Dynamic rigid-plastic deformation of arbitrarily shaped plates

Abstract

A rigid, perfectly-plastic model of solids is applied to study the dynamic behavior of simply supported or clamped, arbitrarily shaped plates on visco-elastic foundation. The role of membrane forces and transverse shear forces in the yield condition and the influence of geometry changes are neglected. The plate is subjected to explosive loads uniformly distributed over the surface. Several mechanisms of dynamic deformation of the plate are considered. For each mechanism, equations of the dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for the limit and high loads and for the maximum final deflections are obtained. Detailed analyses are given for an astroid-shaped plate, for a plate with a contour consisting of two arcs and for a plate with an internal free hole or a rigid insert.

Plastic quasistatic deformation of circular membranes and membrane shells considering thickness variation and hardening

“…It is quite difficult to perform a numerical analysis of the solutions to the problems of plastic quasistatic and dynamic deformation of circular plates, membranes and membrane shells based on the energy dissipation and external load power balance [13][14] or a direct integration of the initial system of nonlinear equations [15][16][17][18][19][20].…”

Modeling of Behavior of Doubly Connected Rigid-Plastic Plateof Arbitrary Form With the Internal Curvilinear Supportunder Explosive Loads

“…2à, á). Ñ÷èòàåì, êàê è â ñëó÷àå êðèâîëèíåéíûõ ïëàñòèí, ðàññìîòðåííûõ â [1,4], ÷òî íà îïîðíîì êîíòóðå óãîë ïîâîðîòà ïëîñêîñòè ïëàñòèíû â íàïðàâëåíèè äåéñòâèÿ íàãðóçêè íå çàâèñèò îò ïàðàìåòðà ν 2 . Îáîçíà÷èì åãî ÷åðåç α.…”

“…Ó÷èòûâàÿ, ÷òî íà ñâîáîäíûõ êîíòóðàõ L 2 è L 3 íîðìàëüíûé èçãèáàþùèé ìîìåíò M nn ðàâåí íóëþ, íà ó÷àñòêàõ ëèíèè l h îí ðàâåí M 0 è íà îïîðå L 1 ðàçðûâ óãëîâîé ñêîðîñòè ðàâåí íóëþ, äåéñòâóÿ, êàê â [1,4,5], äëÿ ìîùíîñòè âíóòðåííèõ ñèë (3) ïîëó÷àåì âûðàaeåíèå . ) (…”