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UBC Theses and Dissertations
Reliability-based structural design optimization for nonlinear structures in OpenSees Liang, Hong
Abstract
The aspiration of this thesis is to provide a tool for engineers in making rational decisions based on the balance between cost and safety. This objective is accomplished by merging the optimization and reliability analyses with sophisticated finite element models that predict structural response. In particular, two state-of-the-art reliability-based design optimization approaches are implemented in OpenSees, a modern and comprehensive finite element software that has recently been extended with reliability and response sensitivity analysis capabilities. These new implementations enable reliability-based design optimization for comprehensive real-world structures that exhibit nonlinear behaviour. This thesis considers the problem of minimizing the initial cost plus the expected cost of failure subject to reliability and structural constraints. This involves reliability terms in both objective and constraint functions. In the two implemented approaches, the reliability analysis and the optimization evaluation are decoupled, although they are not bi-level approaches, thus allowing flexibility in the choice of the optimization algorithm and the reliability method. Both solution approaches employ the same reformulation of the optimization problem into a deterministic optimization problem. The decoupled sequential approach using the method of outer approximation (DSA-MOOA) applies a semi-infinite optimization algorithm to solve this deterministic optimization problem. An important feature of the DSA-MOOA approach is that a convergence proof exists in the first-order approximation. The simplified decoupled sequential approach (DSA-S) utilizes an inequality constrained optimization algorithm to solve the deterministic optimization problem. The DSA-S approach is demonstrated to result in a consistent design, which lacks the convergence proof but requires less computational time than the DSA-MOOA approach. The gradients of the finite element response with respect to model parameters are needed in reliability-based design optimization. These gradients are obtained using the direct differentiation method, which entails the derivation and implementation of analytical derivatives of the finite element response. The potential negative effect of response gradient discontinuities due to sudden yielding events is stressed in the thesis. The problem is remedied through the use of the smooth material model and a section discretization scheme. Object-oriented programming is utilized when extending optimization and sensitivity capabilities to OpenSees. The superior extensibility and maintainability features of this approach are emphasized. A numerical example involving a nonlinear finite element analysis of a three-bay, sixstorey building is presented in the thesis to demonstrate new implementations in OpenSees. Three cases are studied: a linear pushover analysis using elasticBeam elements, a nonlinear pushover analysis using beamWithHinges elements, and a nonlinear pushover analysis using dispBeamColumn elements with fibre sections. This thesis also touches on practical experiences by comparing two implemented approaches, two gradient computation methods, and linear and nonlinear analyses. The experience of speeding up the convergence procedure by removing inactive constraints and scaling the involved functions is also discussed.
Item Metadata
Title |
Reliability-based structural design optimization for nonlinear structures in OpenSees
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2005
|
Description |
The aspiration of this thesis is to provide a tool for engineers in making rational decisions
based on the balance between cost and safety. This objective is accomplished by merging
the optimization and reliability analyses with sophisticated finite element models that
predict structural response. In particular, two state-of-the-art reliability-based design
optimization approaches are implemented in OpenSees, a modern and comprehensive
finite element software that has recently been extended with reliability and response
sensitivity analysis capabilities. These new implementations enable reliability-based
design optimization for comprehensive real-world structures that exhibit nonlinear
behaviour.
This thesis considers the problem of minimizing the initial cost plus the expected cost
of failure subject to reliability and structural constraints. This involves reliability terms in
both objective and constraint functions. In the two implemented approaches, the
reliability analysis and the optimization evaluation are decoupled, although they are not
bi-level approaches, thus allowing flexibility in the choice of the optimization algorithm
and the reliability method. Both solution approaches employ the same reformulation of
the optimization problem into a deterministic optimization problem. The decoupled
sequential approach using the method of outer approximation (DSA-MOOA) applies a
semi-infinite optimization algorithm to solve this deterministic optimization problem. An
important feature of the DSA-MOOA approach is that a convergence proof exists in the
first-order approximation. The simplified decoupled sequential approach (DSA-S)
utilizes an inequality constrained optimization algorithm to solve the deterministic
optimization problem. The DSA-S approach is demonstrated to result in a consistent
design, which lacks the convergence proof but requires less computational time than the
DSA-MOOA approach.
The gradients of the finite element response with respect to model parameters are
needed in reliability-based design optimization. These gradients are obtained using the
direct differentiation method, which entails the derivation and implementation of
analytical derivatives of the finite element response. The potential negative effect of
response gradient discontinuities due to sudden yielding events is stressed in the thesis.
The problem is remedied through the use of the smooth material model and a section
discretization scheme. Object-oriented programming is utilized when extending
optimization and sensitivity capabilities to OpenSees. The superior extensibility and
maintainability features of this approach are emphasized.
A numerical example involving a nonlinear finite element analysis of a three-bay, sixstorey
building is presented in the thesis to demonstrate new implementations in
OpenSees. Three cases are studied: a linear pushover analysis using elasticBeam
elements, a nonlinear pushover analysis using beamWithHinges elements, and a nonlinear
pushover analysis using dispBeamColumn elements with fibre sections. This thesis also
touches on practical experiences by comparing two implemented approaches, two
gradient computation methods, and linear and nonlinear analyses. The experience of
speeding up the convergence procedure by removing inactive constraints and scaling the
involved functions is also discussed.
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Genre | |
Type | |
Language |
eng
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Date Available |
2009-12-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0063317
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2005-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.