Finite Element Method Application for Nonlinear Mechanical Response of Three-Dimensonal Beams Using Mathematica

Abstract

Mechanical behavior of beams under large rotations and displacements was investigated. Using co-rotational approach given by Crisfield, three dimensional beam finite elements was modeled in Mathematica environment. The symbolic process of Mathematica provides keeping the parameters in the model as variables and beams having different geometries can be modelled easily. The yielding non-linear equation system was solved by utilizing Newton-Raphson technique. Dynamic balance equations and numerical time integration method were introduced, the solution process was left as a future work, however. Comparisons with the results of ANSYS and those of the works from the literature are accomplished.