Non-convex Gao model for nonlinear elastic beam with inclined non-penetrating crack

Non-convex Gao model for nonlinear elastic beam with inclined non-penetrating crack Full article

Journal

Mathematics and Mechanics of Solids
ISSN: 1081-2865

Output data

Year: 2026, Volume: 31, Number: 3, Pages: 417–425 Pages count : 9 DOI: 10.1177/10812865251353453

Tags

Nonlinear beam, crack, non-penetration condition, non-convex optimization, variational inequality

Authors

Kovtunenko Victor A ^1,2 , Lazarev Nyurgun P ³

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2	Department of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Graz, Austria
3	Scientific Research Institute of Mathematics, North-Eastern Federal University, Yakutsk, Russian Federation

Funding (1)

Министерство науки и высшего образования Российской Федерации

FWGG-2021-0010

Large deflections of an elastic beam are considered within Euler–Bernoulli hypotheses. The Gao beam model couples nonlinear constitutive equations for longitudinal and vertical displacements. The setting is motivated to describe nonpenetration between surfaces of an inclined crack in the thick beam. The governing relations are established for the cracked beam, which are based on constrained minimization of a non-convex function of the strain energy. The variational solution is proved, optimality conditions are obtained in the form of variational inequality, and the complete system of nonlinear boundary conditions fulfilled at the crack is derived.

Kovtunenko V.A. , Lazarev N.P.
Non-convex Gao model for nonlinear elastic beam with inclined non-penetrating crack
Mathematics and Mechanics of Solids. 2026. V.31. N3. P.417–425. DOI: 10.1177/10812865251353453 WOS Scopus РИНЦ OpenAlex

Submitted:	Apr 13, 2025
Accepted:	Jun 12, 2025

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≡ Scopus:	2-s2.0-105012725316
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