Determination of elastic parameters of the deformable solid bodies with respect to the Earth model

Guliyev, Hatam H.,Javanshir, Rashid J.,Hasanova, Gular H. Techno-Press 2018 Geomechanics & engineering Vol.15 No.5

The study of behavior and values of deformations in the geological medium makes the scientific basis of the methodology of synthesis of true values of parameters of its physico-mechanical and density properties taking into account the influence of geodynamic impacts. The segments of continuous variation of homogeneous elastic uniform deformations are determined under overall compression of the medium. The limits of these segments are defined according to the criteria of instability (on geometric form changes and on "internal" instability). Analytical formulae are obtained to calculate current and limiting (critical) values of deformations within the framework of various variants of small and large initial deformations of the non-classically linearized approach of non-linear elastodynamics. The distribution of deformation becomes non-uniform in the medium while the limiting values of deformations are achieved. The proposed analytical formulae are applicable only within homogeneous distribution of deformations. Numerical experiments are carried out for various elastic potentials. It is found that various forms of instability can precede phase transitions and destruction. The influence of these deformation phenomena should be removed while the physico-mechanical and density parameters of the deformed media are determined. In particular, it is necessary to use the formulae proposed in this paper for this purpose.

Elastodynamic analysis by a frequency-domain FEM-BEM iterative coupling procedure

Soares, Delfim Jr.,Goncalves, Kleber A.,de Faria Telles, Jose Claudio Techno-Press 2015 Coupled systems mechanics Vol.4 No.3

This paper presents a coupled FEM-BEM strategy for the numerical analysis of elastodynamic problems where infinite-domain models and complex heterogeneous media are involved, rendering a configuration in which neither the Finite Element Method (FEM) nor the Boundary Element Method (BEM) is most appropriate for the numerical analysis. In this case, the coupling of these methodologies is recommended, allowing exploring their respective advantages. Here, frequency domain analyses are focused and an iterative FEM-BEM coupling technique is considered. In this iterative coupling, each sub-domain of the model is solved separately, and the variables at the common interfaces are iteratively updated, until convergence is achieved. A relaxation parameter is introduced into the coupling algorithm and an expression for its optimal value is deduced. The iterative FEM-BEM coupling technique allows independent discretizations to be efficiently employed for both finite and boundary element methods, without any requirement of matching nodes at the common interfaces. In addition, it leads to smaller and better-conditioned systems of equations (different solvers, suitable for each sub-domain, may be employed), which do not need to be treated (inverted, triangularized etc.) at each iterative step, providing an accurate and efficient methodology.

On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration

Park, Kyoungsoo,Chi, Heng,Paulino, Glaucio H. North-Holland Pub. Co 2019 Computer methods in applied mechanics and engineer Vol.356 No.-

<P><B>Abstract</B></P> <P>While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field can be further explored and developed. Thus, in this paper, we employ the virtual element method for non-convex discretizations of elastodynamic problems in 2D and 3D using an explicit time integration scheme. In the formulation, a diagonal matrix-based stabilization scheme is proposed to improve performance and accuracy. To address efficiency, a critical time step is approximated and verified using the maximum eigenvalue of the local (rather than global) system. The computational results demonstrate that the virtual element method is able to consistently handle general nonconvex elements and even non-simply connected elements, which can lead to convenient modeling of arbitrarily-shaped inclusions in composites.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Exploring arbitrarily-shaped polygons/polyhedra in computational mechanics. </LI> <LI> The VEM is established for elastodynamics with explicit time integration. </LI> <LI> Novel diagonal matrix-based stabilization scheme improves VEM performance (and accuracy). </LI> <LI> The critical time step is evaluated using the maximum eigenvalue of a system of equations. </LI> </UL> </P>

An analytical solution for equations and the dynamical behavior of the orthotropic elastic material

Ramady, Ahmed,Atia, H.A.,Mahmoud, S.R. Techno-Press 2021 Advances in concrete construction Vol.11 No.4

In this article, an analytical solution of the dynamical behavior in an orthotropic non-homogeneity elastic material using for elastodynamics equations is investigated. The effects of the magnetic field, the initial stress, and the non-homogeneity on the radial displacement and the corresponding stresses in an orthotropic material are investigated. The analytical solution for the elastodynamic equations has solved regarding displacements. The variation of the stresses, the displacement, and the perturbation magnetic field have shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, and the non-homogeneity. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity.

유한요소법을 이용한 과도 선형 동탄성 해석

황은하(Eun-Ha Hwang),오근(Guen Oh) 한국산업융합학회 2009 한국산업융합학회 논문집 Vol.12 No.3

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

Study on the scattering of 2-D Rayleigh waves by a cavity based on BEM simulation

Weiwei Liu,조윤호,PHANHAI DANG,Jan D. Achenbach 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.3

A frequency domain boundary element method is introduced in this paper to simulate the scattering of two-dimensional Rayleigh waves by a cavity on the surface of an elastic half-space. This numerical method allows the Rayleigh wave to escape the truncated boundary without producing any spurious reflections. The numerical results of the displacements and stresses of a 2-D Rayleigh wave which travels along a flat surface of an elastic half-infinite medium are in good agreement when compared with theoretical ones. The problem of a Rayleigh wave scattering by a cavity on the surface of an elastic half-infinite medium is simulated by the proposed numerical method. The result is taken as the benchmark to introduce an approximate analytical method for such problems of scattering by a cavity on the surface. This numerical method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary scheme is discussed in detail.

Analytical solution of wave propagation in a non-homogeneous orthotropic rotating elastic media

A. M. Abd-Alla,S. R. Mahmoud 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.3

In this paper, the natural frequencies of the radial vibrations of a hollow cylinder and hollow sphere with different boundary conditions under influences of rotation and non-homogeneity have been studied. The radial vibrations of orthotropic material as affected by the angular velocity are investigated on the basis of the linear theory of elasticity. The of elastodynamic equations have been solved in analytical form. Numerical results are given and illustrated graphically for each case. Comparisons are made with previous results which given in the absence of rotation and non-homogeneity. The results indicate that the effect of rotation and non-homogeneity is very pronounced.

A study on the topographical and geotechnical effects in 2-D soil-structure interaction analysis under ground motion

Duzgun, Oguz Akin,Budak, Ahmet Techno-Press 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.40 No.6

This paper evaluates the effects of topographical and geotechnical irregularities on the dynamic response of the 2-D soil-structure systems under ground motion by coupling finite and infinite elements. A numerical procedure is employed, and a parametric study is carried out for single-faced slope topographies. It is concluded that topographic conditions may have important effects on the ground motion along the slope. The geotechnical properties of the soil will also have significantly amplified effects on the whole system motion, which cannot be neglected for design purposes. So, dynamic response of a soil-structure systems are primarily affected by surface shapes and geotechnical properties of the soil. Location of the structure is another parameter affecting the whole system response.

A study on the topographical and geotechnical effects in 2-D soil-structure interaction analysis under ground motion

Oguz Akin Düzgün,Ahmet Budak 국제구조공학회 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.40 No.6

This paper evaluates the effects of topographical and geotechnical irregularities on the dynamic response of the 2-D soil-structure systems under ground motion by coupling finite and infinite elements. A numerical procedure is employed, and a parametric study is carried out for single-faced slope topographies. It is concluded that topographic conditions may have important effects on the ground motion along the slope. The geotechnical properties of the soil will also have significantly amplified effects on the whole system motion, which cannot be neglected for design purposes. So, dynamic response of a soil-structure systems are primarily affected by surface shapes and geotechnical properties of the soil. Location of the structure is another parameter affecting the whole system response.

Effects of Surface Shapes and Geotechnical Conditions on the Ground Motion

Oguz Akin Düzgün,Ahmet Budak 대한토목학회 2015 KSCE JOURNAL OF CIVIL ENGINEERING Vol.19 No.5

The influences of surface geometry and local soil properties on ground motion are parametrically studied. The system response is numerically evaluated. In the modelling, finite and infinite elements are applied. Three types of topography (single-faced slopes, canyons and ridges) are taken into account. According to the results, topographic conditions, depth of the rigid bedrock and geotechnical properties have significance in the alteration of ground motion at the irregular soil surface and its surroundings. For all selected surface shapes, the most critical cases occur at top corners especially when the slope gets steeper. These cases are independent on the natural period of structures. The results correspond with those earthquakes where topographical effects are observed and could be seemed to be worthwhile from the perspective of earthquake engineering and seismology.