Free Material Optimization (FMO) is a powerful approach for structural optimization
in which the design parametrization allows the entire elastic stiffness
tensor to vary freely at each point of the design domain. The only requirement
imposed on the stiffness tensor lies on its mild necessary conditions for physical
attainability, in the context that, it has to be symmetric and positive semidefinite.
FMO problems have been studied for the last two decades in many articles
that led to the development of a wide range of models, methods, and theories.
As the design variables in FMO are the local material properties any results
using coarse finite element discretization are not essentially predictive. Besides
the variables are the entries of matrices at each point of the design domain.
Thus, we face large-scale problems that are modeled as nonlinear and mostly non
convex semidefinite programming. These problems are more difficult to solve and
demand higher computational efforts than the standard optimization problems.
The focus of today’s development of solution methods for FMO problems is based
on first-order methods that require a large number of iterations to obtain optimal
solutions. The scope of the formulations in most of the studies is indeed limited
to FMO models for two- and three-dimensional structures. To the best of our
knowledge, such models are not proposed for general laminated shell structures
which nowadays have extensive industrial applications.
This thesis has two main goals. The first goal is to propose an efficient optimization
method for FMO that exploits the sparse structures arising from the
many small matrix inequality constraints. It is developed by coupling secondorder
primal dual interior point solution techniques for the standard nonlinear
optimization problems and linear semidefinite programs. The method has successfully
obtained solutions to large-scale classical FMO problems of simultaneous
analysis and design, nested and dual formulations. The second goal is to extend
the method and the FMO problem formulations to general laminated shell structures.
The thesis additionally addresses FMO problem formulations with stress constraints.
These problems are highly nonlinear and lead to the so-called singularity
phenomenon. The method described in the thesis has successfully solved these
problems. In the numerical experiments the stress constraints have been satisfied
with high feasibility tolerances.
The thesis further includes some preliminary numerical progresses on solving
FMO problems using iterative solvers.
|Publisher||DTU Wind Energy|
|Number of pages||139|
|Publication status||Published - 2014|
|Series||DTU Wind Energy PhD|
- DTU Wind Energy PhD-0041(EN)
- DTU Wind Energy PhD-0041
- DTU Wind Energy PhD-41