A finite element algorithm for incremental analysis of large three-dimensional frictional contact problems of linear elasticity

1993 ◽  
Vol 46 (4) ◽  
pp. 669-677 ◽  
Author(s):  
G. Zboiński
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Frictional Contact ◽  
Three Dimensional ◽  
Contact Problems ◽  
Incremental Analysis ◽  
Element Algorithm

A Three-Dimensional Frictional Contact Element Whose Stiffness Matrix is Symmetric

1999 ◽  
Vol 66 (2) ◽  
pp. 460-467 ◽  
Author(s):  
S. H. Ju ◽  
R. E. Rowlands
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Frictional Contact ◽  
Three Dimensional ◽  
Contact Problems ◽  
Contact Element ◽  
Penalty Function Method ◽  
Element Analysis ◽  
Finite Element Program

A three-dimensional contact element based on the penalty function method has been developed for contact frictional problems with sticking, sliding, and separation modes infinite element analysis. A major advantage of this contact element is that its stiffness matrix is symmetric, even for frictional contact problems which have extensive sliding. As with other conventional finite elements, such as beam and continuum elements, this new contact element can be added to an existing finite element program without having to modify the main finite element analysis program. One is therefore able to easily implement the element into existing nonlinear finite element analysis codes for static, dynamic, and inelastic analyses. This element, which contains one contact node and four target nodes, can be used to analyze node-to-surface contact problems including those where the contact node slides along one or several target surfaces.

Modelling an orthopaedic knee prosthesis as a layered elastic system part 2: Finite element analysis

1995 ◽  
Vol 30 (3) ◽  
pp. 195-203 ◽  
Author(s):  
M P Whelan ◽  
J E Mottershead ◽  
P D Edwards ◽  
E G Little
Keyword(s):  
Finite Element ◽  
Knee Prosthesis ◽  
Three Dimensional ◽  
Contact Problems ◽  
Element Analysis ◽  
Contact Algorithm ◽  
Benchmark Tests ◽  
System Part ◽  
Displacement Constraints ◽  
Element Algorithm

This study deals with the development of a specialized finite element algorithm suitable for a non-linear contact stress analysis of a model of a plastic tibial plateau of a typical unicondylar knee prosthesis. The principle feature of the contact algorithm is the use of Lagrange multiplier methods for the application of displacement constraints to surface Gauss points of a contacting body to prevent mesh overlap. This allows the effective modelling of two- and three-dimensional contact problems, with or without friction, using higher order elements. Through the selection of suitable benchmark tests, the performance and accuracy of the algorithm was assessed prior to the model analysis. Good agreement was obtained between the finite element results for the contact model and existing theoretical and experimental data. It was found that the Hertzian theory failed to accurately predict localized stresses at the contact interface when the indenter was much stiffer than the model.

A Reduced Full-System Finite Element Approach to the Solution of EHL Problems: Line Contacts

2010 ◽  
Author(s):  
W. Habchi ◽  
J. Issa
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Degrees Of Freedom ◽  
Contact Problems ◽  
Full System ◽  
Acceptable Solution ◽  
Line Contacts ◽  
Order Of Magnitude ◽  
Element Approach ◽  
Basis Method

This paper presents a reduced full-system finite element solution of isothermal elastohydrodynamic (EHD) line contact problems. The proposed model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, three different techniques are tested: the classical “Modal reduction” and “Ritz-vector” methods and a novel “EHL-basis” method. The reduction order in the first two appears to be insufficient and a large number of degrees of freedom is required in order to attain an acceptable solution. On the other hand, the “EHL-basis” method shows up to be much more efficient, requiring only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude cpu time gain with errors of the order of only 1‰ for the central and minimum film thicknesses.

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