A New Family of Mixed Finite Elements for Elasticity PDF
Astrid SinwelApplications from engineering sciences, medicine, and other fields demand computational simulations of mechanical problems to predict deformations and stress fields. In a mathematical framework, this leads to partial differential equations which can be effectively treated by the finite element method. State of the art are the primal method using continuous displacements, Hellinger-Reissner and weak symmetry mixed methods. However, all of these methods have their drawbacks, such as locking effects for thin structures or nearly incompressible materials, or high computational complexity. In this work, the TD-NNS (Tangential-Displacement-Normal-Normal-Stress) method is introduced, which overcomes all above difficulties. Here, the displacement is sought in the Sobolev space H(curl), ensuring tangential continuity of the displacement vector. The stresses lie in the newly introduced, normal-normal continuous space H(divdiv). The variational formulation is analyzed thoroughly. A finite element scheme of arbitrary order is presented, stability and optimal orders of approximation are shown. Also, the method is robust when applied to nearly incompressible materials or thin structures.
This paper introduces a new family of nonconforming mixed finite elements for solving the linear elasticity equations on simplicial grids. Besides, this paper describes the construction of the Sinwel, Astrid A New Family of Mixed Finite Elements for ...
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A Mixed Finite Element Method for Elasticity Problem
This work presents a family of stable finite element methods for two- and three- dimensional linear elasticity models. The weak form posed on the skeleton of the ... Key words finite elements, mixed method, elasticity, conforming, symmetric ... stress symmetry methods also introduce a new variable into the formulation that ... that the family of generalized Zienkiewicz spaces presented here differs from the.
A New Family of Efficient Conforming Mixed … A new family of mixed finite elements is proposed for solving the classical Hellinger--Reissner mixed problem of the elasticity equations. For two dimensions, the …
This seminar is about a new family of mixed finite element methods for 2D and 3D compressible and incompressible nonlinear elasticity — compatible-strain mixed finite element methods (CSFEMs). These new computational methods allow one to accurately capture large deformations of solids. They have an outstanding performance for bodies with complex geometries, for … Residual-based a posteriori error estimates for …
This new finite element also works for the elasticity problem, and all estimates are valid ... Key words. mixed finite elements, finite volumes, Stokes flow, elasticity ... [ 19] J. C. NEDELEc,A New Family of Mixed Finite Elements in R3, Numer. A New Stabilization Method for the Elasticity Problem. Share on. Authors: ... Morley, M.: A family of mixed finite elements for linear elasticity. Numer. Math.