An Application of Control Theory Methods to the Optimization of Structures Having Dynamic or Aeroelastic Constraints.
Scientific interim rept.,
STANFORD UNIV CALIF DEPT OF AERONAUTICS AND ASTRONAUTICS
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A great deal of interest and attention has recently been focused on the optimal design of structures. By optimal design it is meant that a structure performs the same function as another similar structure while minimizing some performance index, usually the weight of the structure. This study investigates some simple structures whose weights are minimized subject to several types of constraints involving fixed eigenvalues. These eigenvalues may be related to free vibration, in which case a least weight structure is determined while holding one or more natural frequencies constant. Similarly, the eigenvalues may be related to aeroelastic instabilities where a least weight structure is found while holding the flutter speed constant. With one exception, the models are idealized one-dimensional structures with fixed geometry and spatial dimensions. These models are adequately described by a set of N simultaneous first-order ordinary differential equations which come from the general Nth order equilibrium equation. Methods adapted from optimal control theory are used to develop differential equations and boundary conditions which are necessary to ensure optimality. This optimization problem then becomes a two-point boundary value problem with 2N simulataneous non-linear differential equations. Author
- Theoretical Mathematics