In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions...In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.展开更多
In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By...In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.展开更多
The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. B...The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.展开更多
The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fou...The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.展开更多
文摘In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.
基金Project supported by the SRF for ROCS,SEM,the National Natural Science Foundation of Heilongjiang Province(No.A0301)and the Multidiscipline Scientifc Research Foundation of Harbin Institute of Technology(HIT.MD2001.39).
文摘In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.
基金supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province，哈尔滨工业大学校科研和教改项目
文摘The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.
文摘The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.
