Abstract2018-05-24T12:52:58+00:00

The efficient computation of bounds for functionals of finite element solutions in large strain elasticity

Author (s): J. Bonet, A. Huerta and J. Peraire
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 191, Issue 43
Pages: 4807 – 4826
Date: 2002

Abstract:
We present an implicit a posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications in- volving large strain plane stress incompressible neo-Hookean hyperelasticity

  
  

Bibtex:

@article{JP-BHP:02,
  Author   = {Bonet, Javier and Huerta, Antonio and Peraire, Jaume},
  Title    = {The efficient computation of bounds for functionals of finite element solutions in large strain elasticity},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Eng.},
  Volume   = {191},
  Number   = {43},
  Pages    = {4807--4826},
  Year     = {2002}}