Numerical fundamentals and interactive computer graphics system for the nonlinear analysis of planar frames

<div><p>Abstract Recent scientific and computational advances have facilitated the analysis of slender structural systems subject to instability. With the employment of more sophisticated numerical tools and algorithms, it is possible to accurately determine the critical points (limit and bifurcation loads) as well as the post-critical behavior of the structural system. In the computational context, efficient data structures are needed to enable code and graphic interface expansion for the generation of models and visualization of the results obtained. Thus, an interactive object-orientated graphic computational system is presented herein. It has been developed using MATLAB/GUI, with pre-processing, analysis and post-processing capacities for planar structural frames. The nonlinear finite element developed and implemented for the structure modeling is formulated considering second order effects. Therefore, with the computational tool presented, the geometric nonlinear effects and stability of the structural system can be directly addressed, and the visualization of the numerical results are accessed through interactive controls that permit data inclusion and analysis verification. The engineer-designer can see the structural model discretization, the equilibrium path, its deformation configuration, the force and bending moment diagrams at the moment that he runs the program and in each load step. It is also possible to export the images, videos or tables of the obtained numerical results. The example presented demonstrates the capacity of the developed graphic computational system.</p></div>