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ABSTRACTA general numerical method previously developed for analyzing large dynamic two-dimensional deformations of simple structures (and of large ax 4 ;ymmetric dynamic deformations of plates and shells with rotational symmetry) has been extended and evaluated through comparisons of predictions with experimental dynamic response and permanent-deformation data from explosively-loaded beams and circular rings. The method accounts for elastic, perfectly-plastic, strain hardening, and strain rate behavior of the structural material, and the experimental specimens employed were chosen to emphasize one or more of these characteristics and to provide tests of the adequacy of the theoretical prediction method.The governing finite-difference equations may be interpreted as representing a finite number of concentrated masses connected by straight extensible elements with bending concentrated at the mass locations themselves. The increments in stress resultants and stress couples are determined by idealizing the shell thickness as consisting of n (even) concentrated layers of material separated by a material that cannot carry norma] stress but has infinite shear rigidity. The influences of the number of layers in the idealized-thickness model, the spacing between these layers, the number of masses employed, as well as the aforementioned types of material behavior are demonstrated and discussed in detail. The present method also permits examining the subsequent partitioning of the initial input kinetic energy of impulsively-loaded structures into plastic, elastic, and kinetic forms; this feature iz also illustrated and discussed.iii Transient response comparisons of the present method, ri-id-plastic theory, and experiment show that the present method yields considerably better results with essentially no greater labor than required for the very restrictive rigid-plastic theory. For cases in which the plastic energy absorption is a large fraction of the initial energy input to impulsively-loaded structures, a simple approximate energy method, a rigid-plastic transient-response theory, and the present method predict comparable permanent deformations, but not otherwise.
The axisymmetric responses of shells, plates, rings, and beams to impulsive or blast loading that produces large deformations involving both the elastic and plastic regions of material behavior are analyzed. A general numerical method that includes 1) elastic, 2) perfectly plastic, 3) elastic, strain-hardening, and/or 4) elastic, strain-hardening, strain-rate sensitive material behavior and large structural deflections has been formulated and applied. In the timewise step-by-step numerical analysis, the increments in stress resultants and stress couples are determined by idealizing the shell thickness as consisting of n concentrated layers of materials separated by a material that cannot carry normal stresses but has infinite shear rigidity. The influences of the number of layers employed in the idealized model, as well as the forementioned various types of material behavior, are demonstrated. Theoretical predictions of time history responses and/or final structural deformations are compared with experimental data for impact-loaded spherical shells, for blast-loaded circular plates, and for explosively loaded circular rings and clamped beams.
Based upon the theoretical formulation presented in Part 1 of this paper, improvements in accuracy and computational efficiency are realized. Comparisons of predictions with experimental transient large deformations and strains show good agreement.
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