This article is cited in 3 papers

Short Communication

One approach to determination of the ultimate load-bearing capacity of mechanical systems with softening elements

V. V. Struzhanov^a, A. V. Korkin^b, A. E. Chaykin<sup>b

a</sup> Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation
^b Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, 620000, Russian Federation

Abstract: The fundamental provisions of the limiting load calculation theory are presented for a discrete mechanical system with softening elements. The method is based on the numerical determination of degenerate critical points for the potential function of the system. At these points there is a transition from the stability of the loading process to instability such as a catastrophe or a failure. This approach helps to avoid solving a large number of nonlinear equilibrium equations. The problem of determining the limiting internal pressure in a thin walled cylindrical tank is solved as an example. A unified potential specially defined for a flat square element of material in biaxial tension is used in developing a potential function of the system. It describes all stages of deformation including the softening stage.

Keywords: potential function, degenerate critical points, unified potential, Hesse matrix, thin walled reservoir, limiting pressure.

UDC: 539.3

MSC: 74C10

Received: May 11, 2018
Revised: October 11, 2018
Accepted: November 12, 2018
First online: December 11, 2018

DOI: 10.14498/vsgtu1624

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