Beam elements based on a higher order theory-II. Boundary layer sensitivity and stress oscillations

Abstract

The flexure of deep beams and thick plates and shear flexible (e.g. laminated composite) beams and plates is often approached through a finite element formulation based on the Lo-Christensen-Wu (LCW) theory. A systematic analytical evaluation of beam elements based on the LCW higher order theory was carried out recently. It turns out that the availability of a large number of degrees of freedom to prescribe end/boundary conditions leads to discontinuity effects that trigger off wiggles (sharp oscillations) in some of the higher order displacement terms. These wiggles propagate outward from the point of excitation and disturb the transverse normal stress predictions. This paper examines the origin of these oscillations and how these boundary layer effects can be contained by refined modeling within the boundary layer zone or region when beam elements based on this higher order theory are used. A similar difficulty should be present in plate elements based on the same theory.