Using Laurent’s series in the theoretical solution to estimate the stress resultants of FG-CNTRC plates weakened by a central cutout at different temperatures

Abstract

Conventional ordinary materials have many weaknesses when exposed to extreme loadings. Hence, scientists develop novel engineered materials to address these weaknesses. Functionally Graded Carbon Nanotube Reinforced Composites (FG-CNTRCs) are a modern group of materials that have recently flourished thanks to their excellent and unique mechanical properties. One common loading condition is subjecting FG-CNTRC plates containing cutouts to in-plane loadings. The presence of an opening disturbs the stress field, especially in the proximity of the cutout, and creates stress concentration. This study estimates the stress and moment resultants on the edge of elliptical cutouts in asymmetric FG-CNTRC plates under various loading conditions using a new analysis based on Lekhnitskii’s complex variables method, mapping function, and Laurent series. Unlike previous studies on perforated asymmetric plates, which were based on numerical methods or the Schwartz formulations, this study presents a new solution using Laurent’s series to represent the holomorphic function. In calculating the stress and moment components around the opening, the effect of determining variables is studied. This approach can be generalized to solve different anisotropic body problems (FG_CNTRC, FGM, Laminate composites). Thus, stress and moment components in perforated anisotropic plates can be determined simply and systematically using this method.