SummaryFurther details are given of a recently developed triangular equilibrium element which is then applied, in conjunction with the complementary energy principle, to the finite element analysis of some plate bending problems. The element is demonstrated to have a straightforward and satisfactory application and to possess advantages over the conventional triangular displacement element.

A non-conforming displacement triangular finite element is derived with quadratically varying displacements for use in plate-bending problems. It is shown that the element corresponds with a known constant-bendingmoment element and provides, in consequence, an over-estimate of the influence coefficients. Convergence is also assured in advancing to successively finer mesh sizes. A few simple test problems are computed so as to illustrate the kind of accuracy which can be expected.

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.

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