A further study of the theory of elastic circular plates with non-Kirchhoff-Love assumptions (Q1892004)

Authors try to derive a refined theory for the state of stress and deformation of a linear-elastic and clamped circular plate under axisymmetric loading. Instead of using Kirchhoff-Love's assumptions, they postulate a linear transversal strain and a cubic transversal shear strain (with respect to the transversal coordinate). Starting from the basic equations of three-dimensional linear elasticity and introducing 8 resultant forces and moments respectively, they end up with 6 coupled ordinary differential equations whose solutions are given in closed form for an uniformly distributed load. The numerically evaluated deflection is shown to be larger than the corresponding one of the classical theory. Referee, however, is convinced that only the technique of asymptotic expansions with respect to the thickness-radius-ratio is able to give a reliable answer.