Algoritmo Baseado no método de Potra-Pták para solução não linear de treliças espaciais.

The current tendency of using more slender structures with higher strength makes the stability analysis a subject of fundamental importance. Critical points of force and displacement may arise in the equilibrium path of the structure, especially in problems with severe geometric nonlinearity. Trusses may experience loading conditions that cause large displacements, altering significantly the geometry of the structure. An algorithm based on the Potra-Pták method with order of cubic convergence, associated with the Linear Arc-Length path-following technique, is presented in this paper for the static analysis of space trusses considering the geometric nonlinearity. The Positional Finite Element formulation is used for the discretization of the structure, which is an alternative approach that considers the nodal coordinates as variables of the nonlinear system instead of displacements. It is assumed that the material constituting the bars of the trusses has linear elastic constitutive behavior. Computational simulations of space trusses problems with the program developed in Matlab environment are performed, evidencing the best numerical performance of the proposed algorithm with the Potra-Pták method, compared to the analyzes done with the Standard Newton-Raphson iterative scheme.