The Problem of the Reliability of Bending Models for Composite Plates of Medium Thickness

Abstract

Most refined bending models of medium-thick plates, which consider transverse shear and partial compression deformations, differ little. However, despite a significant increase in the order of the governing differential equations, the results obtained from their equations give mainly a small increase in accuracy compared to the existing theories. On the other hand, such an increase in the order of the constructed systems of differential equations requires a significant increase in the effort required to solve them, complicates their physical interpretation, and narrows the range of people who can use them, primarily engineers and designers. Therefore, developing a plate-bending model that incorporates all the above factors and is on par with previously applied theories regarding the complexity of the calculation equations remains relevant. For example, most of the applied theories that do not consider transverse compression cannot be used to solve problems of contact interaction with rigid and elastic dies and bases because it is impossible to satisfy the conditions at the contact boundary of the outer surface of the plate, as well as the boundary conditions at the edges of the plate. Therefore, to provide guaranteed accuracy of the results, some researchers of these problems have introduced such a concept as “energy consistency” between the functions of representation of the displacement vector components, their number, the order of equations, and the number of boundary conditions. The authors, based on the developed version of the model of orthotropic plates of medium thickness, investigate the problem of taking into account the so-called “energy consistency” effect of the bending model, depending on the order of the design equations and the number of boundary conditions, as well as its usefulness and disadvantages in practical calculations. The equations of equilibrium in displacements and expressions for stresses in terms of force and moment forces are recorded. For rectangular and circular plates of medium thickness, test problems are solved, and the numerical data are compared with those obtained using spatial problems of elasticity theory, as well as the refined Timoshenko and Reissner theories. An analysis of the obtained results is provided.

Keywords

• models of plate bending
• orthotropic material
• hypothesis method
• plates of medium thickness
• boundary conditions
• normal stresses
• self-equilibrium stress state