摘要：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.
其他摘要：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.
