Application of the Galerkin method in the calculation of the stability of compressed rods with the creep
Abstract
Application of the Galerkin method in the calculation of the stability of compressed rods with the creep
Incoming article date: 25.06.2013The resolving equations for the calculation of the stability of polymer compressed rods with the creep using Galerkin method are obtained. The problem is solved in the case of a simply supported pivotally-rod having an initial bending in the plane of the lower stiffness, and in the case of off-center application of force. Galerkin method used in combination with the finite element method, that is the shape functions are taken as the basis functions . The solution is made numerically, using the software package Matlab. There are two variants considered: a variant of the rod with constant and variable in length stiffness. It is shown that for rods with variable cross-sections and the same mass, a critical time has increased by almost 4.5 times. The solution for the rods of constant cross section agrees well with the solutions obtained by the method of finite differences. This may indicate the reliability of the proposed method
Keywords: polymer rod, creep, Galerkin method, stability, variable stiffness