scispace - formally typeset
Search or ask a question
DOI

An Elastic Half Space with a Moving Punch

22 Nov 2021-Vol. 16, pp 245-249
About: The article was published on 2021-11-22 and is currently open access. It has received 3 citations till now.
Citations
More filters
Journal ArticleDOI
TL;DR: In this article , the problems of wave propagation in a half-space due to the indentation by a rigid wedge at a constant speed and by a parabolic punch at constant acceleration have been considered separately.
Abstract: In this work, the problems of wave propagation in a half-space due to the indentation by a rigid wedge at a constant speed and by a parabolic punch at a constant acceleration have been considered separately. The elastodynamics problems of non-symmetric indentation over a contact region expanding at a constant speed and constant acceleration have been solved using the method of homogeneous functions. Following Cherepanov and Cherepanov et al., the general solution of the problems has been derived in terms of an analytic function of complex variables. The expressions for the stress component under the contact region and the torque over the contact region have been derived. Numerical results of the particular cases of the Problems I and III and of the Problems II and IV have been presented in the form of graphs. This work and its applications are expected to be helpful in the study of indentation-related problems of solid mechanics.

1 citations

Journal ArticleDOI
TL;DR: In this paper , the authors considered the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation.
Abstract: There are various numerical methods for solving integral equations. Among the new numerical methods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. We apply various modifications of the basis splines of the seventh order of approximation at the beginning, the middle, and at the end of the integration interval. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order for solving integral equations are given.

1 citations

Journal ArticleDOI
TL;DR: In this article , the authors considered the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation.
Abstract: We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order to solve integral equations are given.
References
More filters
Journal ArticleDOI
TL;DR: A comprehensive survey of recent works on inclusion in an infinite space, a half-space under prescribed surface loading or a halfspace under surface contact loading or in a finite space can be found in this paper.

209 citations

Journal ArticleDOI
TL;DR: In this paper, the contact behavior of a rigid cylindrical punch sliding on an elastically graded half-plane with shear modulus gradient variation in an arbitrary direction is investigated, and the governing partial differential equations and the boundary conditions are achieved with the help of Fourier integral transformation.
Abstract: Contact behavior of a rigid cylindrical punch sliding on an elastically graded half-plane with shear modulus gradient variation in an arbitrary direction is investigated. The governing partial differential equations and the boundary conditions are achieved with the help of Fourier integral transformation. As a result, the present problem is reduced to a singular integral equation of the second kind, which can be solved numerically. Furthermore, the presently general model can be well degraded to special cases of a lateral gradient half-plane and a homogeneous one. Normal stress in the contact region is predicted with different material parameters, which is usually used to estimate the possibility of surface crack initiation. The moment that is needed to ensure stable sliding of the cylindrical punch on the contact surface is further predicted. The result in the present paper should be helpful for the design of novel graded materials with surfaces of strong abrasion resistance.

46 citations

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate how complex variable techniques may be used to obtain closed-form solutions to dynamical problems in the classical theory of elasticity, such as the problem of a pair of punches moving along the lateral boundaries of the elastic strip and opening a crack along the mid surface.

39 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the axisymmetric problem of unilateral frictionless indentation of a thin stiff film bonded to a compliant substrate, which is assumed to be a homogeneous isotropic elastic half-space.

28 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional dynamic analysis of contact and stress loading problems associated with non-symmetric frictionless rigid indentation and plane crack extension under normal stress is presented.
Abstract: Two-dimensional dynamic analyses of contact and stress loading problems associated with non-symmetric frictionless rigid indentation and plane crack extension under normal stress are presented. The extension rates of the contact strip/crack surfaces are assumed to be constant and sub-critical. Homogeneous function techniques are used to derive general mathematical solutions which are then fitted to the physical problem by matching the predicted and prescribed displacement/stress distributions on the contact strip/crack surfaces. By studying several examples, it is seen that coupling between inherently symmetric and antisymmetric components of the mathematical solutions complicates this procedure. Moreover, the relation between loading and solution behavior is not always physically obvious, especially with regard to symmetry/antisymmetry.

21 citations