Friday, March 13, 2009, 2 PM
Olsson Hall 005

Topology Optimization Under Uncertainty

James K. Guest, Ph.D.

Abstract

Topology optimization is a powerful engineering design tool used to identify optimal distributions of material across truss, frame, and continuum domains. Unlike sizing and shape optimization, topology optimization allows for the introduction and removal of structural features and is thus capable of generating new, high performance design ideas. The cost of this freedom is that design spaces are large and discrete. Problems must therefore be simplified to facilitate solution, which often entails assuming linear elastic mechanics and/or deterministic design conditions. Such assumptions in the setting of formal optimization may lead to designs that are physically unrealizable from a manufacturing perspective, or are suboptimal when considering real-world engineering conditions having inherent uncertainties.

This seminar will introduce the topology optimization methodology and present an approach for efficiently incorporating uncertainties into this methodology. The talk will focus on uncertainties in geometric and material properties that may arise from fabrication flaws and use of heterogeneous materials. The method is based on a recently developed perturbation approach that converts these uncertainties in stiffness into mathematically equivalent systems of random loads that can be handled efficiently with adjoint sensitivity analysis. The algorithm is demonstrated on mechanical stiffness design problems and verified using Monte Carlo simulations. The results demonstrate that (i) including geometric and material uncertainties can have dramatic impact on design and (ii) the perturbation approach yields similar results to those found using the Monte Carlo optimization approaches at a fraction of the computational cost. Extensions and limitations of the proposed methodology are also discussed.

Biography

Dr. Guest is an Assistant Professor of Civil Engineering at Johns Hopkins University. He received his Ph.D. in Civil and Environmental Engineering from Princeton University and his B.S.E. in Civil Engineering Systems from the University of Pennsylvania.

The Civil Engineering seminar series is open to the University community.
Civil Engineering undergraduate students are especially invited to attend.