Plane Thermoelastic Deformation of a Multilayer Plate Elastically Coupled with a Rigid Half Plane
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PLANE THERMOELASTIC DEFORMATION OF A MULTILAYER PLATE ELASTICALLY COUPLED WITH A RIGID HALF PLANE N. M. Antonenko
UDC 539.3
We propose a method for the solution of two-dimensional stationary problems of thermoelasticity for a multilayer plate with elastic links between the layers elastically coupled with a rigid half plane. The procedure is based on the method of compliance functions with the use of the one-dimensional Fourier integral transformation. We construct the recurrence relations for the compliance functions that take into account the influence of thermal loads and the elastic links between layers. For a two-layer plate subjected to the action of thermal loads applied to the upper boundary of the plate, we analyze the influence of the elastic links, the coefficients of thermal expansion, and the heat-conduction coefficients on the distributions of normal and tangential stresses on the common boundary of the layers. Keywords: multilayer plate, elastic links, compliance matrices, integral Fourier transformation, stresses, temperature.
The airfield pavements, road surfaces, floors of the plant shops, and elements of engineering structures characterized by insignificant curvatures can be modeled in the form of multilayer plates. These objects suffer not only the action of mechanical loads but also the influence of thermal fields of different nature. Therefore, the problem of joint action of the mechanical and thermal loads on the stress-strain state and the distribution of temperature in layered structures attracts significant attention of the researchers. The thermoelastic deformations of objects of this kind in the case of full contact of the layers were studied in [1–7]. However, the actual structures may also contain intermediate gluing layers, which affect their strength. Therefore, they should be taken into account in the determination of the stress-strain state. In what follows, within the framework of the wellknown model developed in [8], we propose a procedure for the evaluation of the plane thermoelastic state of a layered plate with elastic links between the layers elastically coupled with the rigid half plane. It is assumed that tangential (normal) elastic links between two neighboring layers exist if the differences between the horizontal (vertical) displacements of points of the upper boundary of the lower layer and of the corresponding points of the lower boundary of the upper layer are proportional to the tangential (normal) stresses on their boundary. By the method of compliance functions, the solutions of the first boundary-value problem for these multilayer bodies were obtained in [9, 10] without taking into account the influence of the heat field. By the asymptotic methods, the problem of deformation of layered bodies with elastic links between the layers was studied in [11, 12]. The plane problem of thermoelasticity for a multilayer plate with full contact between the layers was solved in [13]. Statement of the Problem Consider a multilayer plate elastically coupled with a perfectly rigid
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