This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to c...This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).展开更多
The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full sti...The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction.Using the Papkovich-Neuber functions,the Fourier integral transform,and the asymmetric bipolar coordinates,the exact solution is obtained.Unlike the Johnson-Kendall-Roberts(JKR)model,the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses.Besides,it considers the full stick contact which has large values of the friction coefficient between contacting surfaces,contrary to the frictionless contact supposed in the JKR model.The result shows that suitable angles can be found,which makes the contact surfaces difficult to be peeled off or easy to be pressed into.展开更多
The dynamic behavior of two collinear cracks in a piezoelectric layer bonded to two half spaces under harmonic anti-plane shear waves was investigated by means of Schmidt method. The cracks are vertically to The bound...The dynamic behavior of two collinear cracks in a piezoelectric layer bonded to two half spaces under harmonic anti-plane shear waves was investigated by means of Schmidt method. The cracks are vertically to The boundary conditions of the electrical field the interfaces of the piezoelectric layer. were assumed to be the permeable crack surface. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. Numerical examples were presented to show the effect of the geometry of the interacting cracks, the piezoelectric constants of the materials and the frequency of the incident waves upon the stress intensity factors. The results show that the dynamic field will impede or enhance the propagation of the crack in a piezoelectric material at different stages of the frequency of the incident waves. It is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than that for the impermeable crack surface conditions.展开更多
This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surfac...This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.展开更多
The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic mater...The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.展开更多
文摘This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).
基金supported by the National Natural Science Foundation of China(Nos.11972257,11832014,and 11472193)the China Scholarship Council(CSC)the Fundamental Research Funds for the Central Universities(No.22120180223)。
文摘The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction.Using the Papkovich-Neuber functions,the Fourier integral transform,and the asymmetric bipolar coordinates,the exact solution is obtained.Unlike the Johnson-Kendall-Roberts(JKR)model,the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses.Besides,it considers the full stick contact which has large values of the friction coefficient between contacting surfaces,contrary to the frictionless contact supposed in the JKR model.The result shows that suitable angles can be found,which makes the contact surfaces difficult to be peeled off or easy to be pressed into.
文摘The dynamic behavior of two collinear cracks in a piezoelectric layer bonded to two half spaces under harmonic anti-plane shear waves was investigated by means of Schmidt method. The cracks are vertically to The boundary conditions of the electrical field the interfaces of the piezoelectric layer. were assumed to be the permeable crack surface. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. Numerical examples were presented to show the effect of the geometry of the interacting cracks, the piezoelectric constants of the materials and the frequency of the incident waves upon the stress intensity factors. The results show that the dynamic field will impede or enhance the propagation of the crack in a piezoelectric material at different stages of the frequency of the incident waves. It is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than that for the impermeable crack surface conditions.
文摘This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.
文摘The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.
