PYTHON ALGORITHM FOR CALCULATION OF INTERNAL FORCES AND DISPLACEMENTS IN BEAMS USING THE FINITE ELEMENT METHOD

Resumo

A beam finite element under linearly distributed loading is presented. The finite element has two nodes
and two degrees of freedom per node, totaling four degrees of freedom per element. The nodal parameters are
translations and rotations. A cubic polynomial and a linear polynomial are used, respectively, to approximate the
solutions of the problem and describe the loading. The total potential energy functional and the stationarity
principle of energy are used to obtain the finite element equations system. Python 3.9.0 programming language
and PyCharm IDE 2020.2 are used to implement the developed algorithm. After determining the problem

unknowns by solving the system of equations, the internal forces and support reactions are determined in the post-
processing phase. To validate the implemented code, a simply supported beam subjected to a uniformly distributed

load was chosen. The results shown by the algorithm were compared with analytical and FTOOL solutions, and
show that the code was successfully implemented.