A method for producing a three-dimensional fibrous preform having side flanges, comprising: (a) forming an intermediate preform blank (60, 80) by automatically laying up plural layers of fibrous material, said preform blank (60, 80) having a length and two opposing longitudinal side edges along the length dimension; and (b) shaping the intermediate preform blank (60, 80) on a molding tool having a length, a non-planar surface along the length dimension, and two contiguous sidewalls (102, 103) for forming flanges, such that the intermediate preform blank (60, 80) conforms to the non-planar surface and the sidewalls (102, 103) of the molding tool, thereby forming a three-dimensional preform with a non-planar surface and two opposing side flanges (12, 13), wherein the intermediate preform blank (60, 80) at (a) is mostly flat except for two non-planar portions along the longitudinal side edges, each non-planar portion (i) comprises multiple ridges and valleys that taper smoothly from a wavy edge portion to an apex, or (ii) tapers from a wavy edge portion to an apex and comprises multiple ridges and valleys that are parallel to each other, the edge portion of each non-planar portion is located at an intermediary position along each longitudinal side edge, and the apexes of the two non-planar portions are pointing toward each other, wherein each layer of fibrous material is formed at (a) by Automated Tape Laying or Automated Fiber Placement to deposit a plurality of elongated fiber tapes side-by-side on a mold surface comprising surface contours that correspond to the non-planar portions in the intermediate preform blank (60, 80), wherein each elongated fiber tape comprising a nonwoven veil laminated to at least one side of a layer of unidirectional fibers, and the nonwoven veil comprises randomly arranged fibers selected from thermoplastic fibers, carbon fibers, and a combination thereof, and wherein the non-planar surface of the molding tool at (b) has a bent line (or valley) defined by two sloping surfaces, each sloping surface inclining from one end of the molding tool toward the middle. (a) forming an intermediate preform blank (60, 80) by automatically laying up plural layers of fibrous material, said preform blank (60, 80) having a length and two opposing longitudinal side edges along the length dimension; and plural layers of fibrous material, said preform blank (60, 80) having a length and two opposing longitudinal side edges along the length dimension; and (b) shaping the intermediate preform blank (60, 80) on a molding tool having a length, a non-planar surface along the length dimension, and two contiguous sidewalls (102, 103) for forming flanges, such that the intermediate preform blank (60, 80) conforms to the non-planar surface and the sidewalls (102, 103) of the molding tool, thereby forming a three-dimensional preform with a non-planar surface and two opposing side flanges (12, 13), wherein the intermediate preform blank (60, 80) at (a) is mostly flat except for two non-planar portions along the longitudinal side edges, each non-planar portion (i) comprises multiple ridges and valleys that taper smoothly from a wavy edge portion to an apex, or (ii) tapers from a wavy edge portion to an apex and comprises multiple ridges and valleys that are parallel to each other, the edge portion of each non-planar portion is located at an intermediary position along each longitudinal side edge, and the apexes of the two non-planar portions are pointing toward each other, wherein each layer of fibrous material is formed at (a) by Automated Tape Laying or Automated Fiber Placement to deposit a plurality of elongated fiber tapes side-by-side on a mold surface comprising surface contours that correspond to the non-planar portions in the intermediate preform blank (60, 80), wherein each elongated fiber tape comprising a nonwoven veil laminated to at least one side of a layer of unidirectional fibers, and the nonwoven veil comprises randomly arranged fibers selected from thermoplastic fibers, carbon fibers, and a combination thereof, and wherein the non-planar surface of the molding tool at (b) has a bent line (or valley) defined by two sloping surfaces, each sloping surface inclining from one end of the molding tool toward the middle.