高次せん断変形理論に基づく板曲げ要素

抄録

The finite element models of the Kirchhoff (classical thin) plate theory and Mindlin plate theory are now standard. The Mindlin plate theory includes the effect of transverse shear deformation. This theory is called the first-order shear deformation theory. The first author developed a beam element based on a displacement formulation of Mindlin plate theory. The objective of this paper is to present a formulation for plate element based on the refined plate theory of Shimpi. The refined plate theory of Shimpi uses higher-order polynomials in the expansion of the displacement components through the thickness of plate. Furthermore, the transverse displacement ω is given by ω = ω_b + ω_s, where ω_b and ω_s are its components due to bending and shear, respectively. Several numerical experiments are performed and show that the present element gives excellent results for both thin and thick plates.