Innovative Formulation for the Bending of Plates with Reentrant Angles

Abstract

Very recently, an innovative mesh-free method, the so-called line element-less method (LEM), has been proposed to determine the response of plates under uniformly distributed edge moments. However, the previous formulations do not solve the problem related to plates with reentrant angles. In this paper, an innovative formulation is introduced to evaluate the deflection function of a simply supported plate possessing reentrant angles at the boundary and loaded by uniformly distributed edge moments. Framed in the LEM, this formulation consents to obtain a plate deflection function, implementing a simple algorithm within Mathematica software. Compelling savings in terms of time and computational costs are achieved, since there is no need to discretize the domain or the contour. Finally, the accuracy of the proposed results is highlighted by a good match with those achieved by classical methods and the finite-element method.