Application of the Method of Initial Functions to Study Dynamics and Stress Distribution in Structural Members

Abstract

This study investigates plate analyses employing the method of initial functions (MIFs) across various plate geometries and loading conditions. The conclusions derived from thick rectangular plates highlight substantial thickness-induced effects on deflection and stress distributions. For thicker plates, the classical assumption of constant deflection fails, with maximum deflection often occurring at surfaces other than the middle plane. The classical and Reissner theories’ constant deflection assumption leads to significant discrepancies in thick plate deflection estimates, emphasizing the need for MIFs more accurate approach. Similarly, in the case of thick circular plates, deviations from classical theory are evident in radial and shear stress distributions, particularly pronounced closer to the plate edge and support. These deviations dissipate further away from these regions. Moreover, the study delves into free vibration analyses for rectangular and circular plates, revealing that classical theory tends to overestimate frequencies, especially as plate dimensions increase. Mindlin’s theory and MIF approaches showcase improved accuracy with increasing order, converging toward exact solutions. Additionally, Mindlin’s theory effectively captures the behavior of higher vertical modes, showcasing sign changes in characteristic quantities of the plate. The findings underscore the limitations of classical theories in accurately predicting plate behaviors, especially in thicker plates and higher modes of vibration. Conversely, the MIF method, alongside Mindlin’s theory, proves effective in providing nuanced insights into plate behaviors under various conditions, thus offering valuable implications for structural design and analysis.