An Efficient Finite Difference Sensitivity Analysis Method Allowing Remeshing In Large Deformation Problems.

Abstract

The use of finite difference sensitivity analysis in large scale industrial problems is
frequently avoided due to its high computational cost and approximation errors when
compared to the analytical approach. Although in iteratively solved problems the high cost
may be greatly reduced, a major problem of the usual finite difference approach is that it
fails when remeshing is required. This happens because the errors caused by parametric
inversion and interpolation in variables transfer from the old to the new mesh may have the
same order of magnitude than the sought gradient components. This paper presents an
efficient finite difference approach that allows remeshing, not being affected by the mentioned
errors. The low cost and the accuracy of the sensitivity fields obtained after remeshing are
shown in two examples, with shape and constitutive design variables respectively. Although it
is presented in the frame of large strain elastoplasticity with linear isotropic hardening, the
method opens the possibility of dealing in a simple manner with more complex material and
contact laws including thermo-mechanical coupling, damage, etc.