A MATLAB-based educational tool for teaching static and modal analysis of mindlin plates

Abstract

This study presents a MATLAB-based educational tool designed to support the teaching of static and modal analysis of plate structures in undergraduate and early postgraduate courses on finite element analysis and structural dynamics. The program implements a nine-node quadratic quadrilateral Mindlin–Reissner plate element, allowing students to follow the main stages of a finite element solution procedure, including mesh generation, element assembly, boundary condition imposition and post-processing of displacements and mode shapes. The pedagogical motivation is to reduce the black-box use of commercial packages by providing an accessible code structure that links theoretical derivation and numerical implementation. To verify the computational formulation, the program was applied to benchmark problems from the literature and the results were compared with analytical solutions and with SAP2000 and ABAQUS simulations. The numerical results showed close agreement for static displacements, natural frequencies and modal shapes, indicating that the implementation is sufficiently accurate for educational use. The proposed tool can therefore be employed as a didactic resource for teaching plate finite elements, numerical modeling and introductory structural vibration analysis.