On improved rectangular finite element for plane linear elasticity analysis

2005 ◽  
Vol 14 (8) ◽  
pp. 985-997 ◽  
Author(s):  
Mohamed Tahar Belarbi ◽  
Toufik Maalem
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Elasticity Analysis ◽  
Plane Linear Elasticity

An analysis of some mixed-enhanced finite element for plane linear elasticity

2005 ◽  
Vol 194 (27-29) ◽  
pp. 2947-2968 ◽  
Author(s):  
F. Auricchio ◽  
L. Beirão da Veiga ◽  
C. Lovadina ◽  
A. Reali
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Plane Linear Elasticity

Experimental and Theoretical Study of the Contact Mechanics of Five Total Knee Joint Replacements

1995 ◽  
Vol 209 (4) ◽  
pp. 225-231 ◽  
Author(s):  
T Stewart ◽  
Z M Jin ◽  
D Shaw ◽  
D D Auger ◽  
M Stone ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Knee Joint ◽  
Contact Pressure ◽  
Contact Stress ◽  
Linear Elasticity ◽  
Contact Area ◽  
Elasticity Analysis ◽  
Joint Replacements ◽  
Total Knee ◽  
Maximum Contact

The tibio-femoral contact area in five current popular total knee joint replacements has been measured using pressure-sensitive film under a normal load of 2.5 kN and at several angles of flexion The corresponding maximum contact pressure has been estimated from the measured contact areas and found to exceed the point at which plastic deformation is expected in the ultra-high molecular weight polyethylene (UHMWPE) component particularly at flexion angles near 90°. The measured contact area and the estimated maximum contact stress have been found to be similar in magnitude for all of the five knee joint replacements tested. A significant difference, however, has been found in maximum contact pressure predicted from linear elasticity analysis for the different knee joints. This indicates that varying amounts of plastic deformation occurred in the polyethylene component in the different knee designs. It is important to know the extent of damage as knees with large amounts of plastic deformation are more likely to suffer low cycle fatigue failure. It is therefore concluded that the measurement of contact areas alone can be misleading in the design of and deformation in total knee joint replacements. It is important to modify geometries to reduce the maximum contact stress as predicted from the linear elasticity analysis, to below the linear elastic limit of the plastic component.

scholarly journals Domain decomposition and multiscale mortar mixed finite element methods for linear elasticity with weak stress symmetry

2019 ◽  
Vol 53 (6) ◽  
pp. 2081-2108
Author(s):  
Eldar Khattatov ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Normal Stress ◽  
Linear Elasticity ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Decomposition Methods ◽  
Interface Problem ◽  
Element Formulation ◽  
Element Space

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier to impose interface continuity of normal stress or displacement, respectively. By eliminating the interior subdomain variables, the global problem is reduced to an interface problem, which is then solved by an iterative procedure. The condition number of the resulting algebraic interface problem is analyzed for both methods. A multiscale mortar mixed finite element method for the problem of interest on non-matching multiblock grids is also studied. It uses a coarse scale mortar finite element space on the non-matching interfaces to approximate the trace of the displacement and impose weakly the continuity of normal stress. A priori error analysis is performed. It is shown that, with appropriate choice of the mortar space, optimal convergence on the fine scale is obtained for the stress, displacement, and rotation, as well as some superconvergence for the displacement. Computational results are presented in confirmation of the theory of all proposed methods.

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