Flexural properties calculation helps in designing structural elements like beam, cantilever and shafts. Moreover, the flexural properties are of vital importance in engineering and industrial applications such as joints replacements. The purpose of this investigation is to study for the first time, how the friction stir processing (FSP) parameters affects the flexural properties of UHMW-PE composites reinforced with nano particles. The tool rotational speed (ψ), tool feed rate (ƒ), volume percentage (ν) of nano powder and tool shoulder temperature (τ) are selected as the process parameters. The ultimate flexural strength (UFS) and flexural yield strength (FYS) are calculated from the flexural test stress-strain diagrams. The analysis of variance is conducted which reveals that the selected parameters are significant for both UFS and FYS. Macroscopic and microscopic study shows that the FSP parameters affects the mixing of the strengthening particles and hence the flexural properties of the composite. The combinations of low level of ν with medium level values of other parameters results in the highest flexural properties. Moreover, the combinations of higher levels of τ and ψ results in material degradation. At the end, optimum conditions for the highest flexural properties are sorted out and the effect of increasing the number of passes has been investigated which significantly improve the flexural properties of the composite material.

Additive manufacturing (AM) techniques make fabricating complex designs, prototypes, and end-user products possible. Conductive polymer composites find applications in flexible electronics, sensor fabrication, and electrical circuits. In this study, thermoplastic polyurethane (TPU)-based conductive polymer composite samples were fabricated via fused filament fabrication (FFF). The effects of three important process parameters, including infill density (ID), layer thickness (LT), and fan speed (FS), on various mechanical properties (tensile and compressive properties) were investigated. It was observed that all the considered process parameters affect the mechanical properties, and they are significant parameters, as per the analysis of variance (ANOVA). From scanning electron microscopy (SEM) and optical microscopy, various combinations of parameters such as low ID, high LT, and high FS resulted in the formation of defects such as voids, cracks, and warping, which resulted in low mechanical properties. Finally, process parameter optimization was performed, resulting in a conductive polymer composite with the best possible combination of mechanical properties at high ID, low LT, and medium FS.

This paper introduces a novel model involving an integro-differential equation of fractional order characterized by multiple nonlinear terms with Caputo fractional derivatives. We derive conditions ensuring the existence, uniqueness, and stability of the mild solution. Furthermore, we explore a coupled system that includes the proposed equations and extend our analysis to an equation featuring three nonlinearities. The study utilizes Banach's, Krasnoselskii's, and Schaefer's fixed point theorems. Additionally, we investigate various forms of Hyers-Ulam stability for the equation and the coupled system. To demonstrate the practical implications of our findings, illustrative examples are provided.