The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity
Name
HPCES008.pdf
Size
549.4 KB
Format
Adobe PDF
Checksum (MD5)
086b3143d86e851b51df521753bc22b3
Author(s)
Bonet, J.
Huerta, A.
Peraire, Jaime
Date Issued
January 2002
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
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 involving large strain plane stress incompressible neo-hookean hyperelasticity.
Subjects
large strain elasticity
efficient bounds computation
finite element solutions
functional outputs
Persistent DSpace Link
