A finite element solution for the two‐dimensional elastic contact problems with friction
01 Aug 1981-International Journal for Numerical Methods in Engineering (John Wiley & Sons, Ltd)-Vol. 17, Iss: 8, pp 1257-1271
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.
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TL;DR: In this article, a joint/interface element for three-and two-dimensional finite element analysis is presented, which can model joints/interfaces between solid finite elements and shell finite elements.
Abstract: A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.
272 citations
TL;DR: In this article, the numerical behavior of zero thickness interface elements is further investigated, and it is shown that the Newton-Cotes integration scheme has no benefit over Gaussian integration, and that the problem of steep stress gradients is entirely one of inadequate mesh design.
Abstract: Many methods have been proposed to model joints in rocks or the interface between soil and a structure. Many analysts have reported numerical problems when using zero thickness interface elements while others have presented satisfactory results without comment of such difficulties. The numerical behaviour of zero thickness interface elements is further investigated in this paper. Some simple examples illustrate the application of interface elements to practical situations and highlight the numerical difficulties that may be encountered. Both ill-conditioning of the stiffness matrix and high stress gradients were found to cause numerical instability. Ill-conditioning can be reduced by careful selection of the size of the 2D elements adjacent to the interface. The problem of steep stress gradients is entirely one of inadequate mesh design. Contrary to other reports, this paper shows that the Newton–Cotes integration scheme has no benefit over Gaussian integration.
Analyses of a retaining wall using interface elements confirm the analytical values of active and passive earth pressure coefficients which are commonly used in analysis and design of retaining walls.
136 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 article, a numerical procedure for the solution of contact problems with Coulomb friction based on a complementarity problem formulation is developed for an incremental step, where two-dimensional elasticity problems discretized by the boundary element method are used for detailed derivation of the complementarity equations.
77 citations
TL;DR: In this article, a 3D finite element modeling of the nanoindentation test at the grain scale has been developed, making use of crystal plasticity constitutive laws, and six different virtual materials having the same macroscopic behaviour have been built.
72 citations
Cites methods from "A finite element solution for the t..."
...The contact problem is solved with a direct method called flexibility method (Francavilla and Zienkiewicz, 1975; Sachdeva and Ramakrishnan, 1981; Wronski, 1994; Jean, 1995)....
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01 Jan 1971
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
Abstract: Thank you very much for downloading the finite element method in engineering science. Maybe you have knowledge that, people have search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious bugs inside their computer.
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TL;DR: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications, more involved than the standard band–matrix algorithms, but more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes.
Abstract: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications. The technique is more involved than the standard band–matrix algorithms, but it is more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print-out.
884 citations
286 citations
TL;DR: In this paper, a modified finite element method for solving problems of elastic bodies in contact is described, which could be extended to solve other than elastic problems, and sample results agree well with corresponding exact solutions.
221 citations
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.
47 citations