Bounds on dynamic plastic deformation of hexagonal frames

The response of thin walled subassembly ducts of hexagonal cross section to an internal pulse of arbitrary shape is studied. A typical reactor core configuration consists of an array of such constituents, each containing an array of fuel elements, whose failure may expose the duct to an internal pressure pulse, causing permanent deformation that can reach the order of the wall thickness and cause contact between adjacent elements. The purpose of this study is to consider the possibility of application of bounding techniques developed in the dynamics of elastoplastic structures, which permit to bound from above total or permanent displacements under given dynamic actions, with a computational effort moderate with respect to a step-by-step evolutive dynamic analysis. The duct is conceived as a hexagonal frame and the effects of interaction between bending and membrane forces is accounted for, both in the plasticity condition and in its geometric consequences. In particular, attention is drawn on the following points: (1) In the small deformation range the response to different pulse shapes is compared, and some conclusion on the effect of the peak value, total impulse and duration is drawn. (2). The possibility of applying second order theory when the permanent deformation is too large to be studied as in point (1) is considered. The underlying hypotheses and the conditions for the validity of this procedure are indicated. (3) Conditions under which the pulse can be substituted by an initial velocity or by a step pulseof unlimited duration are also discussed. Results are graphically illustrated and compared with those obtained by other authors under the assumption of rigid, perfectly plastic material behavior. Comparisons show good agreement in several cases