Calculation of Deflection of Rectangular Simply Supported Plates Using the Finite Difference Method. Interval Calculus

Abstract:

This paper presents the analysis of deflection of rectangular simply supported thin plates using the finite difference method. The governing fourth-order differential equation of plate bending is discretized and solved numerically within the Mathematica environment. The results are compared with those obtained using the analytical solution and finite element method (SAP2000), showing good agreement and confirming the accuracy of the applied approach. Additionally, interval calculus is introduced to account for uncertainties in input parameters such as load intensity, plate thickness, and material properties. This enables the evaluation of deflection within defined bounds, providing a more comprehensive insight into structural behavior. The study demonstrates that the combined use of the finite difference method and interval calculus represents an efficient and reliable tool for plate analysis.