Dynamic programming and a max-min problem in the theory of structures

✍ Scribed by Nestor Distefano

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 674 KB
• Volume: 294
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(72)90045-2

✦ Synopsis

A max-min problem in the realm of optimum beam design is formulated and thoroughly investigated from a dynamic programming point of view. It is shown that the conditions of optimality can be directly derived from the Hamilton-Jacobi-Bellman equation of the process. The classical Euler-Lagrange equations for the beam are derived from the fundamental partial differential equation. It is shown that the conditions of optimality aseociated with the minimum operation are local expressions of the theorem of Castigliano. An analytical solution for the unconstrained optimum cantilever laying on elastic foundation is presented, and a method of successive approximations consisting in a stable, two-sweep iterative procedure, is developed. Numerical examples are given.