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

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

Mechanical Science and Engineering

Research output: Contribution to journal › Article › 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.

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

Keywords

Adjoint sensitivity analysis
Numerical time integration
Topology optimization

ASJC Scopus subject areas

Software
Control and Optimization
Control and Systems Engineering
Computer Science Applications
Computer Graphics and Computer-Aided Design

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10.1007/s00158-013-1024-4

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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.",

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author = "Jensen, {Jakob S.} and Nakshatrala, {Praveen B.} and Tortorelli, {Daniel A.}",

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AU - Jensen, Jakob S.

AU - Nakshatrala, Praveen B.

AU - Tortorelli, Daniel A.

N1 - Funding Information: The work of Jakob S. Jensen work was supported via ERC-starting grant 279529.

PY - 2014/5

Y1 - 2014/5

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.

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.

KW - Adjoint sensitivity analysis

KW - Numerical time integration

KW - Topology optimization

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

Abstract

Keywords

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