The quadrilateral Mindlin plate elements using the spline interpolation bases

By the Mindlin/Reissner plate theory, the displacement ω and rotations θx,θy are interpolated by independent functions, for which only C0 continuity condition is required. The difficulty for constructing interpolation bases on the quadrilateral element without isoparametric transformation can be overcome by using the spline method. In this paper, two sets of spline interpolation bases are adopted to construct two quadrilateral spline Mindlin plate elements (QSMP1 and QSMP2) with 12 degrees of freedom. The spline elements can be applied for both thick and thin plates, and can converge for the very thin case. Numerical examples are discussed to show that the Mindlin plate element combined with the spline interpolation bases can possess good accuracy.