Uma formulação teórica consistente para análise não linear de estruturas treliçadas espaciais

Abstract

Aiming the study of the non-linear behaviour of space trusses, a general theory for the analysis of such structures by the finite element method is presented. The formulation take into accounts the material and geometric nonlinearities. The theory is developed applying a rigorous Lagrangian formulation where the corotacional thecnique is used to obtain the stiffness matrix of the space truss element. The formulation intends to be as general as possible, allowing for the nodes to undergo large displacements and the bars to undertake large strains. Besides, elasto-plastic material can be used. A static incremental analysis will be perfomed, applying an incremental, monotonic and increasing load, proportional or not, until partial or global failure of the structure occurs. The solution of the problem requires an incremental-iterative procedure, such as the Newton-Raphson Method, to insure the convergence. An easy to use computer program was developed which allows for plane and spatial analyses of trusses taking encompassing second order effects. The computational coding of the element was performed using the PASCAL programming language obeying the DELPHI 2.0 standards. The examples presented were compared with theoretical results and with results produced by some commercial programs, showing the correctness and accuracy of the developed program.