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

## Palavras-chave:

Python algorithm, Finite Element Method, beams, structural analysis## 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.