scholarly journals Triangular finite element in a mixed formulation for a flate problem of elasticity theory

2021 ◽  
Vol 1100 (1) ◽  
pp. 012047
Author(s):  
N A Gureeva ◽  
V V Ryabukha
Keyword(s):  
Finite Element ◽  
Elasticity Theory ◽  
Mixed Formulation ◽  
Triangular Finite Element

Convergence Analysis for the Nested Refinement of Triangular Finite Element

2011 ◽  
Vol 317-319 ◽  
pp. 1926-1930 ◽  
Author(s):  
Qi Sheng Wang ◽  
Yi Gao Zhao
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Convergence Analysis ◽  
Poisson Equation ◽  
Boundary Value ◽  
Triangular Mesh ◽  
Triangular Grid ◽  
Triangular Finite Element ◽  
Convergence Results

In this paper, the method of the nested refinement for triangular mesh and some relevant conclusions are considered. The Κ level triangular grid nested refinement on the plan domain Ω and some related properties are discussed , and the convergence results are obtained for the first boundary value problem of Poisson equation under the nested refinement of triangular finite element.

ON SENSITIVITY AND RELATED PHENOMENA IN THIN SHELLS WHICH ARE NOT GEOMETRICALLY RIGID

1999 ◽  
Vol 09 (01) ◽  
pp. 139-160 ◽  
Author(s):  
EVARISTE SANCHEZ-PALENCIA
Keyword(s):  
Finite Element ◽  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Lagrange Multiplier ◽  
Mixed Formulation ◽  
Thin Shells ◽  
Elastic Shells ◽  
Mixed Formulations

We consider the asymptotic behavior as the thickness 2ε tends to zero of thin elastic shells which are not geometrically rigid for the kinematic boundary conditions (non-inhibited shells). It is known that the limit displacement belongs to the subspace G of inextensional displacements. We write the corresponding mixed formulation with a Lagrange multiplier. It is then proved that the corresponding problem (equations and boundary conditions) is not elliptic, whatever the type of the surface. Examples are given where the interior smoothness of the data does not imply interior smoothness of the solutions. The topology of the space M of the multipliers is weaker than the L2 topology. In some cases it is even weaker than that of distributions (sensitivity phenomenon). As a consequence, the convergence of the problem in mixed formulation for thickness 2ε as ε tends to zero only holds in very poor topologies, implying non-uniformity with respect to ε of the finite element mixed formulations.

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