A directional framework of similarity laws for geometrically distorted structures subjected to impact loads

•The directional framework of similarity laws for structural impact is proposed, especially for geometric distortion.•Spatial directions and structural geometric characteristics are explicitly expressed in dimensionless numbers.•Correction methods of the velocity, the density and the geometry are used to address various distortion problems at scaling.•Various dimensionless response equations can be clearly, concisely and perfectly expressed.•Refined scaling analyses under the proposed framework are given numerically.