On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

Jakob Søndergaard Jensen; Praveen B. Nakshatrala; Daniel A. Tortorelli

doi:10.1007/s00158-013-1024-4

On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

Jakob Søndergaard Jensen, Praveen B. Nakshatrala, Daniel A. Tortorelli

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities. © 2013 Springer-Verlag Berlin Heidelberg.

Original language	English
Journal	Structural and Multidisciplinary Optimization
Volume	49
Issue number	5
Pages (from-to)	831-837
Number of pages	7
ISSN	1615-147X
DOIs	https://doi.org/10.1007/s00158-013-1024-4
Publication status	Published - 2014

Keywords

Adjoint sensitivity analysis
Numerical time integration
Topology optimization

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title = "On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems",

abstract = "Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities. {\textcopyright} 2013 Springer-Verlag Berlin Heidelberg.",

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T1 - On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

AU - Jensen, Jakob Søndergaard

AU - Nakshatrala, Praveen B.

AU - Tortorelli, Daniel A.

PY - 2014

Y1 - 2014

N2 - Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities. © 2013 Springer-Verlag Berlin Heidelberg.

AB - Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities. © 2013 Springer-Verlag Berlin Heidelberg.

KW - Adjoint sensitivity analysis

KW - Numerical time integration

KW - Topology optimization

U2 - 10.1007/s00158-013-1024-4

DO - 10.1007/s00158-013-1024-4

M3 - Journal article

VL - 49

SP - 831

EP - 837

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 5

ER -