SUMMARYThe present paper is concerned with the improvement of a finite element for the analysis of plate bending structures. The element formulation is based upon the Mindlin plate concept. The displacement field of this element is formed by adding non-conforming modes to two rotational displacement components of an 8-node plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in a very thin plate situation, even for irregular meshes.

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The applications of the reduced integration technique. and the addition of non-conforming modes and their coupling to Mindlin plate elements to improve their basic behaviour arc reviewed and the establishment of a series of new plate elements by combined use of these schemes is presented in this paper. The element formulation is based upon the quadratic Mindlin plate concept. The results obtained by new elements converge to thc exact solutions very rapidly as the mesh is refined and show reliablc solutions even for severely distorted meshes. The new elemcnts have the requisite numbers of Yero eigenvaiues associated with rigid body modes to avoid spurious zero energy modes. These elements are shown to solve the shear locking problem completely so that they are applicable to a wide range of plate problems, giving a high accuracy for both thick and thin platcs. 1NTRODUCTlONAs one of the modified versions of the isopararnetric element, the Ahmad type degenerated shell element' has been used successfully in a wide range of structural analysis problems. This degenerated solid apprwch provides a very convenient basis for finite element modelling of shell structures with arbitrary geometries. In addition, the interelement compatibility requirement is easily satisfied in the degenerated shell e!ement because the shape functions require only Go continuity. For plate bending, the dcgenerated solid approach is equivalent to the Mindlin plate iheory'j with the effect of transverse shear included.Unfortunately, however, this element has one significant deficiency, i.e. excessive flexural stiffness due to the transverse displacement constraint^.^' The assumed displacement interpolation functions used in an isoparametric element constrain the element to deform in a shear mode, imposing a large amount of shearing strain in thc bcnding behaviour of a plate element, which causes a very slow convergence. Besides, the ratio of the shear stiffness coefficients to the bending stiffness coefficients is of order (Lit)', and completely dominates the global stiffness, and the *Professor of Civil Engineering 'Senior Researcher, Structural Engineering Department

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