Geodesic
One approach to determination of the ultimate load-bearing capacity of mechanical systems with softening elements
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 4, pp. 762-773

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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, thin walled reservoir, limiting pressure.
Mots-clés : Hesse matrix 
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     title = {One approach to determination of the ultimate load-bearing capacity of mechanical systems with softening elements},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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V. V. Struzhanov; A. V. Korkin; A. E. Chaykin. One approach to determination of the ultimate load-bearing capacity of mechanical systems with softening elements. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 4, pp. 762-773. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_4_a8/