An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To ...An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To solve this problem,a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term.The singular domain integral is transformed into a boundary integral using the radial integration method.Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates.The regular domain integral,after expressing the displacements in terms of the radial basis functions,is also transformed to the boundary using the radial integration method.Finally,a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.展开更多
The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral opera...The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.展开更多
Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We p...Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.展开更多
In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a sy...In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.展开更多
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introduci...The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.展开更多
In this paper, we develop a method for evaluating one dimensional singular integrals (weakly, strongly, and hyper-singular) that converge in the sense of Cauchy principal value and Hadamard finite part integrals. A pr...In this paper, we develop a method for evaluating one dimensional singular integrals (weakly, strongly, and hyper-singular) that converge in the sense of Cauchy principal value and Hadamard finite part integrals. A proof of convergence of this method is also provided.展开更多
In this paper, we study the class of one-dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ...In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.展开更多
In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the b...In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.展开更多
WT5”BZ]In this paper,we have introudced the notion of fuzzy semi-(inf-)singular,and dicussed their algebraic structure and properties.Mainly,we use these concepts and properties to research cancellative properties of...WT5”BZ]In this paper,we have introudced the notion of fuzzy semi-(inf-)singular,and dicussed their algebraic structure and properties.Mainly,we use these concepts and properties to research cancellative properties of fuzzy languages. [WT5”HZ]展开更多
基金supported by the National Natural Science Foundation of China(11172055 and 11202045)
文摘An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To solve this problem,a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term.The singular domain integral is transformed into a boundary integral using the radial integration method.Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates.The regular domain integral,after expressing the displacements in terms of the radial basis functions,is also transformed to the boundary using the radial integration method.Finally,a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.
基金Project supported by the National Natural Science Foundation of China (No. 10771110)the Major Project of the Ministry of Education of China (No. 309018)
文摘The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.
基金supported by NSFC(Nos.11471288,11371136 and 11671363)NSFZJ(LY14A010015)China Scholarship Council
文摘Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.
基金Project supported by the Fund of the State Education Commission of China
文摘In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.
基金Project supported by the National Natural Science Foundation of China (Grant No 10872141)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20060056005)
文摘The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
文摘In this paper, we develop a method for evaluating one dimensional singular integrals (weakly, strongly, and hyper-singular) that converge in the sense of Cauchy principal value and Hadamard finite part integrals. A proof of convergence of this method is also provided.
文摘In this paper, we study the class of one-dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
基金the National Natural Science Foundation of China(11688101 and 11431013)the National Natural Science Foundation of China(12022110,11201347 and 11671306).
文摘In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.
文摘In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.
文摘WT5”BZ]In this paper,we have introudced the notion of fuzzy semi-(inf-)singular,and dicussed their algebraic structure and properties.Mainly,we use these concepts and properties to research cancellative properties of fuzzy languages. [WT5”HZ]
