BENDING ANALYSIS OF HOMOGENEOUS, ISOTROPIC LINEAR ELASTIC SQUARE PLATES UNDER VARIOUS BOUNDARY CONDITIONS

This research investigates the bending behaviour of homogeneous, isotropic linear-elastic square plates under various boundary conditions, with a focus on evaluating deflection and stress. Understanding plate bending is critical for structural integrity in numerous engineering applications. This study uses Standard Plate Theory to derive analytical solutions for flexural parameters. Two scenarios were considered: simply supported plates with a uniformly distributed load and a centrally concentrated load. MATLAB FEA software was utilised for numerical analysis, discretising plates with quadrilateral (four-node Q4) isoparametric elements. Plate thicknesses varied (20mm-100mm) while length and breadth remained constant (a=b=1). Results show numerical solutions from MATLAB FEA align well with analytical findings from Classical Plate Theory. Increasing mesh density from (5x5) to (20x20) improved numerical accuracy, with the (20x20) mesh yielding the highest accuracy. Maximum deflection was consistently observed at the plate's center. Both analytical methods and MATLAB FEA effectively evaluated the bending behaviour. Higher mesh densities in FEA simulations lead to more precise predictions. Results for very thin and moderately thin plates were equivalent, supporting the applicability of Classical plate theory. However, a limitation of this study is the focus on idealized linear-elastic material properties and small deflection theory, which may not fully capture the behavior of plates undergoing large deformations or those made of non-homogeneous materials. Keywords: Classical Plate Theory, Static Bend.