About Influence of Choosing the Force Method Principal System on the Accuracy of Calculations in Solving a Stress-Based Plane Elasticity Problem

Abstract

Introduction. It is known that the solution of a problem in elasticity theory is possible based on displacements, stresses, as well as mixed method. The most common is the displacement-based finite element method (FEM), however, it has its imperfections. The aim of this article is to study the features of numerical solution of a stress-based plane elasticity problem using the finite difference method (FDM) as a possible alternative to the FEM. The options for choosing the force method principal system are considered aiming to obtain the boundary conditions in calculating a rectangular beamwall by the grid method along with the influence thereof on the final result during stresses calculation.
Materials and methods. The calculation of a rectangular beam-wall is made in Balka-Stenka software developed in DSTU. Comparison between a solution made by the finite difference method and a solution made by the displacementbased finite element method is made in the LIRA-SAPR software. The accuracy of calculations is determined by performing the static balance tests of the cut-off part of a structure. For the structure under consideration, the choice of five options of the force method principal system (FMРS) is analysed.
Results. For the first time the conclusion was made that in contrast to the calculation of bar systems, the choice of FMРS does not significantly affect the final stress values in solving a plane elasticity problem.
Discussion and conclusion. The comparison of calculation results made by the displacement-based finite element method and by the finite difference method showed some advantages of the latter. The finite difference method can act as an alternative to the displacement-based finite element method in solving a plane elasticity problem on condition of automation of the process of building the internal forces epures in a wall beam-wall contour.