Stability Implications and the Equivalence of Stability and Optimality Conditions in the Optimal Design of Uniform Shallow Arches,
Abstract
The simple arch and the uniform shallow arch are used to illustrate the possible coalescence of optimality and stability conditions. The calculations for the simple arch are carried out with the initial rise of the arch as a design variable. It is shown that the necessary conditions for the constrained minimum weight arch are sufficient for instability, that the minimum stored energy problem has no solution, and that the necessary conditions arising in the calculation of the natural shapes of the arch, involving the simultaneous minimization of mass and stored energy, turn out to be sufficient for stability. A summary of the results of similar calculations for the optimal design of uniform shallow arches with initial curvature and the axial load as controls is also presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1981
- Accession Number
- ADP000039
Entities
People
- W. Stadler
Organizations
- San Francisco State University