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approximate the doubly curved surface. Such elements present a number of theoretical and computational problems and are not recommended for the analysis of shells. Currently, shell elements degenerated from three-dimensional solid elements are very popular. These elements have been utilized in both ring and quadrilateral forms.

The column region at the base of the shell presents a special modeling challenge. For static analysis, the lower boundary is often idealized as a uniform support at the lintel level. Then, a portion of the lower shell and the columns is considered in a subsequent analysis to account for the concentrated actions of the columns, which may penetrate only a relatively short distance into the shell wall. For dynamic analysis, it is important to include the column region along with the veil in the model. An equivalent shell element has proved useful in this regard if ring elements are used to model the shell [9,10]. It may also be desirable to include some of the foundation elements, such as a ring beam at the base and even the supporting piles in a dynamic or settlement model. Figure 27.16 shows such a finite element model for the final tower design with approximately 51,000 degrees of freedom, shown here in a five times coarser resolution.

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