What was Timoshenko's small-increment method? With an application to low-velocity impact of a wood beam

This study reviews the article by Timoshenko (Z Angew Math Phys 62(1-4):198-209, 5), and how two other researchers have interpreted the numerical method he employed. The numerical method is then compared to some standard contemporary methods, showing the continuous historical development. Additional important contributions in the impact literature are systematically compared and then applied to the low-velocity impact prediction of a wood beam, which has not been done yet. How to obtain the material parameters needed for the prediction are discussed and also how the impact testing can be used to obtain dynamic material properties are discussed in detail. The predictions using the methods developed by past researchers for metals are qualitatively a good starting point, showing where areas in impact testing of wood can be improved.