Comparison of approximate solutions to the quasi-static plate loading problem, obtained by the structural functions method and the finite element method

L. A. Kabanova   ; A. V. Romanov

Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 175-196

Résumé

This paper is aimed on comparison of two types of quasistatic linear elasticity problem approximate solutions. The problem of a multilayered composite rectangular plate bending is considered; the layers of the plate are supposed to be orthotropic, and orthotropy axes are supposed to be parallel to the sides of the plate; the edges of the plate are simply supported. The structural functions method is the main method considered in this paper: this method is in computing the displacements in the abovementioned inhomogeneous plate as a weighted sum of spatial derivatives of the displacements in a homogeneous plate of the same geometry under the same to the inhomogeneous one loadings – that homogeneous plate is called a concomitant one. The coefficients of that weighted sum are named structural functions. In this paper, we pass through all the necessary steps of the structural functions method and derive the formulae for the structural functions of the first and the second order. Also, we present an approach to the choice of the concomitant body elastic characteristics, and compare it with one of the previous approaches. Approximate solutions of the above-stated problem via the structural functions method of first and second order are numerically compared with the finite element method solutions (based on the 8-knot and 20-knot elements), and with well-known N. J. Pagano solution to the same problem in a three-dimensional statement.

Détail

Keywords: structural functions method, multilayered plate.