A cellular composite structure includes a grid having groups of angularly intersecting ribs. The ribs of each group are oriented substantially in the same direction to each other and angularly oriented from the other rib groups. An additional rib defines a composite structure outer perimeter wall and can be differently angularly oriented from the other ribs. A contiguous rib wall is created by segments of ribs defined by rib intersections. The contiguous rib wall bounds a cavity. A multilayer sheet cap member with extending walls to engage the contiguous rib wall is positioned within the cavity. The engagement walls extend from individual sheet perimeter portions angularly oriented to the sheet. The ribs and cap member have pre-impregnated resin. Heating the cap member and ribs activates the resin and co-cures the composite structure.