Determination of elastic stresses from discrete data on stress orientations

Galybin, A.N.; Мухамедиев, Ш. А.

doi:10.1016/j.ijsolstr.2004.04.007

Cited by 32 publications

(25 citation statements)

References 9 publications

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“…Hence, the reconstruction can be performed with high uncertainty. However, in practice, reconstructed plane stress tensors from the data on principal directions obtained from photoelastic experiments show satisfactory correlation with experimental observations and even allow for the determination of isotropic points of different types in the stress trajectory fields (see Galybin & Mukhamediev (2004) for details). It will be seen later on that in the three-dimensional case the reconstruction gives reasonable results for a modest number of data as well.…”

Section: Uniqueness and Connection With Interpolation And Boundary Vamentioning

confidence: 93%

“…Such formulations have been considered for the problem of stress-state identification in the Earth's crust by discrete data on stress orientations. Galybin & Mukhamediev (2004) suggested an approach for two-dimensional cases that has been validated by simulating photoelasticity data. The approach is based on the approximation of complex potentials by polynomials, which restricts higher order approximations for noisy data.…”

Section: Introductionmentioning

confidence: 99%

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On reconstruction of three-dimensional harmonic functions from discrete data

Galybin

Irša

2010

Proc. R. Soc. A.

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This study presents an approach for reconstruction of harmonic functions in three dimensions from the finite number of field and surface measurements. The approach, based on the Trefftz method, performs reconstruction as the best fit to the data and provides smoothness of the reconstructed function. Two particular algorithms are proposed; the first one uses specific radial basis functions and the second one is of finite element type. Either of them can be applied to analyse different data types but the latter can handle larger problems. The data types considered in this study also cover direct and inverse boundary value problems. Therefore, the proposed approach is universal and capable of dealing with both well-posed and ill-posed formulations. Examples from steady heat conduction and elastostatics are examined in order to investigate the efficiency of the approach.

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Section: Uniqueness and Connection With Interpolation And Boundary Vamentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

On reconstruction of three-dimensional harmonic functions from discrete data

Galybin

Irša

2010

Proc. R. Soc. A.

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“…in Galybin and Mukhamediev [17]. The differential equations of equilibrium (DEE) in complex form are used further on:…”

Section: Mathematical Model In Elasticitymentioning

confidence: 99%

Stress field in the Antarctic tectonic plate: elastic and plastic models

Haderka¹,

Galybin²,

Мухамедиев³

2009

Mesh Reduction Methods

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The purpose of this study is to compare different rheological models of tectonic plates for the same set of input data. First, the 2D elastic tectonic stress field in Antarctic plate is modelled by employing experimental data on principal stress orientations. Then the determination of the 2D stress field by assuming the Antarctic lithospheric plate to be in fully plastic state follows. Boundary conditions for the plastic model are specified from the elastic solution. A finitedifference type approach based of alternation of the Cauchy boundary value problems for the construction of the slip lines and the principal stress trajectories is applied to obtain distribution of the mean stress within Antarctic plate. The significance of rheology is underpinned by comparing the elastic and plastic fields of the mean stress.

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“…This structure of the data makes it impossible to directly transfer the methods used in photoelasticity to the problem of stress identification in the lithosphere. Therefore special approaches have recently been developed in [4][5][6]. These approaches make use of mathematical theory of plane elasticity [7], where the mean stress and deviatoric stress functions are described by means of two holomorphic functions, complex potentials.…”

Section: Introductionmentioning

confidence: 99%

FEM type method for reconstruction of plane stress tensors from limited data on principal directions

Irša¹,

Galybin²

2009

Mesh Reduction Methods

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This paper presents a method for reconstruction of maximum shear stress and stress trajectories from discrete data on principal directions. The domain is divided into smaller subdomains where stress potentials are assumed to be linear holomorphic functions. The functions obey continuity along element interfaces, which is used to form the first group of equations. The known data on principal directions are used in the second group of equations. Therefore, no stress magnitudes are involved in formulations, which eventually leads to a homogeneous system of linear algebraic equations. In order to make the system inhomogeneous an extra equation is added. It represents mean value of maximum shear stress over the domain. The reconstructed maximum shear stress, therefore, includes an arbitrary positive multiplicative parameter.

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Determination of elastic stresses from discrete data on stress orientations

Cited by 32 publications

References 9 publications

On reconstruction of three-dimensional harmonic functions from discrete data

On reconstruction of three-dimensional harmonic functions from discrete data

Stress field in the Antarctic tectonic plate: elastic and plastic models

FEM type method for reconstruction of plane stress tensors from limited data on principal directions

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