Approximation of the Axisymmetric Elasticity Equations with Weak Symmetry

04/22/2020
by   Alistair Bentley, et al.
0

In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a two dimensional problem on the meridian domain, involving weighted integrals. The problem is formulated in a mixed method framework with both the stress and displacement treated as unknowns. The symmetry condition for the stress tensor is weakly imposed. Well posedness of the continuous weak formulation and its discretization are shown. Two approximation spaces are discussed and corresponding numerical computations presented.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

11/12/2019

Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems

A hybridizable discontinuous Galerkin (HDG) formulation of the linearize...
11/03/2020

A multipoint stress-flux mixed finite element method for the Stokes-Biot model

In this paper we present and analyze a fully-mixed formulation for the c...
01/14/2020

A coupled multipoint stress – multipoint flux mixed finite element method for the Biot system of poroelasticity

We present a mixed finite element method for a five-field formulation of...
10/29/2020

Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity

We develop non-overlapping domain decomposition methods for the Biot sys...
03/01/2020

Least-squares for linear elasticity eigenvalue problem

We study the approximation of the spectrum of least-squares operators ar...
10/19/2020

A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem

A posteriori error estimates are constructed for the three-field variati...
01/26/2022

A well-posed First Order System Least Squares formulation of the instationary Stokes equations

In this paper, a well-posed simultaneous space-time First Order System L...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.