A finite element model for a higher-order shear-deformable beam theory

Abstract

The theory for a higher order shear-deformable beam model is first developed. It is based on a higher order displacement model and incorporates linear and quadratic variation of transverse normal strain and transverse shearing strain respectively through the beam thickness. The effects of the transverse normal and shear stresses are included in the definition of the material's constitutive law. The warping of the transverse normal cross-section of the beam is automatically incorporated in the mathematical model. The question of selecting a shear correction coefficient as in a first-order shear deformable Timoshenko theory does not arise. A linear two-noded finite element model of this theory is introduced and developed next. Both static and free vibration results of this theory are presented and compared with those of Euler and Timoshenko theories for various boundary and loading conditions.