Mixed Formulations of Bending Problems for Homogeneous Elastic Plates and Beams

Abstract

Mixed formulations of bending problems for homogeneous plates (beams) are proposed, whose essence is that the deformation of a plate (beam) near its fixed boundary is described by the three‐dimensional elasticity equations, and the remaining part by the conventional equations of plate (beam) bending. At the interface between these regions, the solutions of these equations are joined. The mixed formulation allows one to describe the three‐dimensional stress state in the neighborhood of the fixed boundaries of plates (beams) and take into account the complex nature of the fixing conditions. Finite‐element implementation is more efficient for the mixed formulations of plate (beam) bending problems than for the well‐known three‐dimensional formulations.