Structural optimization under equivalent static loads transformed from dynamic loads based on displacement

All loads in the real world act dynamically on structures. Since dynamic loads are extremely difficult 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 finite 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 field in a structure with that from dynamic loads at a certain time. The process is derived mathematically and evaluated. The method is verified through numerical tests. Various characteristics are identified 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 different from those of the dynamic loads. An optimization method is defined to use the equivalent static loads. The developed optimization process has the same effect as dynamic optimization which uses the dynamic loads directly. Standard examples are solved and the results are discussed.