Transformation of dynamic loads into equivalent static loads based on modal analysis

All the forces in the real-world act dynamically on structures. Since dynam ic loads are extremely difficult to handle in analysis and design, static l oads are usually utilized with dynamic factors. Static loads are especially exploited well in structural optimization where many analyses are carried out. However, the dynamic factors are not determined logically. Therefore, structural engineers often come up with unreliable solutions. An analytical method based on modal analysis is proposed for the transformation of dynam ic loads into Equivalent Static Loads (ESLs). The ESLs are calculated to ge nerate an identical displacement field with that from dynamic loads at a ce rtain time. The process is derived and evaluated mathematically by using th e modal analysis. Since the exact solution is extremely expensive, some app roximation methods are proposed. Error analyses have been conducted for the approximation methods. Standard examples for structural design are selecte d and solved by the proposed method. Applications of the method to structur al optimization are discussed. Copyright (C) 1999 John Wiley & Sons, Ltd.