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Structural and Multidisciplinary Optimization

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28.09.2018 | Research Paper

Semi-analytical sensitivity analysis for nonlinear transient problems

verfasst von: Felipe Fernandez, Daniel A. Tortorelli

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2018

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Abstract

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; unfortunately, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

Vorheriger Artikel Adaptive mesh refinement in stress-constrained topology optimization

Nächster Artikel A novel approach to discrete truss design problems using mixed integer neighborhood search

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For α = 0, 1/2, or 1, we recover the forward Euler, Crank-Nicolson, and backward Euler strategies respectively.

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Titel: Semi-analytical sensitivity analysis for nonlinear transient problems
verfasst von: Felipe Fernandez
Daniel A. Tortorelli
Publikationsdatum: 28.09.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 6/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-018-2096-y

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