Torsional warping elastostatic analysis of FGM beams with longitudinally varying material properties

摘要

In this paper, the influence of torsional warping of the cross-sections of thin-walled twisted Functionally Graded Material (FGM) beams on their elastostatic behavior is investigated. The material properties are assumed to vary longitudinally. The variation is described by a polynomial. Secondary deformations, resulting from the angle of twist, are considered. The transfer matrix method serves as the analysis tool. The transfer relations are derived and used for establishing finite element equations for twisted FGM beams in local coordinate systems. The warping part of the first derivative of the twist angle, caused by the bimoment, is considered as an additional degree of freedom at the nodes of the beam elements. The numerical investigation is performed with or without consideration of the Secondary Torsional Moment Deformation Effect (STMDE). It is focused on elastostatic analysis of straight cantilever FGM beams with doubly symmetric open as well as closed cross-sections. The influence of the longitudinal variation of the material properties and of the secondary torsion moment on the deformation and stress state is investigated. The results are compared with the ones obtained by a very fine mesh of standard solid and shell as well as warping beam finite elements.