchers. A good agreement between them confirmed the accuracy of the finite element model.

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In this paper, elastic-plastic symmetrical buckling of a thin solid circular plate of variable thickness, under uniform edge pressure, is investigated, based on both Incremental Theory (IT) and Deformation Theory (DT). Two kinds of simply supported and clamped boundary conditions have been considered. A power-law function was assumed for thickness variation. To minimize the integral uniqueness criterion, based on Rayleigh-Ritz method, transversal displacement was approximated by a test function which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the test function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for circular plate of constant thickness and a good agreement was observed. This clearly shows the validity of presented analysis. Then the effect of thickness variation and boundary conditions type on the critical buckling load was investigated, for commercial aluminum and steel 1403 materials. The results show that when the thickness of circular plate center is 10% greater than its edge thickness the buckling load may increase up to 40% comparing with the circular plate for which the center thickness is 10% less than its edge thickness.

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In this paper, elastic-plastic buckling of a thick rectangular plate has been investigated based on both Incremental (IT) and Deformation (DT) plasticity theories. Uniform biaxial edge traction was assumed as the plate loading while simply supported as the boundary conditions. Integral uniqueness criterion has been minimized to determine the critical buckling traction. Based on Rayleigh-Ritz method, a linear combination of polynomial base functions, which satisfy the geometrical boundary conditions, has been used as the trial functions for rotations and transverse deflection. To validate the analysis, the results for the Mindlin plate theory have been compared with the previously published results and a very close agreement has been observed. Then the effects of thickness ratio, aspect ratio and also different biaxial traction ratios on the buckling traction have been investigated. The results show that for the problem considered here, very close critical buckling traction is predicted by the both Mindlin and sinusoidal plate theories. This implies that Mindlin plate theory is sufficiently accurate to predict critical buckling traction in this problem. Moreover when the loading is gradually changed from biaxial into uniaxial compression or when the thickness-ratio is increased, the difference between the two theories is also increased. Also for compression-tension loading case, the critical buckling traction predicted by deformation theory is much less than the incremental theory.

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This paper deals with studying and developing a proper constitutive model for liver tissue. For this purpose, deformation of liver in uniaxial compression, for two different strain rates, is analytically and numerically studied, based on both hyperelastic and hyperviscoelastic constitutive models. Both of the models are based on a polynomial-form energy function. The stress-strain curves, for uniaxial compression, obtained from these models, have been fitted to the existing experimental data to determine the model coefficients. Moreover the models are examined in uniaxial tension and pure shear loadings. ABAQUS commercial software, in which both of the models are available, has been used for numerical simulations. Then, to evaluate the computational analyses, analytical and numerical results have been compared with each other and also with the existing experimental data. The results show that the presented analytical solution and FE simulation are very close together and also both are accurate enough, compared with the experimental data and an acceptable stability is observed. Furthermore the effect of friction coefficient between the sample and the compressing plate in uniaxial compression test has been investigated. FE simulation results show that the stress will increase with increasing friction coefficient. This implies that friction coefficient must be carefully selected to accurately describe the tissue’s response. Compared with previously published researches on other tissues, the constitutive models adopted here to predict liver behavior is mathematically more complex due to non-zero material constants. Analytical solution of these constitutive models is, in fact, the main challenge and innovation of this paper.

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In this research, the experimental and numerical analysis of the Al. alloy 5083-H321 fracture behavior under uniaxial and bi-axial tension has been investigated. The bi-axial tension cruciform specimens are made by electrochemical methods, according to Lionel model, for considering bi-axial fracture behavior of the material. The specimens are gridded by electrochemical etching method. A dependent bi-axial tension mechanism is fabricated with relatively high precision machining methods. The experimental bi-axial tests have been performed by the mechanism on the INSTRON-1343 uniaxial machine, at ambient temperature and strain rate of 0.0003 1. For comparing the experimental and numerical results, how to fracture the material at the beginning and development of it, the location of fracture on the test section of cruciform specimen, and the force diagrams on the cruciform specimen arms are of interest can be mentioned. The finite element method has been used with regard to the damage conditions of ABAQUS software for simulating the fracture behavior. The experimental results show that fracture at the specimen center does not happen. The fracture of cruciform specimen begins in the test section of specimen and in range with the corners of the specimen. Furthermore, the strains are minimal near cruciform specimen arms and in the test section area. Also, the gradient of stress is towards the test section and along the corners. There was an excellent correlation between theoretical and experimental results for location of damage initiation in the test section, how to fracture in the beginning and after that, and arms forces.