Refined models of contact interaction of a thin plate with positioned on both sides deformable foundations

被引：26

作者：

Badriev I.B. ^{[1
]}

Paimushin V.N. ^{[1
,2
]}

机构：

[1] Kazan (Volga Region) Federal University, Institute of Computational Mathematics and Information Technologies, Kazan

[2] Kazan National Research Technical University, Institute of Aviation, Land Vehicles and Energetics, Kazan

来源：

Lobachevskii Journal of Mathematics | 2017年 / 38卷 / 5期

基金：

俄罗斯科学基金会;

关键词：

contact interaction; elastic support elements; kinematic coupling equations; Kirchhoff–Love model; middle bending; the generalized variational principle; the simplified elasticity equations; Thin plate; Timoshenko model; transversely soft foundation; two-dimensional equations;

D O I：

10.1134/S1995080217050055

中图分类号：

学科分类号：

摘要：

We consider a rectangular plate connected along the outer contour with an absolutely rigid and fixed support through a low tough elastic support elements included in the class of transversely soft foundations. It is assumed that the contact interaction of plate at its points of faces of the connection to the support elements there is no relative slip and separation, and the opposite boundary surfaces of the support elements are fixed. Deformation of plate’s mid-surface is described by geometrically nonlinear relationships of the classical plate theory based on the hypothesis of the Kirchhoff–Love (the first option), and refined Timoshenko model taking into account the transverse shear compression (second version). The mechanics of support elements is described by the linearized equations of three-dimensional theory of elasticity, which have been simplified in the framework of transversely soft layer model. By integrating the latter equations along the transverse coordinate and satisfying to the conditions of the kinematic coupling of plate to the support elements at their initial compression in the thickness direction, two-dimensional geometrical nonlinear equations and their corresponding boundary conditions have been introduced, which describe the contact interaction of elements of the concerned deformable system. Simplification of derived relationships for the case when foundations have a symmetrical layer structure is carried out. © 2017, Pleiades Publishing, Ltd.

引用

页码：779 / 793

页数：14

共 29 条

[1]

Gudimov M.M., Perov B.V., Organic Glass, (1981)

[2]

Kargin V.A., Slonimskii G.L., Short Essays on the Physical Chemistry of Polymers, (1967)

[3]

Hillig W.B., Sources of weakness and the ultimate strength of brittle amorphous solids, Modern Aspects of the Vitreous State, 2, (1962)

[4]

Paimushin V.N., Firsov V.A., A method of mathematical description and solving boundary value problems in the mechanics of deformation of shells lying on a continuous or discrete elastic foundation, Problems of Machine Building, 16, pp. 18-23, (1982)

[5]

Paimushin V.N., Firsov V.A., Equations of the nonlinear theory of contact interaction of thin shells with deformable foundations of variable thickness, Mech. Solids, 20, pp. 118-126, (1985)

[6]

Paimushin V.N., Firsov V.A., Approximate formulation of problems of contact interaction of thin shells with deformable bases in the the contour, Izv. Akad. Nauk, Mekh. Tverd. Tela, 3, pp. 152-159, (1989)

[7]

Paimushin V.N., Firsov V.A., Mamedov K.B., Axisymmetric deformations of aircraft glazing elements with account for support compliance, Sov. Aeronaut., 30, 4, pp. 49-55, (1987)

[8]

Paimushin V.N., Firsov V.A., Glass Shells. Calculation of the Stress-Strain State, (1993)

[9]

Badriev I.B., Makarov M.V., Paimushin V.N., Solvability of physically and geometrically nonlinear problem of the theory of sandwich plates with transversally-soft core, Russ. Math., 59, 10, pp. 57-60, (2015)

[10]

Badriev I.B., Garipova G.Z., Makarov M.V., Paimushin V.N., Khabibullin R.F., Solving physically nonlinear equilibrium problems for sandwich plates with a transversally soft core, Lobachevskii J. Math., 36, pp. 474-481, (2015)

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