Load transfer Ubistar(U**) calculation in structures under dynamic loading

Owing to environmental concerns, fuel conservation and weight reduction are considered to be crucial problems in the automobile industry. Moreover, safety is an important issue, and thus studies on reducing injuries to vehicle occupants are very important and have attracted significant attention. In side collisions involving passenger cars, improvements in the occupant protection system and vehicle body structure are important. To design structures that are stiff and light, it is necessary to understand the load transfer from a moving deformable barrier to the structure of the automobile body. The index Ustar (U*), which is independent of stress and strain, has been introduced by the authors for expressing load transfer in the structure. Although the index Ustar has been successfully applied for performing load path analyses during frontal collisions of passenger cars, the boundary condition of a moving deformable barrier used in a side collision is load-controlled. Thus, the index Ubistar (U**) is preferable. However, the index Ubistar is currently defined under static loading conditions. In this study, the definition of the conventional index Ubistar was extended to ensure that it can be applied even when multi-point loads and inertia forces are applied. Based on the complementary energy, it was shown that the definition of a dynamic Ubistar can be expressed in the same form as that of the conventional static Ubistar. The calculation of the internal compliance matrix is performed only once, and thus its efficiency is higher when compared with that of the index Ustar. Then, the index Ubistar is applied to dynamic loading cases such as a plate with a hole and side collision of a passenger car. The load transfer at an arbitrary instant can be visualized by the Ubistar distribution, and this method aids in the selection of materials, arrangement of structural members, and stiffening of structures.