Finite Element Analysis of Elastic Contact Problems
01 Jan 1972-Jsme International Journal Series B-fluids and Thermal Engineering (The Japan Society of Mechanical Engineers)-Vol. 16, Iss: 95, pp 797-804
TL;DR: In this article, a method for evaluation of contact stresses between two or more elastic bodies with frictional forces on the contact surfaces, by means of a finite element method, is discussed.
Abstract: This paper discusses a method for evaluation of contact stresses between two or more elastic bodies with frictional forces on the contact surfaces, by means of a finite element method. The matrix equation is solved by some nodal points being prepared on the contact surfaces. These nodal points are classified into "adhere to" or "slide over" one another categories, depending upon whether frictional forces are greater than the shearing forces or not, and contact conditions are applied for each case. For example, numerical results for two rectangular plates and two cylindrical columns having different sizes and Young's moduli which are compressed into one another are obtained. Contact pressure along the contact surface of rectangular plates without friction is in good agreement with the exact solution for semi-infinite plate, except near the end of the contact surface. Also the influences of friction on the contact stresses are discussed.
Citations
More filters
TL;DR: In this paper, a finite element solution of structural mechanics problems with surface nonlinearities is presented, where only a few of the total number of degrees of freedom involved in the nonlinearity are eliminated by using the superelement technique.
162 citations
TL;DR: In this paper, a numerical procedure developed for solving the two-dimensional elastic contact problems with friction is presented, which is a generalization of a procedure developed by Francavilla and Zienkiewicz to include frictional effects under proportionate loading.
Abstract: A numerical procedure developed for solving the two-dimensional elastic contact problems with friction is presented. This is a generalization of a procedure developed by Francavilla and Zienkiewicz to include frictional effects under proportionate loading. The method uses the flexibility matrix obtained by inversion of condensed stiffness matrix formed by eliminating all the nodes except those where contact is likely to take place and those with external forces. Compatibility of displacements for both normal and tangential directions is applied to those nodes which do not slip. However, for the nodes which slip, compatibility of displacements is applied for normal direction only and slip condition is applied in the tangential direction. The technique has been applied to several problems and very good results have been obtained. The number of iterations needed are very small.
104 citations
TL;DR: In this article, a concise survey of the literature related to the large deformation elasto-plasticity problems including unilateral contact and friction is presented together with an extension of the friction law for large deformability analysis.
85 citations
TL;DR: In this paper, a finite-element technique for solving frictional contact problems is described based on logical steps to establish the contact geometry and regions of slip and nonslip, which can be extended readily to multiple contact surfaces.
60 citations
TL;DR: A review of contact algorithms under the aspects of mathematical exactness and practical applicability is given, and recommendations are given for a synthesis of different approaches.
47 citations
References
More filters
TL;DR: In this paper, the generalized Michell's stress function is used to obtain the solution for displacement and stress fields in a semi-inflnite elastic solid compressed by a rigid body with an arbitrary shape.
Abstract: In this paper, the analytical method of the axisymmetrical problem of elasticity by Hankel transforms, which was succesfully used by Sneddon for various interesting problems, is extended to the general asymmetrical problem by the aid of the generalized Michell's stress function. Furthermore, the general method is used to obtain the solution for displacement and stress fields in a semi-inflnite elastic solid compressed by a rigid body with an arbitrary shape. Numerical calculation is carried out for a simple case and the distributions of stresses in a e1astic solid have been made clear.
4 citations