Stress analysis of an elastic layer attached to an elastic half space of the same material

Unstable deformations of an elastic or elastoplastic layer on an elastic or elastoplastic half space, are studied under compressive forces. Various combinations of material properties are considered, e.g., an elastic layer on an elastoplastic half space, elastoplastic layer on an elastic half space, etc. Both the flow and the total deformation plasticity models are used and the corresponding results compared. The results seem to have relevance to the problem of folding of geological formations and crustal buckling under tectonic stresses.

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

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/10033 ◽

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.

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Accuracy of Stress Analysis Using Numerical Integration of Elastic Half-Space

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.300-301.1127 ◽

2013 ◽

Vol 300-301 ◽

pp. 1127-1135 ◽

Cited By ~ 14

Author(s):

Radim Čajka

Keyword(s):

Finite Element ◽

Stress Analysis ◽

Numerical Integration ◽

Half Space ◽

Elastic Half Space ◽

Rigidity Matrix ◽

Interaction Solutions ◽

Proposed Model ◽

Isoparametric Elements

In case of constructions placed on subsoil, it is necessary to create a rigidity matrix for the element subsoil. That rigidity matrix should be then added up in respective positions with the rigidity matrix of an element. To clarify the proposed model of the subsoil, a method is derived for determination of vertical subsoil stress analysis under any shape of a slab construction by means of numerical integration and theory of isoparametric elements using the Jacobian transformation. This approach is rather original and represents the key contribution of this work in interaction solutions. Using the proposed approach, the method can be employed for any shape of a finite element.

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