An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three comer nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements. 1.A particular shell theory is used and discreti~,ed.'*~ 2. Three-dimensional continuum equations are used and discretized (isoparametric elements) (References 6 and 7, etc.). 3. Plate bending and membrane element stiffnesses are superimposed and assembled in a global co-ordinate system (References 8 and 9, etc.).The three approaches have advantages and disadvantages, and it is still difficult to state which of the three approaches is most effective based on criteria combining accuracy, computational cost and simplicity in use (in the data input phase as well as in the interpretation of results). Approach 3 received a great deal of attention for the linear analysis of shell structures in the mid-l960s," but the activities related to approaches 1 and 2 have dominated the past 10 years. It is only recently that a new impetus has been given to the analysis of shells using approach 3. 0029-598 1 /80/ 12 15-177 1 $01 .OO Considering this approach, triangular flat elements having displacements and rotations at the corner nodes as degrees-of-freedom-the engineering dof-are particularly appealing for many practical reasons; for example, arbitrary shell geometries, general supports and cut-outs, and beam stiffeners can be modelled. These elements have a total of 18 dof (3 translations and 3 rotations at each node) or 15 dof (3 translations and 2 rotations) depending on whether the rotation about the normal is included as a dof. The element formulation is based on a superposition of membrane and bending actions. Among the most recent papers on this subject, References 12 and 13 deal with the linear analysis, whereas References 9,14,8 and 15 deal with the geometrically nonlinear analysis of shells with large displacements and rotations. In References 1 2 , 9 and 14 the hybrid stress formulations are used, whereas in References 13, 8 and 15, displacement-type formulations are employed.A very important consideration in the development of these shell elements is the representation of the bending behaviour. Although several theoretical and numerical studies on plate bending finite elements have appeared in the past 15 years, a detailed recent study and comparison of triangular plate bending elements with only 3 dof at the corner nodes (displacement w and rotations & and By...

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A review of 4-node, 12 degrees-of-freedom quadrilateral elements for thin plates is presented. A new element called DKQ is discussed. The formulation is based on a generalization of the efficient and reliable triangular element DKT presented in References 1 and 2 and on the rectangular element QC presented in Reference 3. These elements are derived using the so-called discrete Krichhoff technique. A detailed numerical evaluation of the behaviour of the DKQ element for the computation of displacements and stresses for thin plate bending problems is presented and discussed. The DKQ element appears to be a simple and reliable 12 degrees-of-freedom thin plate bending element.

This paper deals with the formulation and the evaluation of a new three node, nine d.0.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the D K T (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory. 534 J. L. BATOZ AND P LARDELR Hybrid Stress Model (HSM), Hsieh-Clough-Tocher (HCT) and Mindlin Selective Reduced Integration (SRI) elements were made. The DKT element appeared to be a simple but reliable and effective triangular bending element for the evaluation of displacements, stresses and eigcnfrcquencies. Since 1981 only a few attempts havc been made to formulate new nine d.0.f. triangular elements: Wui6 combined the hybrid stress Mindlin model with discrete Kirchhoff constraints along the sides, Belytschko et al." worked on the SRI element with mode decomposition, Bergan and co-workers employed the free formulation,'*-20 Karamanlidis er a/." presented the results of a hybrid element that coincides with those of HSM,' Tesslerl and Tessler and Hughes2' suggested the 'interdependent variable interpolations with appropriate shear correction factors' and the M IN3 element, FrickerZ3 improved the A-9 element of R a~z a q u e~~ (A-9 is equivalent to HSM) and compared his results with those given by DKT"."' and by the free formulation,'8 FrickerZ6 has also considered three methods to include shear deformation in the element discussed in Reference 23, Argyris et ~2 1 .~' have discussed and evaluated the TRUNC, TRUMP elements based on the natural approach, MacNeal" discussed the TRIA3 element of NASTRAN and Jeyachandrabose and Kirkhope28 have proposed and evaluated two new elements by combining the DKT formulation and the least-square technique.