Quasistatic Delamination of Sandwich-Like Kirchhoff-Love Plates

Freddi, Lorenzo; Roubíček, Tomáš; Zanini, Chiara

doi:10.1007/s10659-012-9419-9

Cited by 14 publications

(11 citation statements)

References 49 publications

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“…A repeated Roman subscript signifies summation from 1 to 2. Equations (8) and (10) are equilibrium equations for the elastic part of the plate with respect to the (x 1 , x 2 )-plane and x 3 -axis, respectively. Conditions (13)- (15) are the complementarity conditions for contact of the crack faces.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

Rudoy

Shcherbakov

2020

Appl Math Optim

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Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.

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Section: Formulation Of the Problemmentioning

confidence: 99%

First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

Rudoy

Shcherbakov

2020

Appl Math Optim

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“…Условия непроникания, используемые для моделирования дефектов, обобщают нелинейные краевые условия, описывающие трещины без трения на берегах. Последние десятилетия характеризуются активным изучением задач равновесия в рамках моделей с нелинейными краевыми условиями, которые описывают поведение упругих тел и пластин с трещинами [4,5,6,7,8,9,10,11,12]. Задачи равновесия с краевыми условиями непроникания на берегах трещины для двуслойных конструкций впервые были рассмотрены в работах [13,14].…”

Section: Introductionunclassified

On the equilibrium problem for a two-layer structure with the upper layer covering a defect tip

Frankina¹

2020

Sib. Elektron. Mat. Izv.

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The equilibrium problem of a two-layer elastic structure is investigated. In the lower layer there is a rectilinear defect. The upper layer covers one of the defect tips and is glued to the lower layer along its edge. Nonlinear boundary conditions are used to model the defect. Using the variational approach, the existence of a solution of the problem is established. Passages to the limit in the problem with respect to a parameter characterizing the elasticity of the upper layer, as well as to the defect damage parameter are carried out. The optimal control problem is considered, in which the cost functional is the derivative of the energy functional with respect to the defect length, and two parameters mentioned above act as control functions. The solvability of the optimal control problem is proved.

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“…С такой точки зрения наиболее подходящими для описания поведения конструкций с дефектами являются модели с нелинейными условиями непроникания, допускающими только касание или расхождение берегов. Последние десятилетия ведется активная работа, относящаяся к исследованию нелинейных задач с краевыми условиями непроникания (см., например, [4,5,6,7,8,9,10,11]). Первыми работами, в которых в рамках моделей с условиями непроникания изучались задачи равновесия для двуслойных конструкций, являются статьи [12,13].…”

Section: Introductionunclassified

On equilibrium problem for a two-layer structure in the presence of a defect

Frankina¹

2019

Sib. Elektron. Mat. Izv.

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The equilibrium problem of the structure, which consists of two elastic plates, is considered. It is assumed that the plates are flatly deformed, and the layers are modeled as elastic bodies. Plates are glued along a given line. In addition there is a defect along the gluing line in one of the layers. On the defect faces, nonlinear boundary conditions containing the damage parameter are established. Using the variational approach, the solvability of this problem is proved. In the problem, the passage to the limit is carried out when the damage parameter tends to zero and to infinity. Differential formulations for the corresponding limit problems are obtained. The case of the rigidity of one of the layers tends to infinity is considered; the obtained limit problem is analyzed.

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Quasistatic Delamination of Sandwich-Like Kirchhoff-Love Plates

Cited by 14 publications

References 49 publications

First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

On the equilibrium problem for a two-layer structure with the upper layer covering a defect tip

On equilibrium problem for a two-layer structure in the presence of a defect

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