Nonlinear stability analysis of the frame structures

Abstract

In this doctoral thesis, the nonlinear stability analysis of frame structures is presented. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to the exact solution of the differential equation of bending according to the second-order theory. When the buckling of structure occurs in the plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et that is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this thesis, the computer program ALIN was created. This program is developed in the C++ programming language. In this thesis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3) and national (JUS) standards for the steel structures. By the presented procedure it is also possible to follow the behavior of the plane frames in the plastic domain and to calculate the real critical load in that domain.