Consistent thick shell element

Thick shell finite element with transverse shear deformation have required the use of reduced integration to provide improved results for thin plates and shells, due to the presence of spurious transverse shear strain modes. It has been found that the spurious transverse shear strain modes result from inconsistencies in the displacement fields used in the formulation of these elements. A new thick shell element has been formulated. By providing cubic polynomials for approximation of displacements, and quadratic polynomials for approximation of rotations a consistent formulation is ensured thereby eliminating the spurious modes. Rotational degrees of Freedom which vary quadratically through the thickness of the element are included. This allows for a parabolic variation of the transverse shear strains and hence eliminates the need for use of the shear correction factor kappa as required by the Mindlin plate theory. These rotational degrees of freedom also provide cubic variations of the displacements through the thickness of the element. Thus, the normal to the middle surface is neither straight nor normal after shearing and bending, allowing for warping of the cross-section. Material non-linearities are also incorporated, along with the modified Newton-Raphson method for nonlinear analysis. Comparisons are made with the available elasticity solutions and those predicted by the eight and nine-node isoparametric shell elements. The results indicate that the consistent thick shell element provides excellent predictions of the displacements, stresses and plastic zones for both thin and thick plates and shells. (C) 1997 Published by Elsevier Science Ltd.