Intrinsic formulation of the Kirchhoff–Love theory of nonlinearly elastic plates

Abstract

The classical Kirchhoff–Love theory of a nonlinearly elastic plate provides a way to compute the deformation of such a plate subjected to given applied forces and boundary conditions by solving the Euler–Lagrange equation associated with a specific minimization problem, whose unknown is the displacement field of the middle surface of the plate. We show that this Euler–Lagrange equation is equivalent to a boundary value problem whose sole unknowns are the bending moments and stress resultants inside the middle surface of the plate, without any reference to the displacement field in its formulation. As a result, computing the stresses inside deformed plate can be done without using the derivatives of the corresponding displacement field, usually a source of numerical instabilities.