Matrix structural analysis of beams on elastic supports: implementation in Python

Resumo

Technological resources have made it possible to model natural phenomena and engineering problems more accurately, thus allowing better results. This article presents the computational implementation of a procedure for matrix structural analysis of beams. Both rigid and elastic supports were considered to represent the contact between the structural model and the external environment. A computational code was created in Python language. The matrix method allows a detailed analysis of the structural response. The developed code calculates stiffness matrices and force vectors of beam elements, which are assembled into a global stiffness matrix and a global force vector, and the equilibrium equation system is then solved. Results such as nodal displacements and slopes, support reactions, and internal forces are obtained. Different support conditions, namely fixed, hinged, and elastic supports, as well as different loading conditions, were investigated for beams. Results highlight that the presence of elastic supports can significantly affect the overall structural behavior of the system. By incorporating these effects into the analysis, more accurate predictions of structural response can be obtained, leading to safer and more economical solutions. The article provides a basis for further investigation of the behavior of complex structural systems. The use of Python language can be justified as it provides a versatile and efficient platform for conducting structural analysis and is suitable for future advances in the field of structural engineering.