Shape optimal design and free boundary value problems
Abstract
A unified formulation and efficient numerical technique is presented to perform shape optimal design. It is also shown that free boundary-value problems can be formulated and solved as shape optimal design problems. Although the former problem is a design problem and the latter is an analysis problem; in both cases it is the shape of the mechanical component or the free boundary that is directly treated as the unknown. Shape optimal design problems involving eigenvalues in a membrane and elastic bars in torsion are formulated and solved numerically to demonstrate that the unified scheme developed performs well. The utilization of a variational formulation for the state equations is important, since material derivatives can be employed to find the domain variation. An adjoint variable technique is then introduced to express gradients as functionals of the normal movement along the boundary. A linearization method of optimization and a sparse matrix technique used in numerical calculation are also discussed.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1983
- Bibcode:
- 1983PhDT........30H
- Keywords:
-
- Boundary Value Problems;
- Design Analysis;
- Eigenvalues;
- Optimization;
- Shape Control;
- Shapes;
- Elastic Properties;
- Inequalities;
- Mathematical Models;
- Plastic Properties;
- Fluid Mechanics and Heat Transfer