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.
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 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.