We consider the problem of structural optimization which has many important applications
in the engineering sciences. The goal is to find an optimal distribution of the
material within a certain volume that will minimize the mechanical and/or thermal
compliance of the structure. The physical system is governed by the standard models
of elasticity and heat transfer expressed in terms of boundary-value problems for elliptic
systems of partial differential equations (PDEs). The structural optimization problem
is then posed as a suitably constrained PDE optimization problem, which can be solved
numerically using a gradient approach. As a main contribution to the thesis, we derive
expressions for gradients (sensitivities) of different objective functionals. This is done
in both the continuous and discrete setting using the Riesz representation theorem and
adjoint analysis. The sensitivities derived in this way are then tested computationally
using simple minimization algorithms and some standard two-dimensional test problems. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/27463 |
| Date | 04 1900 |
| Creators | Baczkowski, Mark |
| Contributors | Protas, Bartosz, Kim, Ill Yong, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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