- The purpose of this study is to analyze thin axisymmetric shells with the aid of finite elements based on cubic B-splines. The elements are isoparametric, i.e., both geometry and displacements are described by cubic B-splines., In the interior of the shell, the degrees of freedom are the nodal displacements. Three degrees of freedom are used at the edge nodes: two displacements and the rotation of the meridian. Since these edge degrees of freedom are also present in most bending elements, the spline element is kinematically compatible with most finite element models. In other words, the shell can be incorporated in any finite element computer program in the form of a "superelement" or substructure., and The use of cubic splines offers the following advantages over conventional finite element models: (i) Smoothness, in the form of continuity of the meridional curvature before and after deformation, is automatically ensured by cubic spline interpolation. This desirable feature cannot be enforced in a simple manner with conventional finite elements. (ii) Since moments are related to the second derivative of the normal displacement, continuity of moments at the interelement nodes is maintained. Conventional cubic hermite polynomials fail to ensure this continuity, unless mixed variational method is used. Mixed variational method, on the other hand, would require a higher number of degrees of freedom. (iii) For a given number of elements, the cubic spline model involves fewer degrees of freedom than other thin shell finite elements. Therefore, it is more efficient in the storage and solution of simultaneous equations.
- Dissertation Note:
- Ph.D. The Pennsylvania State University 1986.
- Source: Dissertation Abstracts International, Volume: 47-04, Section: B, page: 1624.
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