Accurate non-linear bending analytical solutions setting new benchmarks for rectangular thin plates with four simply supported edges

Abstract

In the field of nonlinear structural analysis, the ability to provide accurate and reliable analytical solutions is of paramount importance. This paper presents more accurate nonlinear analytical solutions for rectangular plates with four simply supported edges, establishing a new benchmark that replaces and complements Lévy’s manual analytical solutions. These accurate solutions can serve as a reference for validating various nonlinear numerical and approximate analytical solutions, thereby providing a robust basis for engineering design. Notably, the central deflection error in this study is less than 0.005%, while the central stress error remains below 0.4%. The accuracy of the present solutions provided significantly exceeds that found in the existing literature.