Simplified Analysis of Rectangular Plates with Stepped Thickness

This paper presents a simplified analytical method for rectangular plates with arbitrarily and eccentrically stepped thickness, such as building slabs, under the validity of the Kirchhoff-Love hypotheses. The discontinuous variation in bending stiffness due to the variation of the thickness can be expressed continuously by the use of an extended Heaviside function, which is defined as a Dirac function existing continuously in a prescribed region. Since the bending stiffness used here is given exactly by the actual bending stiffness at each point, a modification of the bending stiffness used in an equivalent plate analogy is unnecessary. The governing equations are formulated by means of Hamilton's principle. Static and dynamic approximate but accurate solutions are obtained from the proposed governing equation by the use of the Galerkin method. The numerical results obtained from the proposed theory for simply supported and clamped plates with stepped thickness show good agreement with results obtained from the finite element method using the code NASTRAN.