This paper presents the exact integral equation of Hertz's contact problem, which is obtained by taking into account the horizontal displacement of points in the contacted surfaces due to pressure.
Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first...Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.展开更多
The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state of axisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with...The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state of axisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with respect to time. Interpolation functions were introduced to approximate two unknown functions in each time subinterval and two new recursive formulae are derived. By using the recursive formulae, numerical results were obtained step by step. Under the same time step, the accuracy of the numerical results by the present method is much higher than that by the traditional quadrature method.展开更多
Through defining slide yield function and floating potential function of thermo-contact surface, the complementary equation of thermo-contact boundary has been reached, the fundamental equations to solve 3D thermo-con...Through defining slide yield function and floating potential function of thermo-contact surface, the complementary equation of thermo-contact boundary has been reached, the fundamental equations to solve 3D thermo-contact coupled problem have been listed. On this foundation, the finite element equation and definite solution condition of contact heat transfer have been given out. Based on virtual work principle and contact element technology, the finite element equation of 3D elastic contact system has been deduced under the effect of thermal stress. The pseudo load brought by contact gap have been introduced into this equation in order to reflect the contact state change. During iteration, once contact rigidity matrix is formed, it won’t change, which will make calculation reduce greatly.展开更多
The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), com...The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.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
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress func...After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.展开更多
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be dire...By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.展开更多
In the paper, we develop the fundamental solutions for a graded half-plane subjected to concentrated forces acting perpendicularly and parallel to the surface. In the solutions, Young’s modulus is assumed to vary in ...In the paper, we develop the fundamental solutions for a graded half-plane subjected to concentrated forces acting perpendicularly and parallel to the surface. In the solutions, Young’s modulus is assumed to vary in the form of E(y)=E0eαy and Poisson’s ratio is assumed to be constant. On the basis of the fundamental solutions, the singular integral equations are formulated for the unknown traction distributions with Green’s function method. From the fundamental integral equations, a series of integral equations for special cases may be deduced corresponding to practical contact situations. The validity of the fundamental solutions and the integral equations is demonstrated with the degenerate solutions and two typical numerical examples.展开更多
文摘This paper presents the exact integral equation of Hertz's contact problem, which is obtained by taking into account the horizontal displacement of points in the contacted surfaces due to pressure.
基金Supported by Natioal Science Foundation of China （10171073）.
文摘Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.
基金Project supported by the National Natural Science Foundation of China (No. 10472102) and Postdoctoral Foundation of China (No.20040350712)
文摘The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state of axisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with respect to time. Interpolation functions were introduced to approximate two unknown functions in each time subinterval and two new recursive formulae are derived. By using the recursive formulae, numerical results were obtained step by step. Under the same time step, the accuracy of the numerical results by the present method is much higher than that by the traditional quadrature method.
文摘Through defining slide yield function and floating potential function of thermo-contact surface, the complementary equation of thermo-contact boundary has been reached, the fundamental equations to solve 3D thermo-contact coupled problem have been listed. On this foundation, the finite element equation and definite solution condition of contact heat transfer have been given out. Based on virtual work principle and contact element technology, the finite element equation of 3D elastic contact system has been deduced under the effect of thermal stress. The pseudo load brought by contact gap have been introduced into this equation in order to reflect the contact state change. During iteration, once contact rigidity matrix is formed, it won’t change, which will make calculation reduce greatly.
基金supported by the National Natural Science Foundation of China (Grant No. 10871124)the Innovation Program of Shanghai Municipal Education Commission (Grant No. 09ZZ99)the ShanghaiLeading Academic Discipline Project (Grant No. J50103)
文摘The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.
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After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.
文摘By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.
基金supported by the National Natural Science Foundation of China ( No.10502040)the National Basic Research Program(No.2007CB707705)
文摘In the paper, we develop the fundamental solutions for a graded half-plane subjected to concentrated forces acting perpendicularly and parallel to the surface. In the solutions, Young’s modulus is assumed to vary in the form of E(y)=E0eαy and Poisson’s ratio is assumed to be constant. On the basis of the fundamental solutions, the singular integral equations are formulated for the unknown traction distributions with Green’s function method. From the fundamental integral equations, a series of integral equations for special cases may be deduced corresponding to practical contact situations. The validity of the fundamental solutions and the integral equations is demonstrated with the degenerate solutions and two typical numerical examples.
