Purpose The purpose of this paper is to use three-dimensional printers to fabricate functionally graded porous (FGP) beams, carry out impact loading and provide innovative equations. Design/methodology/approach In this study, using the three-dimensional printer, polylactic acid beams containing internal holes with distribution two-dimensional FGP beams of type X are fabricated. A simple tensile test and also a drop-weight impact test are performed to determine the mechanical and low-velocity impact properties of the beams. Inverse-tangent shear–strain function theory, together with the energy method, is used to derive the motion equations of low-velocity impact on the beam. A range of impact energies from 1.5 to 12 J and holes with diameters of 2 and 3 mm are used in the drop-weight impact testing machine. Findings As the hole diameter enlarges, there is a decrease in contact force and energy absorption levels. The larger hole diameter results in an extended contact duration, increased maximum impactor displacement, and a higher remaining impactor velocity. The innovative linear equations with a maximum error of 5.18% and nonlinear equations with a maximum error of 0.01% provide an acceptable result for the maximum contact force. For predicting the absorbed energy, the linear equation with a maximum error of 90.69% does provide an unacceptable result, and the nonlinear equation with a maximum error of 4.51% provides a reasonable result. Originality/value The originality of this research is in fabricating FGP beams with a three-dimensional printer to conduct impact tests and generate creative equations.
