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By C. R. Scott

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Fig. 2-8(u) Fig. 2-8(w) WaIDe Slab, Library, St. 7 Gaussian Curvature Fig. 2-8(x) Folded Plate Roof, Law School, St. 8 Specialization of Shell Geometry Because of the wide variety of plate and shell structures encountered in engineering practice, several geometrical classes are of particular interest. 1 Shallow Shells: The theory of shallow shells has wide application for roof shells that have a relatively small rise as compared to their spans. Considering ~O~__________~~-+__~__________~y Fig.

TpB, .. + Btp,.. 18c) Now consider the component oft.. ,.. in the tp direction, given by tp' t .. ,... We take the derivative of the product t ... tp with respect to Q( (t.. • t p), .. = tp' t .. ,.. + t .. · t p,.. Since t ... tp = 0, tp·t .. , .. = - t.. ·tp, .. 18e) We replace t p, .. 18c) to get 1 tp' t .. ,.. = - B t .. · [ - tpH, .. t 13 a,a + t .. 17). The other components of the derivatives of ta and tp in the Q( and P directions may be verified in a similar manner. 3 (III) Derivatives of tn.

M. Lindberg, M. D. Olson, "A Shallow Shell Finite Element of Triangular Shape," International Journal of Solids and Structures 6, no. 8 (1970): 1133-1156. 9. H. Reissner, Spannungen in Kugelschalen (Leipzig: Muller-Breslau-Festschrift, 1912), pp. 181-193. 10. V. Z. : National Aeronautics and Space Administration, 1964), pp. 5-13. 17). 37). 45c). 4) and figure 2-11. (a) Choosing Z and 8 as the curvilinear coordinates, compute expressions for the first and second quadratic forms. Note that if the alternate Cartesian axes shown in Figure 2-13 are used, the parametric equation must be modified.

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