Modelling of the Effect of a Thin Stiffener on the Boundary of a Nonlinear Thermoelastic Plate

Abstract

Abstract. We consider a dynamic nonlinear model for a heterogeneous thermoelastic plate consisting of a thin highly rigid body of high thermal conductivity perfectly glued on a portion of the boundary of an elastic plate. This model, which describes the nonlinear oscillations of a plate subjected to thermal effects is referred to as the "full von Karman thermoelastic system". Our aim is to model this junction and reproduce the effect of the thin body by means of approximate boundary conditions, obtained by an asymptotic analysis with respect to the thickness of this body.

Multi-scale asymptotic expansion for a singular problem of a free plate with thin stiffener

“…Such structures are widely used in many engineering applications and their mathematical analysis has received a lot of attention in recent years. Besides, problems involving thin layers have been extensively investigated by several authors and a large amount of research has been carried out in this area (see [2][3][4][5][6]13,16,26,27] for acoustic or electromagnetic problems, [1,24] in the thermic framework, [14,19,21,22,28,29,31] for mechanical applications). These studies are in particular devoted to the question of the derivation of approximate boundary conditions that replace "in an approximate way" the effect of the thin layer.…”

Theoretical justification of Ventcel's boundary conditions for a thin layer three-dimensional thermoelasticity problem

“…The analysis of such kind of problems in the two-dimensional case can be found in [4,6,11,12,16,[22][23][24][25]. Let us mention the works [1,3,7,14] in the three-dimensional case.…”