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

Abstract

Criteria are derived for the adoption by bidirectional fabrics, without wrinkling or having to be cut, of the shapes of regular and truncated four-sided pyramids. Pyramids have topological kinship with general convex shapes. Also, their covering by fabrics is fairly simple, and the flat surfaces result in distinct deformation zones that can be compared with experiment. Only the major mode of fabric deformation, trellis shear, was considered. A fishing net analysis was applied to fabrics in specific orientations. The criterion 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 peak must equal the sum of angles of the four faces of the pyramid. Short truncated pyramids can often be covered without wrinkling even when a taller pyramid having sides of similar steepness cannot. The criterion is again a match of angle sums. For taller truncated pyramids, the condition required for covering the corresponding non-truncated pyramid also applies.