Parkes neglected elastic strains and examined a classical problem of rigid- plastic structural dynamics for finding the deformation of a cantilever beam carrying a mass at its tip which is subjected to a short pulse loading. Symonds and Fleming examined the Parkes problem by making comparison between exact numerical solutions obtained from an ABAQUS program for an elastic-plastic beam and the rigid-plastic solution slightly modified to allow for large deformation. Further observation is acquired by comparision also with a simplified elastic-plastic approach based on treatment of elastic and plastic action in artificially separated stages. and Yu examined the Parkes problem associated with the elastic deformation by introducing root rotational spring of the beam, they indicate that the dynamic response of the spring-rigid plastic system is of three modes : (i) mode I , (il) mode IIa ;and (iii) mode IIb. This paper introduce and compare the theory between the Parkes , Symonds and Fleming and the Wang and Yu models. Basing on the extension of theoretical derivation one can find the difference among them. This difference can be used three non-dimensional parameters, that is, (1) t/T (The action time divides by the time taken for the plastic hinge to travel from the cantilever tip to the root.), (2) s/L (The distance from the traveling hinge to the tip of the beam divides by the length of the beam. ), (3) V/Vo (The absolute velocity of the striker divides by the initial yelocity of the striker.) are used to present it. For very small β and small ζ until tp/T - 0 of the mode I developed by Wang and Yu is similar to Parkes' models. No matter what value of β , the cantilever behavior of mode Ila is the same as that of mode IIb so long as the value of ζ is equal. The initial value of v* for the Wang-Yu model will approach Parkes only under the conditions of t*<< 1 andζ 0. β→∞ is approximated elastic analysis while β→0 tends to plastic analysis . The plastic behavior is very significant in the range of 0.1 <ζ< 0.5 for the same value of β in mode II.
Liang, M.T. and Chan, D.B.
"Note on Effect of Elastic Deformation at the Root of a Cantilever Beam,"
Journal of Marine Science and Technology: Vol. 3:
1, Article 4.
Available at: https://jmstt.ntou.edu.tw/journal/vol3/iss1/4