In this paper, a MINDLIN rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress THEORY. In order to consider the small scale effects, the modified couple stress THEORY, with one length scale parameter, is used. In modified couple stress THEORY, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. After obtaining the strain and kinetic energy, external work and substituting them in the Hamilton’ s principle, the main and auxiliary equations of the nanoplate are obtained. Then, by manipulating the boundary conditions the governing equations are solved using Navier approach for bending and vibration of the nanoplate. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load and different mode frequencies are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The effect of material length scale, length, width and thickness of the nanoplate on the bending and vibration ratios are investigated and the results are presented and discussed in details.

One of the factors that can be the link between our intentions and actions and their external consequences is human agency, which indicates the conscious design and intentional execution of actions by the individual in order to influence future events.Objective and Method: This research with a developmental approach of psychometric method and method 1, examines the psychometric indices of the Human Factor Characteristics Scale using the classical THEORY of test score measurement and the graduated question-answer THEORY. The purpose of this study, which included high school students in Tehran, was selected by cluster sampling of 500 people as a sample size and statistical analysis was performed on 481 data. To collect the data, the ion Human Agent Characteristics Scale (2011) was used and the research questions were evaluated using IRTPRO and SPSS software.Results:The assumption of local independence based on Pearson x2 index was established by applying Simjima's calibrated question-answer THEORY and the assumption of being one-dimensional based on the analysis of multidimensional question-answer THEORY. Diagnosis parameters with question-answer approach and classical approach Test score Both item 25 approach had the lowest and item 2 had the highest diagnosis parameter. The answer thresholds for all the questions were so far apart that no option was covered by the other option, and the options were independently selected by individuals at intervals of theta. The total scale was calculated with Cronbach's alpha of 0.945, intentionality of 0.894, foresight of 0.780, self-reactivity of 0.871 and rethinking of 0.762. Also, the role of each item in internal consistency was investigated by the loop method, which all questions had a favorable role in internal consistency of this scale. The value of the validity coefficient obtained from the question-answer THEORY was obtained by marginal method for intentionality 0.92, forethought 0.85, self-reaction 0.91, rethinking 0.83..

Circular Plates are one of the types of structural members that have been analyzed for many different loadings, boundary conditions and types of analyses-viz: elastic, elastoplastic, geometrically linear & nonlinear. The assumptions used in most of the above mentioned types of analysis are those of Kirchhoff However, in this analysis the effect of shear in the deformation of the plate through thickness is taken into account. Consequently the effect of the shearing force is not eliminated. The number of equilibrium equations has increased from two to three and as a result two more shear strain expressions are introduced.An extra feature introduced in the present analysis is the variable thickness with positive or negative slope towards the centre of the plate, the loading is uniform pressure and finally the boundary conditions considered are in-plane fixed and free with simply supported or clamped edge restraints. The Dynamic Relaxation iterative technique in co-operation with the finite difference discretization is used to obtain numerical results. The results are compared with a similar results obtained via different methods for thin plates. The agreement is satisfactory.

The effect of central opening on the buckling and nonlinear post-buckling response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on buckling and post-buckling behavior are analyzed. In order to derive the basic formulations of plate the MINDLIN plate THEORY is applied. Furthermore, nonlocal elasticity THEORY is applied to consider the size-dependent effect. Analytical approach and Newton-Raphson iterative technique are utilized to calculate the impact of cut out on the buckling and nonlinear post-buckling response of micro composite plate. The variation of buckling and post-buckling of micro composite cut out plate based on some significant parameters such as volume fraction of CNTs, small scale parameter, aspect ratio, square cut out and elastic medium were discussed in details. According to the results, it is concluded that the aspect ratio and length of square cut out have negative effect on buckling and post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the buckling and post-buckling behavior of plate. Meanwhile, considering elastic medium increases the buckling and post-buckling load of system.

Abstract: Circular Plates are one of the types of structural members that have been analyzed for many different loadings, boundary conditions and types of analyses-viz: elastic, elastoplastic, geometrically linear & nonlinear. The assumptions used in most of the above mentioned types of analysis are those of Kirchhoff. However, in this analysis the effect of shear in the deformation of the plate through thickness is taken into account. Consequently the effect of the shearing force is not eliminated. The number of equilibrium equations has increased from two to three and as a result two more shear strain expressions are introduced.An extra feature introduced in the present analysis is the variable thickness with positive or negative slope towards the centre of the plate, the loading is uniform pressure and finally the boundary conditions considered are in-plane fixed and free with simply supported or clamped edge restraints. The Dynamic Relaxation iterative technique in co-operation with the finite difference discretization is used to obtain numerical results. The results are compared with a similar results obtained via different methods for thin plates. The agreement is satisfactory.

Electrical energy can be harvested from the vibrations of piezoelectric plates. The behavior of the piezoelectric plate is simulated using electromechanical coupling. Given the large strain experienced by the flexible plate, the linear THEORY is inadequate; therefore, the effect of Von Karman strain must be considered. This paper investigates and validates the vibrational behavior of a piezoelectric nonlinear plate. Specifically, it employs coupled equations for a multilayered plate, incorporates Von Karman’s nonlinear strain, and applies MINDLIN’s first-order shear deformation THEORY. The electrical response is obtained through finite element analysis of the piezoelectric nonlinear plate in Matlab. Different boundary conditions are considered to verify the results, including clamped edges, simply supported edges, and a combination of two simply supported and two clamped edges. The electrical response of the open-circuit case under harmonic excitation is presented. Furthermore, the phenomenon of voltage cancellation during plate vibrations is studied, and a method for enhancing energy harvesting performance using separated electrodes is proposed. The results indicate that, across all cases, the voltage response with a continuous electrode is lower than with segmented electrodes at the first natural frequency.