Large Deformation Plate Bending with Application to Solar Collectors

International Solar Energy Society
Publication Type:
Conference Proceeding
Third International Solar Energy Society Conference - Asia-Pacific Region, Sydney, 2008, pp. 1 - 10
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In a typical trough solar collector, a reflective sheet is shaped by a set of ribs with parabolic cutouts. This paper proposes the alternative simple construction method of pushing a thin elastic plate inwards on opposite edges, allowing the plate to adopt its minimum bending energy shape. Analytical solutions are derived for the shape, parameterised by the tangent angle at the plate edges. The limiting shape for a small bend is shown to be a cosine, even up to 15o edge angle. For edge angle between 40o and 52o, the shape is remarkably close to a parabola, differing by less than 2% of the shape height. Measured profiles of a thin metal strip accurately follow the analytic curves see figure below. The ability of the shape to focus parallel light by reflection is assessed. For circular section collectors, the maximum concentration factor (trough width to collector diameter catching all reflected light) is 26 for edge angle 53o and the collector centre dropped by 0.163 of the trough width. For planar collectors, the maximum factor is not as high, only 8.2, achieved in the small bend limit with the collector well above the trough. The results are also relevant to solar trough collectors shaped by ribs, since minimum distortion between the ribs will be obtained by using edge compression and edge angles in the range around 35o 55o, to give a free shape which is close to parabolic, thus needing minimal tuning by the ribs
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