Keywords: domes, underwater structures, membrane analysis, least weight design, shooting method, optimization.

This paper is concerned with the optimal design of submerged domes. In addition to the hydrostatic pressure, the dome structure has to carry its own weight and a skin cover load. The loads are assumed to be transmitted through the dome structure to the supporting ring foundation via membrane forces only. By adopting a fully stressed design, the problem in hand is to determine the shape and thickness variation of the submerged dome. Equations governing the geometry of fully stressed submerged domes under combined hydrostatic pressure, selfweight and skin cover load are derived. These equations describe the curvature and thickness variation of the dome as well as the Cartesian coordinates of its meridian. The set of nonlinear differential equations and boundary conditions constitute a two-point boundary problem that can be solved by the shooting-optimization method proposed by Wang and Kitipornchai [1]. For the special case of a weightless dome without skin cover load, the thickness of the dome was found to be constant when subjected to hydrostatic pressure only. The shape of the dome was also found to agree well with the shape currently reported in the literature [2,3,4]. Based on a family of fully stressed designs associated with a given water depth and dome height, the optimal dome shape for minimum weight is determined.

Although the set of governing equations for submerged domes is highly nonlinear, the shooting optimization technique currently available in the literature was found to be well suited for solving this problem. A notable advantage of the equations derived in this paper is the parameterization of the equations using the arc length s as measured from the apex of the dome. Such a parameterization allows the entire shape of the submerged dome to be determined in a single integration process whereas previous methods [2,3,4] cannot determine the Cartesian coordinates of the dome once vertical or infinite slope is encountered in the meridian. Parametric studies of dome shapes under different water depths and selfweights also led to an investigation of the optimal shape of submerged domes. Numerical examples indicated that the airspace enclosed by the optimal dome reduces in the presence of large hydrostatic pressure.

1

Wang, C.M. and Kitipornchai, S., "Shooting-optimization technique for large deflection analysis of structural members", Engineering Structures, 14(4), 231-240, 1992. doi:10.1016/0141-0296(92)90011-E

2

Timoshenko, S.P. and Woinowsky-Krieger, Theory of Plates and Shells, New York, McGraw-Hill, 2nd Edition, 1959.

3

Royles, R., Sofoluwe, A.B., Baig, M.M. and Currie, A.J., "Behavior of underwater enclosures of optimum design", Strain, 16(1), 12-20, 1980. doi:10.1111/j.1475-1305.1980.tb00311.x

4

Sofoluwe, A.B., Royles, R. and Ibidapo-Obe, O., "An improved numerical approach to the analysis of the Echinodome", Mechanics Research Communications, 8(4), 237-243, 1981. doi:10.1016/0093-6413(81)90059-8

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