Análise de deformações em vigas com comportamento geometricamente não-linear

Abstract

Is show in this work four approximated methods solutions to obtain the vertical and angular displacements of a cantilever beam with geometrically nonlinear behavior. To compare the solutions will be used a beam under a concentrated load in its free end. The problem is represented by the second order nonlinear differential equation whose exact solution is not available in the literature. The first method is the linearization of the equation that consists of despising the term of the differential equation that contains the square of the slope, facilitating the use of analytic solution for obtaining of the elastic line. The second is the fourth order Runge- Kutta method in the solution of the differential equation in its completes form. The third method is the pseudolinear equivalent system whose solution results in the same deflection curve of the initial nonlinear problem. In this last method, the nonlinear differential problem is transformed into a system that can be solved using the linear analysis. The fourth is finite elements method applied in the linear and nonlinear analysis of beams. Such methods will have its compared results so much for small as for great displacements and angular deformations. The conclusion are that for the conventional structures, such as structures that use materials as steel and aluminum, the linear method is acceptable. While for materials that allow large deformations in the elastic regime, as some polymeric ones, another method among them studied should be used.