COMPUTER SIMULATION IN THE PROBLEMS OF STABILITY OF THIN-WALLED RODS OF AN OPEN PROFILE WITH SHAPE IMPERFECTIONS

Abstract

The presented numerical methodology is based on the finite element method (FEM) and computational procedures of the NASTRAN software package. It allows to investigate the influence of geometric imperfections in the shape of thin-walled rods of open profile on the critical values of the load, the shape of the stability loss and the stress-strain state. It has been developed an algorithm for computer modeling of initial imperfections in the shape of thin-walled rods, which is implemented in the NASTRAN software package using a neutral NASTRAN PC file and a specially developed program written in FORTRAN language and adapted to this software package. Geometric imperfections of the rods can be represented as their form of loss of stability or the form of deformation from the action of the load with the possibility of varying the maximum value of the imperfections amplitude. Computational procedures for solving the Lanczos stability problem and the geometrically nonlinear static problem by the Newton-Rafson method can be used to model imperfections. The program developed by the authors allows to form new nodal coordinates of a finite-element model of rods and to visualize geometric imperfections in a given scale. The article provides a step-by-step description of finite-element construction models of thin-walled rod of open profile with an ideal surface and taking into account the imperfection of the form, which is presented as the first form of loss of rod stability from longitudinal load applied with eccentricity. With the help of the FEMAP NASTRAN preprocessor is forming the geometry of the middle surface of an ideal rod, and setting the mechanical characteristics of the material, boundary conditions and load. The middle surface of the rod is fed as a set of flat quadrangular finite elements with six degrees of freedom in the node. In the article, a linear calculation of the stability by the Lanzosch method is performed to obtain the form of rod geometric imperfection. Setting the maximum amplitude of imperfections was performed using the program developed by the authors. Using the Newton-Rafson method, the geometrically nonlinear problem of rod statics with a given shape imperfection is solved, the critical value of the longitudinal load is determined, and the corresponding form of the rod stability loss is obtained. The presented numerical technique and the developed algorithm of computer modeling of shape imperfections allow to investigate in nonlinear formulation the stability of open profile thin-walled rods taking into account geometric imperfections of different amplitude as different forms of rod deformation, including the form of stability loss, to assess the impact of imperfections on the critical value of the load, the form of stability loss and stress-strain state. The presented algorithm and numerical technique can be used to study the stability of such thin-walled structural elements as shells, plates and others.