Optimization of structural dynamic behaviour based on effective modal parameters (original) (raw)
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An optimality criterion method for dynamic optimization of structures
International Journal for Numerical Methods in Engineering, 1989
This paper presents an optimality criterion method for the determination of the least weight design of a structural system which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn-Tucker optimality criterion based on choosing a single value of the Lagrange multiplier which minimizes the sum o f the squares of residuals. The method has been applied to a variety of structures. Results assert that the method is capable of locating the optimal design in a small number of redesign cycles. The method avoids the scaling of design variables. It can treat non-structural masses and is applicable to structural elements with a wide variety of size-stiffness. The procedure has been completely automated in a computer program on an IBM-PC microcomputer.
All loads in the real world act dynamically on structures. Since dynamic loads are extremely dicult to handle in analysis and design, static loads are utilized with dynamic factors. The dynamic factors are generally determined from design codes or experience. Therefore, static loads may not give accurate solutions in analysis and design. An analytical method based on modal analysis in ®nite element analysis is proposed for the transformation of dynamic loads into equivalent static load sets. Equivalent static load sets are calculated to generate an identical displacement ®eld in a structure with that from dynamic loads at a certain time. The process is derived mathematically and evaluated. The method is veri®ed through numerical tests. Various characteristics are identi®ed to match the dynamic and static behaviors. For example, the opposite direction of a dynamic load should be considered due to the vibrational response. A dynamic load is transformed into multiple equivalent static load sets according to the number of critical times. The places of the equivalent static loads can be dierent from those of the dynamic loads. An optimization method is de®ned to use the equivalent static loads. The developed optimization process has the same eect as dynamic optimization which uses the dynamic loads directly. Standard examples are solved and the results are discussed.