Asymptotic study of thin elastic layer

2013 ◽  
Vol 7 ◽  
pp. 5385-5396
Author(s):  
M. Verid Abdelkader ◽  
A. Ait Moussa
Keyword(s):  
Elastic Layer ◽  
Asymptotic Study ◽  
Thin Elastic Layer

Multiply Loaded Timoshenko Beam on a Stressed Orthotropic Half-Plane via a Thin Elastic Layer

1993 ◽  
Vol 60 (2) ◽  
pp. 541-547 ◽  
Author(s):  
H. Bjarnehed
Keyword(s):  
Half Plane ◽  
Timoshenko Beam ◽  
Elastic Layer ◽  
Beam Theory ◽  
Singular Integral Equations ◽  
Uniaxial Stress ◽  
Shear Stresses ◽  
Fe Model ◽  
Tangential Load ◽  
Thin Elastic Layer

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.

Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer

1992 ◽  
Vol 59 (2S) ◽  
pp. S115-S122 ◽  
Author(s):  
Hans L. Bjarnehed
Keyword(s):  
Half Plane ◽  
Elastic Layer ◽  
Singular Integral Equations ◽  
Free Edge ◽  
Shear Stresses ◽  
Rigid Punch ◽  
Fem Model ◽  
Frictionless Contact ◽  
Thin Elastic Layer ◽  
Elastic Cushion

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.

Evolution of localized folding for a thin elastic layer in a softening visco-elastic medium

1996 ◽  
Vol 146 (2) ◽  
pp. 229-252 ◽  
Author(s):  
G. W. Hunt ◽  
H-B. M�hlhaus ◽  
A. I. M. Whiting
Keyword(s):  
Elastic Medium ◽  
Elastic Layer ◽  
Thin Elastic Layer

scholarly journals Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the  Rayleigh wave H/V ratio.

3D structure–2D plate interaction model

2019 ◽  
Vol 24 (10) ◽  
pp. 3354-3377 ◽  
Author(s):  
Matko Ljulj ◽  
Josip Tambača
Keyword(s):  
Elastic Layer ◽  
3D Structure ◽  
Three Dimensional ◽  
Interaction Model ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Model ◽  
Limit Model ◽  
Two Dimensional Model ◽  
Thin Elastic Layer

In this paper, we derive models for the interaction of a linearized three-dimensional elastic structure with a thin elastic layer of possibly different material attached to it. Rigorous derivation is performed by considering a thin three-dimensional layer and the asymptotics of the solution of the full remaining three-dimensional problem when the thickness [Formula: see text] of the thin layer tends to zero. Furthermore, the attached thin material is assumed to have the elasticity coefficients which are of order [Formula: see text], for [Formula: see text] with respect to the coefficients of the three-dimensional body. In the limit, five different models are obtained with respect to different choices of p, namely [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Furthermore a three-dimensional–two-dimensional model is proposed that has the same asymptotics as the original three-dimensional problem. This is convenient for applications because one does not have to decide in advance which limit model to use.

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