Sequential optimal truss generator for frequency ranges. (English) Zbl 0633.73096
The concept of an ordered set of optimum designs is introduced here and all the design variables and behavioral variables belonging to the optimum designs are represented by successive piecewise Taylor series. A most natural, direct, and efficient way of generating or sweeping out all the optimum designs sequentially in the set is devised. The procedure is started with the eigenvalue analysis on the truss defined by the set of all the minimum cross-sectional areas. Neither any further eigenvalue analysis nor application of any optimization technique is required in the proposed procedure. It is demonstrated that the proposed method is efficient not only for an ordered set of optimum designs of a large truss associated with the single lowest eigenvector but also for that associated with multiple lowest eigenvectors.
MSC:
| 74P99 | Optimization problems in solid mechanics |
| 65K10 | Numerical optimization and variational techniques |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 49K40 | Sensitivity, stability, well-posedness |
Keywords:
sequential optimal truss generator; bi-modal formulation; ordered set of optimum designs; successive piecewise Taylor series; eigenvalue analysis; minimum cross-sectional areas; single lowest eigenvector; multiple lowest eigenvectorsReferences:
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