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Ho Chi Minh City, Vietnam

In this paper the interval-valued second-order differential equations under generalized Hukuhara differentiability (ISDEs) are introduced. Under suitable conditions we obtain the existence and uniqueness results of solutions to ISDEs. To prove this assertion we use idea of contraction principle and successive approximations. Furthermore, we use the method based on properties of linear transformations (LTM) to find the explicit solution of initial value problem for linear second-order differential equation with interval-valued forcing function and with interval initial values (IIVP). We apply the linear transformations method to two example problems including a vibrating mass and an electrical circuit. Finally, the method based on the analysis of a solution to real-valued second-order differential equation is investigated to solve interval-valued second-order differential equations with interval-valued coefficients, interval-valued forcing function and interval initial values. Some examples are presented to illustrate applicability of the proposed method. © 2015 Elsevier Inc. Source

Nguyen-Truong H.T.,Ton Duc Thang University
Journal of Physical Chemistry C | Year: 2015

We derive an analytical formula for the electron inelastic mean free path (IMFP) from its definition within the dielectric formalism. The parameters in this formula are determined solely by the optical energy-loss function of the material of interest. This formula is valid for electrons of energy larger than 500 eV, including relativistic electrons. © 2015 American Chemical Society. Source

Phung-Van P.,Ton Duc Thang University | Nguyen-Thoi T.,National University of Civil Engineering | Luong-Van H.,Ho Chi Minh City University of Technology | Lieu-Xuan Q.,Nguyen Tat Thanh University
Computer Methods in Applied Mechanics and Engineering | Year: 2014

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-MIN3 is extended to geometrically nonlinear analysis of functionally graded plates (FGPs) subjected to thermo-mechanical loadings. In the FGPs, the material properties are assumed to vary through the thickness by a simple power rule of the volume fractions of the constituents. The nonlinear formulation is based on the C0-type high-order shear deformation plate theory (C0-HSDT) and the von Kármán strains, which deal with small strains and moderate rotations. In the analysis process, both thermal and mechanical loadings are considered and a two-step procedure is performed including a step of analyzing the temperature field along the thickness of the plate and a step of analyzing the geometrically nonlinear behavior of the FGPs subjected to both thermal and mechanical loadings. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of available other numerical results. © 2013 Elsevier B.V. Source

Nguyen-Truong H.T.,Ton Duc Thang University
Applied Physics Letters | Year: 2016

We show that the dielectric approach can determine electron inelastic mean free paths in materials with an accuracy equivalent to those from first-principle calculations in the GW approximation of many-body theory. The present approach is an alternative for calculating the hot-electron lifetime, which is an important quantity in ultrafast electron dynamics. This approach, applied here to solid copper for electron energies below 100 eV, yields results in agreement with experimental data from time-resolved two-photon photoemission, angle-resolved photoelectron spectroscopy, and X-ray absorption fine structure measurements in the energy ranges 2-3.5, 10-15, and 60-100 eV, respectively. © 2016 Author(s). Source

Nguyen-Xuan H.,University of science | Thai C.H.,Ton Duc Thang University | Nguyen-Thoi T.,University of science
Composites Part B: Engineering | Year: 2013

We present in this paper a simple and effective formulation based on a fifth-order shear deformation theory (FiSDT) in combination with isogeometric finite element analysis (IGA) for composite sandwich plates. The FiSDT yields non-linear distribution of the transverse shear stresses through the plate thickness and ensures a prior tangential stress-free boundary condition. The IGA uses same basis functions, namely B-splines or non-uniform rational B-splines (NURBS), for preserving the precisely geometric representation and providing the numerical solution. It enables to achieve easily the smoothness with arbitrary continuity order and in the present method the C1-continuity requirement of higher order shear deformation models is fulfilled. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical examples are given to show high accuracy of the proposed method. © 2013 Elsevier Ltd. All rights reserved. Source

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