Deflection Surface Analysis of Thin Plate Structures Using Regression Technique

Abstract

Deflection analysis of any structure is of common interest while designing the structure. Analysis for deflection in thin plate structures is generally done with the help of Kirchhoff’s plate theory, also known as classical plate theory. Kirchhoff’s plate theory helps in developing a fourth-order partial deflection equation relating the deflection of a plate to the loading condition on the plate and the material or bending rigidity of the plate. The present study focuses on the analysis of a simply supported thin concrete plate that is subject to uniform loading over the entire plate area. The deflection surface of the plate is developed using Navier’s double trigonometric Fourier series. Regression analysis is done to understand how various plate parameters like material rigidity, loading on the plate, and area of the plate could affect the magnitude of deflection of the plate. Also, the effect of the mentioned plate parameters on the magnitude of bending moments, twisting moments, and shear forces acting on the plate is studied. Regression modelling is used to achieve the same. Statistical metrics like R-squared error, Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) are used to check the efficiency of regression analysis. In the present study, the regression modelling technique is also used to solve the fourth-order partial differential equation. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.