Transformation of Dynamic Loads into Equivalent Static Load based on the Stress Constraint Conditions

Abstract

Due to the difficulty in considering dynamic load in the view point of a computer resource and computing time, it is common that external load is assumed as ideal static loads. However, structural analysis under static load cannot guarantee the safety of design of the structures under dynamic loadings. Recently, the systematic method to construct equivalent static load from the given dynamic load has been proposed. Previous study has calculated equivalent static load through the optimization procedure under displacement constraints. However, previously reported works to distribute equivalent static load were based on ad-hoc methods. Improper selection of equivalent static loading positions may results in unreliable prediction of structural design. The present study proposes the selection method of the proper locations of equivalent static loads to dynamically applied loads when we consider transient dynamic structural problems. Moreover, it is appropriate to take into account the stress constraint as well as displacement constraint condition for the safety design. But the previously reported studies of equivalent static load design methods considered only displacement constraint conditions but not stress constraint conditions. In the present study we consider not only displacement constraint but also stress constraint conditions. Through a few numerical examples, the efficiency and reliability of proposed scheme is verified by comparison of the equivalent stress between equivalent static loading and dynamic loading.

Dynamic Analysis of Encastre Beams by Modification of the System’s Stiffness Distribution

“…where a is dimensionless constant equal to 3 24 ⁄ . Equation ( 24) is substituted into Equation ( 6)and ( 8) to obtain an expression for Aj and Mj.…”

“…Most real loads on structures are dynamic in nature [1], [2]. To make the analysis simpler the static equivalent of the dynamic load is used [3]- [5]. Dynamic loads cause structures that have mass and elasticity to vibrate [6].…”