Mathematical model for lateral deflection of a circular plate under the cosine load – spherical rigid body application

Purpose The purpose of this paper is to present a mathematical model to calculate the lateral deflection of a circular isotropic plate with constant thickness under the cosine load within the plate theory limitations. Design/methodology/approach The mathematical model is derived on the basis of the governing nonhomogeneous differential equation for the plate theory, where the function of lateral deflection is shown in the form of a cosine integral and power series form, respectively. The accuracy of the mathematical model is verified by numerical analyses performed by the finite element method. Findings A good agreement between the presented model and numerical analyses is obtained in terms of the elastic theory and the assumption of small deformation, as well as when using the model for a spherical rigid body loading within the studied conditions, where all discrepancies are below 4.2%. The presented mathematical model may be applied to calculate the lateral deflection of a plate loaded by a spherical rigid body where the cosine load is assumed on the basis of the bearing hypothesis. Research limitations/implications The research limitations fall into the constant thickness, homogenous and isotropic material, small deformation theory and axisymmetric behavior of the studied parts. Originality/value Except the pure cosine load, applied on the entire plate surface, a partially placed load is investigated as well, which has a practical relevance when loading the plate by a spherical rigid body. The presented mathematical model provides a convenient calculation when numerical analysis is not available, while the paper shows a load diversity under different magnitudes as well.