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Numerical solutions for cracks in an elastic half-plane

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Acta Mechanica Sinica 2019年第1期35卷 212-227,I0006页

作者： N.R.F.Elfakhakhre N.M.A.Nik Long Z.K.eshkuvatov Mathematics Department Faculty of ScienceUniversiti Putra Malaysia43400 SerdangSelangorMalaysia Institute for Mathematical Research Universiti Putra Malaysia43400 SerdangSelangorMalaysia Faculty of Science and Technology Universiti Sains Islam Malaysia71800 NilaiNegeri SembilanMalaysia

The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks.

关键词： Elastic half-plane Multiple cracks Singular integral equation Sine-shaped crack

Stress Intensity Factor for the Interaction between a Straight Crack and a Curved Crack in Plane Elasticity

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Acta Mechanica Solida Sinica 2016年第4期29卷 407-415页

作者： M.R.Aridi N.M.A.Nik Long Z.K.eshkuvatov Institute for Mathematical Research Universiti Putra Malaysia College of Foundation and General Studies Universiti Tenaga Nasional Mathematics Department Faculty of Science Universiti Putra Malaysia

Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.

关键词： hypersingular integral equation complex variable function method curved length coordinate method stress intensity factor

NUMERICAL SOLUTIONS FOR A NEARLY CIRCULAR CRACK WITH DEVELOPING CUSPS UNDER SHEAR LOADING

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Acta Mechanica Solida Sinica 2011年第5期24卷 439-449页

作者： N.M.A.Nik Long L.F.Koo Z.K.eshkuvatov Department of Mathematics Faculty of ScienceUniversity Putra Malaysia Institute for Mathematical Research University Putra Malaysia

In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.

关键词： nearly circular crack numerical method Galerkin method stress intensity factors hypersingular integral equation shear loading conformal mapping

Ionospheric precursors of strong earthquakes observed using six GNSS stations data during continuous five years(2011-2015)

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Geodesy and Geodynamics 2023年第1期14卷 65-79页

作者： H.E.eshkuvatov B.J.Ahmedov Y.A.Tillayev M.Arslan Tariq M.Ali Shah Libo Liu Ulugh Beg Astronomical Institute Astronomy St.33Tashkent 100052Uzbekistan National University of Uzbekistan University St.4Tashkent 100174Uzbekistan Institute of Fundamental and Applied Research National Research University TIIAMEKori Niyoziy 39Tashkent 100000Uzbekistan Centre for Earthquake Studies National Centre for PhysicsIslamabadPakistan Key Laboratory of Earth and Planetary Physics Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina College of Earth and Planetary Sciences University of Chinese Academy of SciencesBeijing 100049China Heilongjiang Mohe Observatory of Geophysics Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina

This study reports the morphological characteristics of anomalous variations in Global Navigation Satellite System Total Electron Content(GNSS-TEC) prior to the strong local earthquakes(EQ) that occurred during the period of *** have analyzed 20 earthquakes of magnitude M> 5.6.A statistical technique is implemented on the data of six GNSS stations located in Tashkent,Kitab,and Maidanak in Uzbekistan,and Islamabad,Multan,Quetta in *** results show continuous anomalous variations in TEC during 24 h befo re the occupancy of local *** is shown that the precursors before the occurrence of strong earthquakes,in particular of magnitude 5.7,7.7,7.5,7.8 and 7.3 are detected near Eastern Uzbekistan(26 May 2013),Southwestern Pakistan(24 September 2013),Hindukush region of Afghanistan(26 October 2015),and Central Nepal(25 April 2015) and(12 May 2015),*** ionospheric anomalies appearing before the strong earthquakes at six GNSS stations are registered in 14cases(70%) out of 20 selected *** is depicted that anomalies referred to as ionospheric precursors appeared about 1-7 days prior to the occurrence of strong earthquakes.

关键词： GNSS TEC Earthquakes Ionospheric precursors

Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

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Journal of Applied Mathematics and Physics 2014年第5期2卷 225-234页

作者： M. R. Aridi N. M. A. Nik Long Z. K. eshkuvatov Institute for Mathematical Research Universiti Putra Malaysia Serdang Selangor Malaysia Department of Mathematics Universiti Putra Malaysia Serdang Selangor Malaysia

In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.

关键词： Hypersingular Integral Equation Complex Variable Function Method Stress Intensity Factor

A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems

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Applied Mathematics 2018年第7期9卷 789-805页

作者： R. D. Aloev Z. K. eshkuvatov M. U. Khudayberganov N. M. A. Nik Long Faculty of Mathematics and Mechanics National University of Uzbekistan (NUUz) Tashkent Uzbekistan Faculty of Science and Technology Universiti Sains Islam Malaysia (USIM) Nilai Malaysia Institute for Mathematical Research (INSPEM) UPM Kuala Lumpur Malaysia Department of Mathematics Faculty of Science Universiti Putra Malaysia (UPM) Kuala Lumpur Malaysia

The class of three-dimensional quasilinear hyperbolic systems is studied. The initial boundary value problem for this class of quasilinear hyperbolic systems is given. By constructing the energy’s integral, a priori estimate for the solution of the initial boundary value problem is obtained. Difference scheme is constructed and an a priori estimate for its solution is obtained. Numerical example exhibits the efficiency and accuracy of the method.

关键词： Hyperbolic Systems Stability Quasilinear Equations