A Triangular Equilibrium Element with Linearly Varying Bending Moments for Plate Bending Problems

Work on the finite element analysis of flat plates in bending has been directed towards elements which satisfy kinematic conditions between the adjacent elements in conjunction with the theorem of minimum potential energy, eg Argyris, Bazeley et al, Clough and Veubeke. The purpose of this Note is to provide the main details of a triangular element which satisfies equilibrium conditions between the adjacent elements and which is used in conjunction with the complementary energy principle. The bending moments vary linearly within the element and use is made in the derivation of the analogy (see eg Southwell, Fox, Fung and Morley that exists between problems of plane stress and plate bending. In particular, many of the present details are taken directly from the plane stress analysis of Veubeke who, along with Argyris, considers a displacement triangular element with linearly varying strain.