# COMPUTATIONAL TOOL FOR BUCKLING ANALYSIS VIA POSITIONAL FINITE ELEMENT METHOD

## Palavras-chave:

Buckling analysis, Thin-walled profiles, Positional FEM, Computational tool## Resumo

In this work, a computational program is developed to perform stability analysis of thin-

walled profiles employing the positional formulation of the Finite Element Method (FEM). The profiles

are discretized in shell finite elements, which, unlike the traditional formulation, have position and un-

constrained vector as nodal parameters. Besides, the formulation considers a parameter corresponding to

the rate of thickness variation, which makes the kinematics of the element more general than Reissner-

Mindlin. Due to the use of unconstrained vector instead of rotation, it was necessary to use a strategy

to perform the coupling between non-coplanar elements. This coupling was accomplished by means

of a one-dimensional element connecting the end of the non-coincident vectors of a node. A nonlinear

geometric formulation of FEM is adopted, using the total Lagrangian description of the equilibrium. The

material is assumed to be elastic linear, represented by the Saint-Venant-Kirchhoff constitutive law. To

incorporate the stability analysis, a technique based on the decomposition of the stiffness matrix in the

elastic and geometric parts is used. This technique consists of determining eigenvalues and eigenvectors,

which corresponds, respectively, to buckling loads and instability modes of the resulting generalized ei-

genvalue problem. A graphical interface for the program is developed, making it easier to use. For this,

an algorithm for triangular and quadrilateral finite element mesh generation was also developed, as well

as a post-processing viewer, avoiding possible dependencies with external programs. Finally, numerical

examples are presented to validate the developed code and demonstrate the program functionalities.