International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000451

On The Influence of Polar Moment Inertia of a
Right-Angled Bent Cantilever Under Dynamic
Loading – Part 1: Analytical Modeling

Bin Wang¹ and Xiao Wu^{1,2 1}School of Engineering and Design, Brunel University, UK. ²School of Mechanical Engineering, Southwest Jiaotong University, P. R. China.

ABSTRACT

In the analysis of the dynamic plastic behavior of beam-like structures, it is often to neglect the influence of transverse shear, and those of the second moments of inertia of the torsional J-term and the bending I-term. This is due to their generally limited influences on the overall response of structures and it usually leads to substantial simplification of the analysis. However, there are cases which show significant influences of these factors. Some work has been reported with consideration of the effects of shear and I-term, such as Drucker [1956] and Jones and Oliverira [1979]. But little has been seen on the J- term influence. This paper, as a first approach to introduce the polar moment inertia J into the analysis, presents a theoretical model for a right-angled bent cantilever beam subjected to an out-of-plane impulsive (velocity) loading. It is assumed that a projectile strikes normal to the plane of a right-angled bent beam at the beam tip and adheres there, resulting in the second beam segment undergoing combined bending and torsional deformation. It is found that a traveling hinge will form at the bend and move towards the root of the beam. Differences between the models with and without the J-term, such as the energy dissipation, were discussed.

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