Finite Element Analysis of Plate and Shell Vibrations

In practical engineering applications, plate and shell structures are typically analyzed using two primary theories based on Kirchhoff and Hencky assumptions. The classical thin plate/shell theory derived from Kirchhoff assumptions neglects shear deformation effects, making it suitable for thin structural analysis, while the thick plate/shell theory based on Hencky assumptions accounts for shear deformation, providing accurate results for moderately thick structures. Unlike Hencky's approach, Kirchhoff plate/shell governing equations involve higher-order partial differential equations, requiring C1-continuous interpolation functions for displacement fields in finite element implementation - a significant computational challenge. This program implements a finite element model using Hencky theory, where