The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Nicolas Burq - One of the best experts on this subject based on the ideXlab platform.
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Random data Cauchy Theory for supercritical wave equations I: Local Theory
Inventiones mathematicae, 2008Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in H ^ s ( M ), s
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random data cauchy Theory for supercritical wave equations i Local Theory
Inventiones Mathematicae, 2008Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in Hs(M), s<1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct Local strong solution for a large set of initial data in Hs(M), where s≥1/4 in the case of a boundary less manifold and s≥8/21 in the case of a manifold with boundary.
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random data cauchy Theory for supercritical wave equations i Local Theory
arXiv: Analysis of PDEs, 2007Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct Local strong solution for a large set of initial data in $H^s(M)$, where $s\geq 1/4$ in the case of a boundary less manifold and $s\geq 8/21$ in the case of a manifold with boundary.
Nikolay Tzvetkov - One of the best experts on this subject based on the ideXlab platform.
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Random data Cauchy Theory for supercritical wave equations I: Local Theory
Inventiones mathematicae, 2008Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in H ^ s ( M ), s
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random data cauchy Theory for supercritical wave equations i Local Theory
Inventiones Mathematicae, 2008Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in Hs(M), s<1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct Local strong solution for a large set of initial data in Hs(M), where s≥1/4 in the case of a boundary less manifold and s≥8/21 in the case of a manifold with boundary.
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random data cauchy Theory for supercritical wave equations i Local Theory
arXiv: Analysis of PDEs, 2007Co-Authors: Nicolas Burq, Nikolay TzvetkovAbstract:We study the Local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct Local strong solution for a large set of initial data in $H^s(M)$, where $s\geq 1/4$ in the case of a boundary less manifold and $s\geq 8/21$ in the case of a manifold with boundary.
S.h. Hosseini - One of the best experts on this subject based on the ideXlab platform.
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eccentric impact analysis of pre stressed composite sandwich plates with viscoelastic cores a novel global Local Theory and a refined contact law
Composite Structures, 2014Co-Authors: M Shariyat, S.h. HosseiniAbstract:Abstract A novel double superposition power-exponential global–Local Theory and a refined contact law are developed to investigate eccentric low-velocity impact responses of rectangular sandwich plates with viscoelastic cores. The continuity conditions of the transverse normal and shear stresses at the interfaces between layers is satisfied a priori. Stiffness of the underneath layers is considered in the contact law as well, for the first time. The non-linear integro-differential governing equations are solved by a second-order finite element and a special numerical time integration procedure. Effects of the pre-stresses on the indentation and contact force are investigated for the first time. Moreover, effects of the eccentricity on the impact responses of the sandwich plates are discussed in detail, for the first time. Verification of the results is accomplished through comparing present results with experimental results of a known reference. Results show that in the eccentric impacts, the contact force and the absorbed energy increase. Therefore, the failure occurrence can be more likely in the eccentric impacts. Furthermore, by utilizing a viscoelastic core, the apparent stiffness of the contact region increases and consequently the impact force and the absorbed energy increase. Biaxial tension increases the impact force and consequently, leads to premature failures.
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Eccentric impact analysis of pre-stressed composite sandwich plates with viscoelastic cores: A novel global–Local Theory and a refined contact law
Composite Structures, 2014Co-Authors: M Shariyat, S.h. HosseiniAbstract:Abstract A novel double superposition power-exponential global–Local Theory and a refined contact law are developed to investigate eccentric low-velocity impact responses of rectangular sandwich plates with viscoelastic cores. The continuity conditions of the transverse normal and shear stresses at the interfaces between layers is satisfied a priori. Stiffness of the underneath layers is considered in the contact law as well, for the first time. The non-linear integro-differential governing equations are solved by a second-order finite element and a special numerical time integration procedure. Effects of the pre-stresses on the indentation and contact force are investigated for the first time. Moreover, effects of the eccentricity on the impact responses of the sandwich plates are discussed in detail, for the first time. Verification of the results is accomplished through comparing present results with experimental results of a known reference. Results show that in the eccentric impacts, the contact force and the absorbed energy increase. Therefore, the failure occurrence can be more likely in the eccentric impacts. Furthermore, by utilizing a viscoelastic core, the apparent stiffness of the contact region increases and consequently the impact force and the absorbed energy increase. Biaxial tension increases the impact force and consequently, leads to premature failures.
Zhen-gong Zhou - One of the best experts on this subject based on the ideXlab platform.
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Non-Local Theory behavior of multiple cracks in a functionally graded piezoelectric medium
Engineering Fracture Mechanics, 2016Co-Authors: Hai-tao Liu, Zhen-gong ZhouAbstract:Abstract In this paper, the non-Local Theory solution of multiple cracks in a functionally graded piezoelectric medium (FGPM) under the permeable electric boundary condition have been investigated. Overcoming the mathematical difficulty, a one-dimensional non-Local kernel is used instead of a two-dimensional one for the fracture problem to obtain stress and electric displacement fields near the crack tips. By using Fourier transform techniques, the present problem was reduced to the solution of dual integral equations, which unknown variable is jumps of displacement across the crack surface. The present solution exhibits no stress and electric displacement singularities at the crack tips when non-Local was used to investigate the problem. The non-Local solution yields a finite hoop stress at the crack tips, thus allows us to use the calculated maximum stress as a fracture criterion.
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Non-Local Theory solution to a rectangular crack in a 3D infinite orthotropic elastic medium
International Journal of Solids and Structures, 2015Co-Authors: Hai-tao Liu, Zhen-gong ZhouAbstract:Abstract The non-Local Theory solution to a rectangular crack in a 3D infinite orthotropic elastic medium is investigated by using the generalized Almansi’s theorem and the Schmidt method in the present paper. The problem is formulated through the double Fourier transform into three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Numerical examples are provided to illustrate the effects of the geometric shape of the rectangular crack and the lattice parameter on the stress fields near the crack edges. Different from the classical solutions, the present solutions exhibit no stress singularity along the rectangular crack edges in an orthotropic elastic medium. Thus, this allows us to use the maximum stress as a fracture criterion.
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Investigation of the behavior of a mode-I crack in functionally graded materials by non-Local Theory
International Journal of Engineering Science, 2007Co-Authors: Zhen-gong Zhou, Pei-wei ZhangAbstract:In this paper, the behavior of a mode-I crack in functionally graded materials is investigated by means of the non-Local Theory. The traditional concepts of the non-Local Theory are firstly extended to solve the mode-I crack fracture problem in functionally graded materials, in which the shear modulus varies exponentially with coordinate parallel to the crack. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are jumps of displacements across crack surfaces, not the dislocation density functions or the analysis functions. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near crack tips. The non-Local elastic solutions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. Numerical examples are provided to show the effects of the crack length, the parameter describing functionally graded materials, the lattice parameter of materials and the material constants upon the stress fields near crack tips.
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Non-Local Theory solution for a Mode I crack in piezoelectric materials
European Journal of Mechanics - A Solids, 2006Co-Authors: Zhen-gong ZhouAbstract:In this paper, the non-Local Theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric materials subjected to a uniform tension loading. The permittivity of the air in the crack is considered. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the materials constants, the electric boundary conditions and the lattice parameter on the stress and the electric displacement fields near the crack tips. It can be obtained that the effects of the electric boundary conditions on the electric displacement fields are large. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-Local elastic solutions yield a finite hoop stress at the crack tips, thus allowing us to use the maximum stress as a fracture criterion.
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The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-Local Theory
International Journal of Engineering Science, 2002Co-Authors: Zhen-gong Zhou, Biao WangAbstract:In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material plane under anti-plane shear waves is investigated by using the non-Local Theory for impermeable crack face conditions. For overcoming the mathematical difficulties, a one-dimensional non-Local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-Local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the circular frequency of incident wave and the lattice parameter. For comparison results between the non-Local Theory and the Local Theory for this problem, the same problem in the piezoelectric materials is also solved by using Local Theory.
M Shariyat - One of the best experts on this subject based on the ideXlab platform.
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Higher-order global-Local Theory with novel 3D-equilibrium-based corrections for static, frequency, and dynamic analysis of sandwich plates with flexible auxetic cores
Mechanics of Advanced Materials and Structures, 2018Co-Authors: A. Ghaznavi, M ShariyatAbstract:ABSTRACTIn the present article, a high-order global-Local Theory with three-dimensional elasticity corrections is employed to trace the Local and instantaneous variations of lateral deflections and...
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eccentric impact analysis of pre stressed composite sandwich plates with viscoelastic cores a novel global Local Theory and a refined contact law
Composite Structures, 2014Co-Authors: M Shariyat, S.h. HosseiniAbstract:Abstract A novel double superposition power-exponential global–Local Theory and a refined contact law are developed to investigate eccentric low-velocity impact responses of rectangular sandwich plates with viscoelastic cores. The continuity conditions of the transverse normal and shear stresses at the interfaces between layers is satisfied a priori. Stiffness of the underneath layers is considered in the contact law as well, for the first time. The non-linear integro-differential governing equations are solved by a second-order finite element and a special numerical time integration procedure. Effects of the pre-stresses on the indentation and contact force are investigated for the first time. Moreover, effects of the eccentricity on the impact responses of the sandwich plates are discussed in detail, for the first time. Verification of the results is accomplished through comparing present results with experimental results of a known reference. Results show that in the eccentric impacts, the contact force and the absorbed energy increase. Therefore, the failure occurrence can be more likely in the eccentric impacts. Furthermore, by utilizing a viscoelastic core, the apparent stiffness of the contact region increases and consequently the impact force and the absorbed energy increase. Biaxial tension increases the impact force and consequently, leads to premature failures.
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Eccentric impact analysis of pre-stressed composite sandwich plates with viscoelastic cores: A novel global–Local Theory and a refined contact law
Composite Structures, 2014Co-Authors: M Shariyat, S.h. HosseiniAbstract:Abstract A novel double superposition power-exponential global–Local Theory and a refined contact law are developed to investigate eccentric low-velocity impact responses of rectangular sandwich plates with viscoelastic cores. The continuity conditions of the transverse normal and shear stresses at the interfaces between layers is satisfied a priori. Stiffness of the underneath layers is considered in the contact law as well, for the first time. The non-linear integro-differential governing equations are solved by a second-order finite element and a special numerical time integration procedure. Effects of the pre-stresses on the indentation and contact force are investigated for the first time. Moreover, effects of the eccentricity on the impact responses of the sandwich plates are discussed in detail, for the first time. Verification of the results is accomplished through comparing present results with experimental results of a known reference. Results show that in the eccentric impacts, the contact force and the absorbed energy increase. Therefore, the failure occurrence can be more likely in the eccentric impacts. Furthermore, by utilizing a viscoelastic core, the apparent stiffness of the contact region increases and consequently the impact force and the absorbed energy increase. Biaxial tension increases the impact force and consequently, leads to premature failures.
