Computer Science Technical Reports
CS at VT

Tracking Structural Optima as a Function of Available Resources by a Homotopy Method

Shin, Yung S. and Haftka, Robert T. and Watson, Layne T. and Plaut, Raymond H. (1988) Tracking Structural Optima as a Function of Available Resources by a Homotopy Method. Technical Report TR-88-43, Computer Science, Virginia Polytechnic Institute and State University.

Full text available as:
PDF - Requires Adobe Acrobat Reader or other PDF viewer.
TR-88-43.pdf (1925711)


Optimization problems are typically solved by starting with an initial estimate and proceeding iteratively to improve it until the optimum is found. The design points along the path from the initial estimate to the optimum are usually of no value. The present work proposes a strategy for tracing a path of optimum solutions parameterized by the amount of available resources. The paper specifically treats the optimum design of a structure to maximize its buckling load. Equations for the optimum path are obtained using Lagrange multipliers, and solved by a homotopy method. The solution path has several branches due to changes in the active constraint set and transitions from unimodal to bimodal solutions. The Lagrange multipliers and second-order optimality conditions are used to detect branching points and to switch to the optimum solution path. The procedure is applied to the design of a foundation which supports a column for maximum buckling load. Using the total available foundation stiffness as a homotopy parameter, a set of optimum foundation designs is obtained.

Item Type:Departmental Technical Report
Subjects:Computer Science > Historical Collection(Till Dec 2001)
ID Code:128
Deposited By:User autouser
Deposited On:05 December 2001