Multiscale effects on structural behavior: nonlocal displacement in cylinders and piezoelectric stress in semiconductor layers

This research investigates the complex interplay between nonlocal effects, piezoelectric properties, and their influence on the mechanical behavior of cylindrical and layered structures. Focusing on two distinct scenarios, we aim to provide valuable insights for the design and analysis of robust and efficient structures. Firstly, we explore the displacement variations in clamped-clamped cylinders, considering the impact of nonlocal effects on the displacement field. The analysis utilizes polar coordinates and examines how these effects alter the structural response under various conditions. This emphasizes the importance of incorporating nonlocal effects in the design and analysis of cylindrical structures, especially at small scales. Secondly, we delve into the stress distribution in semiconductor layers, focusing on the influence of the piezoelectric effect. Analyzing a layered composite structure, we compare stress distribution with and without considering the piezoelectric parameters E3 and d31. Our results highlight the significant impact of piezoelectric properties on stress distribution, leading to higher stress magnitudes. This underscores the critical need to account for piezoelectric effects in the design of semiconductor devices to ensure structural integrity and reliability. By examining these two distinct scenarios, this study emphasizes the importance of considering nonlocal effects and piezoelectric properties in the design and analysis of small-scale structures. Our findings contribute to a deeper understanding of the complex interplay between these phenomena and their influence on structural behavior. By incorporating these effects, engineers can develop more robust, efficient, and reliable structures for various applications, including those involving cylindrical structures and semiconductor devices.