A Pure bending model to predict the large deformations of thin rectangular isotropic plates subject to uniform lateral load

Abstract

Pure bending and large displacements are crucial in plate analysis since they are evident in the majority of structures. However, plates with large displacement theory are difficult to simulate. The goal of this work is to present a simple generalized framework for the simulation of pure bending in isotropic rectangular thin plates with large displacement theory with the aid of Ritz energy methodology. The relations between strains and displacements are imposed to the total Ritz potential energy functional for a plate forced to uniformly distributed load. This was found to derive a generalized mathematical relation for large displacement lateral force for isotropic rectangular thin plates simulation. With the aid of polynomial displacement shape profile regarding a plate simply supported at all sides (SSSS), both the bending and membrane stiffness of the plate were calculated and imposed to the general expression to attain the specific expression regarding SSSS isotropic thin rectangular plate. With altering displacement to thickness ratio chosen, numerical values were attained as proportions of the load parameter and lateral load at large dimension of the plate. To verify the new model, comparison was made with existing work. The results reveal a very close agreement with the compared results having maximum percentage deviation of 0.64% for small deflection load parameter, and the minimum and maximum percentage deviations of 0.52% and 1.48% respectively for large displacement lateral load coefficient. These values are sufficiently small and are within the acceptable limits in engineering tolerance. Therefore, the conclusion is that the new expression of the present work is sufficient for the simulation of isotropic rectangular thin plates.