A method for patching a hole in a composite parent structure. The method comprises: inserting an insert in the hole; placing a composite patch having a multiplicity of curved flexible members on one side of the composite parent structure in a position where a central portion of the composite patch overlies the insert and the flexible members confront opposing portions of the composite parent structure providing adhesive between the composite patch, the insert, and the composite parent structure; pressing the composite patch against the composite parent structure with sufficient pressure to force the flexible members to conform to the shape of the composite parent structure; and while the flexible members are in a stressed state, curing the adhesive in a manner that causes the flexible members to bond to the parent structure.