Abstract
A circular plate resting on an elastic halfspace is considered. The plate is deflected downward by a uniform load and sometimes additional edge loads and moments. Translational and rotational supports at the edge are included in some cases. The interface between the plate and the halfspace is assumed to be frictionless. The plate has piecewise-constant thickness, and the segment thicknesses and radii are allowed to vary. For given total volume of the plate, the difference between the maximum deflection (which occurs at the centre) and minimum deflection (which occurs at the edge) is minimized. Optimal solutions depend on the relative stiffness between the plate and the halfspace. The results can be applied to the bottom plate of a ground-supported liquid storage tank.
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Zmerli, M., Plaut, R.H. Design of a circular plate on an elastic halfspace for minimum differential settlement. Structural Optimization 6, 52–58 (1993). https://doi.org/10.1007/BF01743174
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DOI: https://doi.org/10.1007/BF01743174