Multi-level modelling of beam-type structures by finite element methods

Abstract

The multi-level approach to modelling of beam-type structures is presented in this report. The attention is focused to the level of equations of the beam and to the level of macroelement. The semi-analytical finite element method (FEM) is proposed for modelling of equations where the cross-section of beam as an assemblage of semi-analytical elements is assumed. The semi-analytical FEM is formulated using independent approximations of the three-dimensional fields of displacements and stresses within the cross-section. The thin-walled beam is presented as an example. The structural elements with the small number of degrees of freedom (DOF) on boundary and large number of internal DOF are defined as macroelements. They are described analogously to convention finite elements while characteristic matrices of them are obtained by numerical experiments.

Pateikiamas daugiapakopis požiūris į strypinių konstrukcijų modeliavimą. Akcentuojami lygčių ir makroelementų lygiai. Pasiūlytas ir aptariamas strypų lygčių sudarymas panaudojant pusiauanalitinius baigtinius elementus.