A new plate bending element based on orthogonal polynomials expansion of the curvature field

A new approach to derive finite elements for the thin plate model is presented. The proposed method approximates compatible Kirchhoff formulations by means of orthogonal polynomials expansion of the curvature field depending only on the element boundary traces. With respect to the compatible formulation the proposed method produces elements that beneficially underestimate the deformation energy. A simple triangular element is developed and investigated from both the theoretical and the numerical point of view and numerically compared with other two well-known elements.