Open AccessApplication of Direct Integration Methods in the solution of a nonlinear beam problem
Author(s) -
Raul Carreira Rufato,
Santos Alberto Enriquez-Remigio,
Tobias Morais
Publication year - 2021
Publication title -
remat
Language(s) - English
Resource type - Journals
ISSN - 2447-2689
DOI - 10.35819/remat2021v7i1id4277
Subject(s) - discretization , nonlinear system , finite element method , matlab , fortran , convergence (economics) , computer science , beam (structure) , superposition principle , software , direct integration of a beam , work (physics) , numerical integration , computational science , mathematical optimization , mathematics , algorithm , mathematical analysis , structural engineering , engineering , mechanical engineering , physics , programming language , quantum mechanics , economics , economic growth
This work applies different numerical methods involved in the solution of a nonlinear clamped beam problem. The methodology used in the discretization of the dynamic problem is based on the Finite Element Method (FEM), followed by mode superposition, where a localized nonlinearity is applied at the free end of the beam. The solution of the nonlinear problem is performed by five different integration methods. The solution code is implemented in FORTRAN language, validated with ANSYS and the dynamic response and the graphs are obtained with the help of MATLAB software. The work shows the convergence of the implemented methods with various validation problems.