Técnica de elementos finitos para análise limite de pórticos planos associada à automação do processo de modelagem 3d de estruturas reticuladas via cad

Abstract

The present work presents a finite element technique for the limit analysis of plane frames using linear programming (LP). The formulation is integrated with a CAD (Computer Aided Design) system developed to automate the modeling of threedimensional and two-dimensional reticular structures. The CAD system developed, named structural modeler, works as pre and post-processor for the conceived limit analysis technique. The application uses object orientedprogramming (OOP) and the application programming interface (API) ObjectARX (AutoCAD Runtime eXtension), that allows extensions and customization of the software AutoCAD. The 3D modeler allows the lauching of the structure using bars, nodes materials and cross sections.The plane frame limit analysis technique uses the kinematic approach to determine upper bounds of the collapse load factor, êc, as well as the corresponding collapse mechanism. The proposed solution transforms the structural problem into a LP problem. Minimization of the load factor is achieved by applying the Principle of Virtual Work (PVW) to the frame possible collapse mechanisms. The structure is discretized in twonodes finite elements with a linear interpolation and the constraint equations of the LP problem are obtained by the compatibility of displacements and strain. For the implementation of the technique an application was developed, using C++, the paradigms of the OOP and some software design patterns. Finally, the contributions of this work to other areas, the limitations of the resulting applications and suggestions for future work are also discussed.