Solution of a delamination problem for the Timoshenko plate with bio-inspired hinge joint inclusions

Solution of a delamination problem for the Timoshenko plate with bio-inspired hinge joint inclusions Full article

Journal

Algorithms
ISSN: 1999-4893

Output data

Year: 2026, Volume: 19, Number: 10, Article number : 892, Pages count : DOI: 10.3390/a19100892

Tags

Newton algorithm; delamination; nonpenetration condition; hinge joint; Timoshenko plate; rigid inclusion

Authors

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

Affiliations

1	Scientific Research Institute of Mathematics, North-Eastern Federal University, Yakutsk 677000, Russia
2	Department of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria
3	Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk 630090, Russia

Inspired by bio-medical applications, a new mathematical model of the equilibrium of a heterogeneous Timoshenko plate with two thin rigid inclusions connected by a hinge joint is studied. It is assumed that one inclusion is not delaminated from the plate’s elastic matrix, while the second inclusion is delaminated on both sides, thus generating two cracks. Nonlinear conditions of the non-penetration type are imposed on the delaminated cracks. The existence of a variational solution to the delamination problem is established based on the Weierstrass theorem. Optimality conditions characterizing the solution in the domain, as well as on the curves describing the cracks and the inclusion, are derived in the form of a primal-dual system. For its solution, a semi-smooth Newton algorithm is provided rigorously and tested numerically.

Lazarev N.P. , Kovtunenko V.A.
Solution of a delamination problem for the Timoshenko plate with bio-inspired hinge joint inclusions
Algorithms. 2026. V.19. N10. 892 . DOI: 10.3390/a19100892

Submitted:	Sep 16, 2026
Accepted:	Oct 15, 2026
Published print:	Oct 18, 2026

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