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
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
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.
