Dynamics of a rigid-plastic curvilinear plate of varying thickness with an arbitrary hole

Abstract

A perfect rigid-plastic body is used as a model to develop a general procedure for analyzing the dynamic behavior of an arbitrary curvilinear plate of variable thickness with an arbitrary internal hole. The plate is subjected to an arbitrary, uniform, short-term dynamic surface load. Two plate deformation patterns are considered. Analytic formulas for plastic zones, ultimate loads, and residual deflections are presented. Numerical examples are given Keywords: perfect rigid-plastic plate, curvilinear boundary, explosive load, free hole, ultimate load, residual deflectionIntroduction. The dynamic behavior of various curvilinear thin-walled structural elements under explosive loading is of interest because they are used as components of many engineering structures. The solutions to the bending problem for plastic plates with a free hole known from the literature are related to the dynamic behavior of the following plates of constant thickness: annular plates [12,14,15], curvilinear plates [5, 6], circular plates with an arbitrary hole [9], and to the limiting analysis of annular [1] and square [10,16] plates.We will analyze the dynamic behavior of hinged and clamped arbitrary curvilinear plates with varying thickness and an arbitrary free hole. An elliptic plate with a free rhombic hole and with piecewise-linear thickness function will be considered as an example.1. Model, Assumptions, and Equations of Motion. Let us consider a hinged or clamped perfect rigid-plastic plate with varying thickness and arbitrary smooth convex boundary L 1 (Fig. 1).There is a free hole with an arbitrary boundary L 2 in the middle of the plate. The plate is subject to a high explosive load P t ( ) uniformly distributed over the surface of the plate, instantaneously peaking (P P t

Modeling of Rigid-Plastic Dynamic Bending of Reinforced Layeredcircular Plates With Arbitrary Hole on Viscous Foundationunder Explosive Loads

“…Âåëè÷èíà d îïðåäåëÿåòñÿ èç óñëîâèÿ ìèíèìóìà ïðåäåëüíîé íàãðóçêè ïëàñòèíû. Ïðè äîñ-òàòî÷íî âûñîêèõ çíà÷åíèÿõ P max (ïðè «âûñîêèõ» íàãðóçêàõ) âîçìîaeíà ñõåìà 2, â êîòîðîé, êàê è äëÿ îäíîðîäíûõ ïëàñòèí [16,22,24,25], äåôîðìèðîâàíèå ñîïðîâîaeäàåòñÿ âîçíèêíîâåíèåì íåñòàöèîíàðíîé ïëàñòè÷åñêîé øàðíèðíîé îêðóaeíîñòè l, äâèaeóùåéñÿ ïîñòóïàòåëüíî (ðèñ. 2).…”

“…Èç (19) (10), (22). Äâèaeåíèå øàðíèðíîé ëèíèè l îïðåäåëÿåòñÿ èç (24). Äëÿ îáîèõ âàðèàíòîâ ñõåìû 2 (à è á) ëèáî ñóùåñòâóåò ìîìåíò âðåìåíè t 1 , êîãäà âûïîëíÿåòñÿ ðàâåíñòâî ) ( ) (…”

Plain deformation of elastoplastic material with profile shaped as a compact specimen (dynamic loading)

“…To study the processes of material fracture, in addition to experimental methods, it is also proposed to use numerical methods [1][2][3][4][5][6][7][8]. An approach of numerical modeling on the basis of a quasistatic model was developed in [1].…”

“…A method for numerical modeling of crack extension on the basis of a nonstationary elastoplastic model was developed in [5][6][7]. The stress-strain state of a rigid-plastic curvilinear plate of variable thickness with an arbitrary hole under dynamic loading was determined in [8]. In the present paper, the stress-strain state of an isotropic bar with a saw-cut crack is determined by solving a plane problem in the elastoplastic dynamic statement.…”