Three-dimensional fiber reinforcement shapes obtainable from flat, bidirectional fabrics without wrinkling or cutting. Part 1. A single four-sided pyramid

Criteria are derived for the adoption by bidirectional fabrics, without wri nkling or having to be cut, of the shapes of regular and truncated four-sid ed pyramids. Pyramids have topological kinship with general convex shapes. Also, their covering by fabrics is fairly simple, and the Rat surfaces resu lt in distinct deformation zones that can be compared with experiment. Only the major mode of fabric deformation, trellis shear, was considered. A fis hing net analysis was applied to fabrics in specific orientations. The crit erion for a fabric, to cover a pyramid having four faces rising to a peak, is that the sum of angles of the fabric quadrants arrayed around the peal; must equal the sum of angles of the four faces of the pyramid. Short trunca ted pyramids can often be covered without wrinkling even when a taller pyra mid having sides of similar steepness cannot. The criterion is again a matc h of angle sums. For taller truncated pyramids, the condition required for covering the corresponding non-truncated pyramid also applies. (C) 2000 Els evier Science Ltd. All rights reserved.