Python Program for 3D Linear Dynamic Reticular Structural Analysis Based on Finite Element Method

Resumo

Dynamic structural analysis in civil engineering is the method, in which, the vibrations response, modes,
frequencies, displacements, velocities and accelerations, of a real-world structure caused by arbitrary external
excitements is predicted, before its design and construction. But even for simple structures, to conceive the analysis
by hand, without relying on simplifications, for which, by themselves, sacrifices precision of the analytical
solutions, is hard. Therefore, a computational method to solve these structures is needed. But these softwares come
at a high monetary cost, causing an inaccessibility for students to have access to, even for confirming and/or
learning purposes. For such, a computational tool development, capable of linear structural analysis, both in 2D
and 3D, in dynamic regime, open-source for all, were proposed. To make it possible, the Finite Element Method
(FEM), for structural discretization, the Rayleigh damping model, for viscous approximation, the Newmark's
numerical method, for vibration analysis, and the Eigen-vectors and values, for modal analysis, and Python, for
the programming language, were used. And to a reticular structures, they were applied. Then, with examples found
in the available literature in the subject of dynamic structural analysis, were tested and compared. The results from
examples tested, errors ranging from 10-5 to 10-2 were shown by the tool, in the same unit as the mesh and properties
and time discretization, inputted in the program, compared to examples available in the literature.