scholarly journals Finite element approximations for near-incompressible and near-inextensible transversely isotropic bodies

2018 ◽  
Vol 117 (6) ◽  
pp. 693-712 ◽  
Author(s):  
F. Rasolofoson ◽  
B. J. Grieshaber ◽  
B. D. Reddy
Keyword(s):  
Finite Element ◽  
Transversely Isotropic ◽  
Finite Element Approximations ◽  
Isotropic Bodies

Analysis of Embedded and Surface Elliptical Flaws in Transversely Isotropic Bodies by the Finite Element Alternating Method

1991 ◽  
Vol 58 (2) ◽  
pp. 435-443 ◽  
Author(s):  
H. Rajiyah ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Transversely Isotropic ◽  
Generalized Solution ◽  
Solution Procedure ◽  
Isotropic Case ◽  
The Finite Element Method ◽  
Crack Face ◽  
Elastic Symmetry ◽  
Alternating Method ◽  
Isotropic Bodies

The general analytical solution to the problem of a flat elliptical crack embedded in an infinite, transversely isotropic solid, oriented perpendicular to the axis of elastic symmetry, is derived along the lines of Vijayakumar and Atluri’s solution procedure for the isotropic case. The prior work of Kassir and Sih on this problem is limited to some constant and linear variations of normal and shear tractions on the crack face. The generalized solution is employed in the Schwarz-Neumann alternating method in conjunction with the finite element method. Such a method of analysis is shown to be an efficient way to evaluate the stress intensity factors along the flaw border.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

scholarly journals On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations

2013 ◽  
Vol 51 (3) ◽  
pp. 1585-1609 ◽  
Author(s):  
Mark Ainsworth ◽  
Alejandro Allendes ◽  
Gabriel R. Barrenechea ◽  
Richard Rankin
Keyword(s):  
Finite Element ◽  
Adaptive Selection ◽  
Stabilized Finite Element ◽  
Finite Element Approximations ◽  
Selection Of
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