Comparison between exact and approximate methods for geometrically nonlinear analysis prescribed in design standards for steel and reinforced concrete structures

abstract: Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the γ z coefficient method, from NBR 6118:2014; the P-Delta iterative method and the α c r coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.

Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

Numerical and Analytical Investigation of Stability of the Reinforced Plate

The work is aimed at the construction of an algorithm for studying the equilibrium states of a reinforced plate near critical points, using the first (cubic terms) nonlinear terms of the potential energy expansion. Using geometrically nonlinear analysis of displacement, deformation and stress fields, the Eigenforms of buckling were calculated and bifurcation solutions and solutions for equilibrium curves with limit points were constructed depending on the initial imperfections.

Comparison of nonlinear solution techniques named arc-length for the geometrically nonlinear analysis of structural systems

The nonlinearity issue is one of the promising fields in the engineering area. Particularly, the geometric nonlinearity bears big importance for the structural systems showing a tendency of larger deflection. In order to obtain a correct load-deflection relation for the structural system subjected to any external load, an advanced incremental-iterative based approach has to be utilized in the analysis of nonlinear responses. Arc length method has been proven to be the most perfect one among the nonlinear analysis approaches. Thus, it is extensively applied to the structural systems with pin-connected joints. This study attempts to compare two variations of arc length method named “spherical” and “linearized” for the nonlinear analysis of structural system with rigid-connected joints. Also, two different element formulations are utilized to discretize the structural systems. Two open-source coded programs, Opensees and FEAP, are employed for six benchmark structural systems in order to compare the performance of employed arc-length techniques. Furthermore, in order to make a further observation in the nonlinear behavior of application examples, their simulations are not only sketched using graphs, but also displayed through the movies for each of benchmark tests. Consequently, the linearized type arc length technique implemented in FEAP shows a more success with a better prediction of load-deflection relation, noting that Opensees has a big advantage of having an element, which is capable of simulating the geometric nonlinearity.