Optimal Control of the Obstacle Inclination Angle in the Contact Problem for a Kirchhoff–Love Plate

被引：0

作者：

N. P. Lazarev ^{[1
]}

G. M. Semenova ^{[1
]}

E. D. Fedotov ^{[1
]}

机构：

[1] North-Eastern Federal University, Yakutsk

来源：

Lobachevskii Journal of Mathematics | 2024年 / 45卷 / 11期

关键词：

contact problem; Kirchhoff–Love plate; optimal control; Signorini condition; variational problem;

D O I：

10.1134/S1995080224606635

中图分类号：

学科分类号：

摘要：

Abstract: A family of contact problems depending on a parameter which determines an obstacle inclination angle for a Kirchhoff–Love plate is studied. Namely, we assume that in the initial state a given part of the boundary of the plate top surface touches a nondeformable obstacle. Furthermore, we assume that the obstacle shape composed by rectilinear segments and each segment (generatrix) forms an angle with the plane of the plate corresponding to its front surface. A boundary condition of Signorini’s type is imposed in the form of inequality, which depends on a slope coefficient or the obstacle inclination angle. The parameter varies in a given closed interval and determines variation of the angles between generatrices and the plate front surface. Taking the mentioned parameter as a control, we formulate an optimal control problem for a cost functional that characterizes the deviation of the solution from the specified displacements. We prove existence of a solution for the optimal control problem. The continuous dependence of solutions on the parameter is also established. © Pleiades Publishing, Ltd. 2024.

引用

页码：5383 / 5390

页数：7

共 34 条

[1]

Piersanti P., On the improved interior regularity of the solution of a second order elliptic boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle, Discrete Contin. Dyn. Syst, 42, pp. 1011-1037, (2022)

[2]

Regularity results for solutions to a class of obstacle problems, ’’ Nonlin. Anal. Real World Appl., 62, (2021)

[3]

Piersanti P., Asymptotic analysis of linearly elastic flexural shells subjected to an obstacle in absence of friction, J. Nonlin. Sci, 33, (2023)

[4]

Lazarev N.P., Nikiforov D.Y., Romanova N.A., Equilibrium problem for a Timoshenko plate contacting by the side and face surfaces, Chelyab. Phys. Math. J, 8, pp. 528-541, (2023)

[5]

Lazarev N.P., Kovtunenko V.A., Asymptotic analysis of the problem of equilibrium of an inhomogeneous body with hinged rigid inclusions of various widths, J. Appl. Mech. Tech. Phys, 64, pp. 911-920, (2023)

[6]

Rudoy E.M., Itou H., Lazarev N.P., Asymptotic justification of the models of thin inclusions in an elastic body in the antiplane shear problem, J. Appl. Ind. Math, 15, pp. 129-140, (2021)

[7]

Rudoy E., Sazhenkov S., Variational approach to modeling of curvilinear thin inclusions with rough boundaries in elastic bodies: Case of a rod-type inclusion, Mathematics, 11, (2023)

[8]

Fankina I.V., Furtsev A.I., Rudoy E.M., Sazhenkov S.A., A quasi-static model of a thermoelastic body reinforced by a thin thermoelastic inclusion, Math. Mech. Solids, 29, pp. 796-817, (2024)

[9]

Fankina I.V., Furtsev A.I., Rudoy E.M., Sazhenkov S.A., ‘The homogenized quasi-static model of a thermoelastic composite stitched with reinforcing threads, J. Comput. Appl. Math, 434, (2023)

[10]

Lazarev N.P., Romanova N.A., Optimal control of the angle between two rigid inclusions in an inhomogeneous 2D body, Math. Notes NEFU, 30, pp. 38-57, (2023)

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