The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space S-1/2(Delta(mn)(2*)) on non-uniform type-2 triangulation. Based on the operators, we construct cu...The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space S-1/2(Delta(mn)(2*)) on non-uniform type-2 triangulation. Based on the operators, we construct cubature formula for two-dimensional hypersingular integrals. Some computing work have been done and the results are quite satisfactory.展开更多
Provides information on a study which proposed a spline method for solving two-dimensional Fredholm Integral Equations of second kind space with hypersingular kernels. Details on the quasi-interpolating operators; Inf...Provides information on a study which proposed a spline method for solving two-dimensional Fredholm Integral Equations of second kind space with hypersingular kernels. Details on the quasi-interpolating operators; Information on the cubature formulas; Formulas of the approximation method.展开更多
By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. I...By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.展开更多
In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansio...In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rec tangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.展开更多
Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is...Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method. In order to verify the method, several numerical examples are carried out. The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.展开更多
文摘The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space S-1/2(Delta(mn)(2*)) on non-uniform type-2 triangulation. Based on the operators, we construct cubature formula for two-dimensional hypersingular integrals. Some computing work have been done and the results are quite satisfactory.
基金the National Natural Science Foundation of China, and the Foundation for Doctoralprogram of the State Education Commission of
文摘Provides information on a study which proposed a spline method for solving two-dimensional Fredholm Integral Equations of second kind space with hypersingular kernels. Details on the quasi-interpolating operators; Information on the cubature formulas; Formulas of the approximation method.
基金supported by the National Natural Science Foundation of China (No. 10872213)
文摘By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.
文摘In this paper, we presen t the composite rectangle rule for the comp ut at ion of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel l/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rec tangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.
基金The project supported by the Foundation of the Science Research of the State Education Commission of the People's Republic of China
文摘Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method. In order to verify the method, several numerical examples are carried out. The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.
