A consistent model for first-order moderate rotation plate theory

The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of t the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant stiffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one- and two-dimensional structures, in order to assess the performance nr the von Kàrmàn, finite elasticity, classical and the proposed moderate rotation theories.