A dynamic programming approach to the optimization of elastic trusses |
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Authors: | N. Distefano A. Rath |
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Affiliation: | 1. Departments of Civil Engineering and Architecture, University of California, Berkeley, California 2. Departments of Civil Engineering and Industrial Engineering and Operations Research, University of California, Berkeley, California
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Abstract: | The optimal design of elastic trusses is discussed from a dynamic programming point of view. Emphasis is placed on minimum volume design of statically determinate trusses with displacement and stress constraints in the discrete case, i.e., when the cross-sectional areas of the bars are available from a discrete set of values. This, a design constraint usually very difficult to handle with standard nonlinear programming algorithms, is naturally incorporated in the present formulation. In addition, the functional equation approach is shown to furnish a direct solution to the problem of determining a design, among all possible ones satisfying certain volume and displacement constraints, for which the maximum stress is a minimum. A successive approximation approach is briefly indicated as an extension of the method to solve statically indeterminate trusses. Finally, several numerical examples are presented and the main features of the methods are briefly exposed. |
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