Warping torsion of FGM beams with spatially varying material properties

Abstract

This contribution extends the author’s previous research results concerning effect of spatially varying material properties on warping torsion of beams with open cross-section made of Functionally Graded Material (FGM). The author’s FGM WT beam finite element is used in the calculations of the primary quantities. The secondary deformations due to the angle of twist is considered. The warping part of the first derivative of the twist angle, caused by the bimoment, is accounted as an additional degree of freedom at the beam nodes. The author’s Reference Beam Method, (RBM), is used for homogenization of the spatially varying material properties in the real beam onto effective constant or longitudinally varying stiffnesses for the homogenized beam. Enhanced equations for calculation of the normal and shear stresses with the influence of the deformation effect caused by the primary and secondary torsion moment are established. These equations also contain effect of the warping ordinate function and its gradients that depend on spatially varying material properties. The focus of the numerical investigation is on non-uniform torsional analysis of straight FGM cantilever beams with I- cross-section. An effect of the warping ordinate function and its gradients on the normal and shear stresses is evaluated and discussed. A significant effect of the spatial variability of material properties on the deformation as well as on the stress state in the FGM beams with I-cross-section, has been found. The real beams with spatially varying material properties are modelled with only a single FGM WT beam finite element. Obtained results for the primary and secondary variables are compared with the ones calculated by a very fine mesh of standard 3D-solid finite elements. A very good agreement of all the results has been achieved.