Sensitivity analysis based multi-scale methods of coupled path-dependent problems
| Autor: | Nina Zupan, Jože Korelc |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Scale (ratio)
Computational Mechanics Ocean Engineering Matrix (mathematics) sensitivity analysis mreža-v-elementu metode na več skalah dvo-nivojsko sledenje poti Applied mathematics Boundary value problem Sensitivity (control systems) FE$^2$ mesh-in-element Mathematics Applied Mathematics Mechanical Engineering Order (ring theory) Tangent občuljivostna analiza two-level path-following Computational Mathematics Computational Theory and Mathematics Rate of convergence udc:531/533 Schur complement multi-scale methods |
| Zdroj: | Computational mechanics, vol. 65, no. 1, pp. 229-248, 2020. |
| ISSN: | 1432-0924 0178-7675 |
| Popis: | In the paper, a generalized essential boundary condition sensitivity analysis based implementation of $$\text {FE}^2$$FE2 and mesh-in-element (MIEL) multi-scale methods is derived as an alternative to standard implementations of multi-scale analysis, where the calculation of Schur complement of the microscopic tangent matrix is needed for bridging the scales. The paper presents a unified approach to the development of an arbitrary MIEL or $$\text {FE}^2$$FE2 computational scheme for an arbitrary path-dependent material model. Implementation is based on efficient first and second order analytical sensitivity analysis, for which automatic-differentiation-based formulation of essential boundary condition sensitivity analysis is derived. A fully consistently linearized two-level path-following algorithm is introduced as a solution algorithm for the multi-scale modeling. Sensitivity analysis allows each macro step to be followed by an arbitrary number of micro substeps while retaining quadratic convergence of the overall solution algorithm. |
| Databáze: | OpenAIRE |
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