A critical study of stresses of FG Timoshenko Beams using B-spline Collocation

Abstract

A functionally graded material beam of rectangular cross-section is studied for bending and shear stresses under uniformly distributed mechanical load. The gradation is assumed to be along the height of the beam and follows power law. The governing equations are derived using principle of virtual work in the framework of Timoshenko beams which is solved numerically using sixth order B-spline collocation technique with Greville abscissa as collocation points. The variation in the position of neutral axis, variations in bending (axial) and shear stresses at different positions along a cross-section corresponding to different power law index values have been reported. It has been observed that shift in neutral axis governs the stress distribution along the cross-section.