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This paper uses the finite element method to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, in which the flexoelectric effect is taken into consideration. The finite element formulations are established by employing a new type of shear deformation theory, which does not need any shear correction factors, but still accurately describes the stress field of the plate. The numerical results show clearly that the flexoelectric effect has a strong influence on the mechanical responses of the nanoplates. In particular, the normal stress distribution in the thickness direction is no longer linear when the flexoelectric coefficient is large enough, and this phenomenon differs completely from that of conventional plates. In addition, the distribution of the electric field and the polarization also depend on boundary conditions, which were not investigated in the published works.

Improving the surface quality after burnishing operation has been the subject of various published investigations. Unfortunately, the trade-off analysis between the energy consumption and surface characteristics of the internal burnishing has been not addressed due to the expensive cost and huge efforts required. The objective of the present work is to optimize burnishing factors, including the spindle speed, burnishing feed, depth of penetration, and the number of rollers for minimizing the energy consumed in the burnishing time, as well as surface roughness and maximizing Rockwell hardness. An adaptive neuro-based-fuzzy inference system (ANFIS) was used to develop burnishing objectives in terms of machining parameters. The optimization outcomes were selected using an evolution algorithm, specifically the non-dominated sorting particle swarm optimization (NSPSO). The results of the proposed ANFIS models are significant and can be employed to predict response values in industrial applications. The optimization technique comprising the ANFIS and NOPSO is a powerful approach to model burnishing performances and select optimal parameters as compared to the trial and error method as well as operator experience. Finally, the optimal solution can help to achieve the improvements in the energy consumed by 16.3 %, surface roughness by 24.3 %, and Rockwell hardness by 4.0 %, as compared to the common values.

The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work's results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.

In the current investigation, two primary indicators, including the average roughness (AR) and Brinell hardness (BH) of the roller burnishing operation are enhanced using the optimal inputs (the spindle speed-S, feed rate-f, and depth of penetration-D). The performance measures are developed using the Kriging approach and optimal outcomes are generated by the Crow Search Algorithm (CSA). The optimal outcomes generated by the CSA of the S, f, and D were 832 rpm, 112 mm/min, and 0.12 mm, while the AR was reduced by 37.0% and the BH was increased by 29.9%, respectively. The optimal findings could be utilized in the practice for enhancing the burnished quality and to develop a professional system related to the roller burnishing operation. The Kriging-based AR and BH correlations could be used to present nonlinear experimental data. The optimizing technique could be utilized to deal with optimizing problems for different machining operations.