The elastic buckling behavior of quadrilateral single-layered graphene sheets (SLGS) under bi-axial compression is studied employing nonlocal continuum mechanics. Small-scale effects are taken into consideration. The principle of virtual work is employed to derive the governing equations. The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis. The buckling load of skew, rhombic, trapezoidal, and rectangular nanoplates considering various geometrical parameters are obtained. It is shown that nonlocal effects are very important in arbitrary quadrilateral graphene sheets and their inclusion results in smaller buckling loads. Also the effects of geometrical parameters such as aspect ratio, angle, and mode number on the buckling load decrease when scale coefficient increases, for all arbitrary quadrilateral SLGS.
The plastic responses of clamped mild steel, copper, and aluminum circular plates subjected to blast loads are investigated. In this way, extensive experimental results concerning the variations of central deflection and natural strain distributions are presented. The effects of plate thickness, stand-off distance, and material properties on the mid-point deflection, on the deformation profile and on the natural strain distributions are considered. Moreover, the influence of impulse on the mid-point deflection and strain distribution are demonstrated. The applied impulse imparted to the plate was obtained from the recorded motion of the ballistic pendulum. Using the obtained experimental input-output data, closed form mathematical models based on nondimensional analysis and Singular Value Decomposition method have been found. The comparisons of the closed form mathematical models of this work with those in literature illustrate the robustness and the efficacy of this approach.
This paper presents an analytical method for determining deflection of fully clamped thin circular plates. The plates are made from a rigid perfectly plastic material and subjected to a transverse localized and uniform blast loading. The essence of the model is to describe the deformation profile with the aid of a zero-order Bessel function and to perform energy analysis. This provides a method for predicting the plastic deformation of circular plates under impulsive loading. It can be also regarded as an attempt to use the energy method for different impulsive loading conditions. Calculations of the cases indicate that the proposed analytical models are based on reasonable assumptions. The solutions obtained are in very good agreement with different sets of experimental results.A list of symbols can be found on page 320.
This paper studies the dynamic plastic response of thin quadrangular mild steel plates subjected to uniform and localized impulsive loading. For this, two new dimensionless numbers based on dimensionless governing equation of plates have been suggested. Four different effective parameters such as plate geometry, inertia of applied load, mechanical properties of material and strain rate sensitivity have been considered in suggested dimensionless numbers. The unknown coefficients of these numbers have been calculated by using singular value decomposition method. In order to illustrate the ability of empirical constitutive equations for predicting the maximum deflection, these equations are compared with different sets of experimental results that have been performed by various researchers. The comparison between the results of present empirical equations and the other theoretical and experimental ones shows that these models are more accurate than the other ones and are suitable to use for predicting the maximum deflection of all quadrangular mild steel plates subjected to uniform and localized loading.
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