On dimensionless numbers for dynamic plastic response of structural members

Abstract

A dimensional analysis is reported for the dynamic plastic response and failure of structural members, which includes material strain hardening, strain rate and temperature effects. Critical shear failure conditions are also discussed based on the dimensional analysis results. It is shown that the response number R n proposed in [3], is an important independent dimensionless number for the dynamic plastic bending and membrane response of structural members. However, additional dimensionless numbers are necessary when transverse shear, strain hardening, strain rate, and temperature effects are important. IntroductionThe dimensionless numbers obtained from dimensional analysis are useful for scaling purposes and for organising experimental model tests and numerical calculations to avoid any unnecessary repetition of the results in dimensionless space. A general dimensional analysis for structural mechanics has been discussed in [1], where important physical quantities in the dynamic inelastic response are considered in developing a complete set of dimensionless numbers using Buckingham P theory. The complete set of dimensionless numbers, although unique in number, may take different forms, so that the relative importance of various dimensionless numbers has to be determined by other means.To identify various impact regions in metals, Johnson [2] has used a damage numberwhere V 0 is the impact velocity, q is material density and r 0 is the mean¯ow stress.Recently, a new dimensionless response number, R n I 2 e qr 0 H 2 L H 2 was suggested in [3] for the dynamic plastic response of beams and plates made of rigidperfectly plastic materials, in which I e is the effective loading parameter de®ned later in Eq. (29) and L and H are the characteristic in-plane and transverse dimensions of the structural member, respectively. For impulsive loading, the response number can be expressed as R n D n L H 2 X 2Actually, this dimensionless number has been used extensively for the dynamic plastic response of structures for many years, [1]. The derivation of the response number in [3] is

Parkes' Problems Revisited: Application of Response Number

“…[2,3,4,6,7], it has been demonstrated that the response number is an important dimensionless number extensively utilized for dynamic plastic response of structures made of rigid-perfectly plastic materials. Actually, it should be pointed out that Zhao's response number can be used to study the elastic, plastic and dynamic plastic problems, and this dimensionless number would have a more extensive utilization for structural dynamics.…”

“…A general dimensional analysis for structural mechanics has been discussed by Jones in [1], where important physical quantities in the dynamic inelastic response are considered in developing a complete set of dimensionless numbers using Buckingham Π theorem. The dimensionless numbers obtained from dimensional analysis are useful for scaling purpose and for organizing experimental model tests and numerical calculations to avoid any unnecessary repetition of the results in dimensionless space [2], Recently, a new dimensionless number, response number,…”

“…Now R"(n) has been used for the dynamic plastic response of structural members in [2], structural bifurcation buckling in [4], plates in [6], and shells in [7] under uniformly distributed loading.…”

“…The response number R"{n) is an important independent dimensionless number [2] and might be used extensively for the dynamic plastic response of structure. Now R"(n) has been used for the dynamic plastic response of structural members in [2], structural bifurcation buckling in [4], plates in [6], and shells in [7] under uniformly distributed loading.…”

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AbstractResponse number R n (ft), proposed in [3,4], is an important independent dimensionless number for the dynamic response of structures [2], In this paper, the response number is applied to the dynamic plastic response of the well-known Parkes' problem, i.e., beams struck by concentrated mass.

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