Suggestion of a Framework of Similarity Laws for Geometric Distorted Structures Subjected to Impact Loading

Abstract

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

Material similarity of scaled models

“…For impact mechanics with strain hardening and strain-rate sensitive materials, recent researchers have developed several effective similarity systems [11,19,[21][22][23][24] to derive scaling factors. As a more concise, clear and effective system, the density-lengthvelocity (DLV) dimensional analysis system [23] was expressed as the seven main…”

“…Similar studies in previous works also define the correction factor of density and the geometry (for geometrically-distorted scaling). Since the three correction methods can convert to each other [23,24], the velocity correction factor Eq. (3), as one of the typical representatives, is mainly discussed in this paper.…”

“…However, this method can only provide inexact prediction ability and usually result in obvious errors for similarity. In further research, Wang and Xu et al [23,24] proposed geometric distortion similarity ability that adding a basic correction factor of geometrical thickness to compensate distortion of the different materials. But the average strain and average strain rate of the structure was required in the basic correction factor.…”