Structural Optimization under Equivalent Static Loads transformed from Dynamic Loads based on Displacement

Abstract

All loads in the real world act dynamically on structures. Since dynamic loads are extremely diÅcult to handle inanalysis and design, static loads are utilized with dynamic factors. The dynamic factors are generally determined fromdesign codes or experience. Therefore, static loads may not give accurate solutions in analysis and design. An analyticalmethod based on modal analysis in Ænite element analysis is proposed for the transformation of dynamic loads intoequivalent static load sets. Equivalent static load sets are calculated to generate an identical displacement Æeld in astructure with that from dynamic loads at a certain time. The process is derived mathematically and evaluated. Themethod is veriÆed through numerical tests.Various characteristics are identiÆed to match the dynamic and static behaviors. For example, the opposite directionof a dynamic load should be considered due to the vibrational response. A dynamic load is transformed into multipleequivalent static load sets according to the number of critical times. The places of the equivalent static loads can bedi erent from those of the dynamic loads. An optimization method is deÆned to use the equivalent static loads. Thedeveloped optimization process has the same e ect as dynamic optimization which uses the dynamic loads directly.Standard examples are solved and the results are discussed.”2000 Elsevier Science Ltd. All rights reserved.