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.

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.

In experimental design theory, plans with two or three levels of influence are the most often employed. The total factor experiment includes N=2^k experiments with two levels of change in the influencing variables, and N=3^k experiments with three levels of change in the influencing factors. The 2^k plan, in particular, is often utilized throughout the early stages of research and even while conducting explorations with a high number of influencing variables. The number of influencing variables, for example, would be k=15, and the number of experiments, N=2¹⁵=32768. Not just on actual devices, but also in computer simulations, this is virtually impossible. As a result, the number of experiments must be reduced to a manageable amount. The method of influencing factors space reduction can be implemented in the following ways. (i) Preliminary influencing factor analysis is used to screen for influencing factors with no or little value, i.e., variables that have little or no impact on the objective function. (ii) Using partial plans (or, as the theory of experimental planning calls them, partial responses) when the number of variables remaining after screening for null factors is still very large. This article will discuss one method for doing a preliminary screening of the initial influencing factors in order to identify those that have either no influence at all or a small effect on the objective function that is the subject of the investigation.