Mathematical modeling of flexible printed circuit configuration: a study in deformation and optimization.

This manuscript offers an exhaustive analysis of Flexible Printed Circuits (FPCs), concentrating on enhancing their design to surmount two primary challenges. Firstly, it seeks to obviate contact with proximate components. Secondly, it aspires to adhere to pre-established curvature constraints. Predicated on the curvature properties of FPCs, we have developed a model adept at accurately forecasting FPC deformation under diverse conditions. Our inquiry entails a thorough examination of various FPC configurations, including bell, 'U', and 'S' shapes. Central to our methodology is the strategic optimization of FPC spatial arrangements, aiming to avert mechanical interference and control curvature, thus mitigating mechanical strain. This dual-faceted strategy is pivotal in enhancing the durability and operational reliability of FPCs, particularly in contexts demanding elevated flexibility and precision. Our research offers essential insights into the refinement of FPC design, skillfully addressing the complexities associated with curvature and physical interaction. Collectively, this study advocates a comprehensive framework for the design and implementation of FPCs, significantly advancing the field of contemporary electronics by ensuring these components meet the evolving demands of the industry.