بحث بعنوان Similitude and Scaling Laws – Static and Dynamic Behaviour Beams

بحث بعنوان
Similitude and Scaling Laws – Static and Dynamic Behaviour Beams
and plates
Shadi Balawia* , Owais Shahida, Mohammad Al Mullaa
aKhalifa University, Department of Aerospace Engineering, PO Box 127788, Abu Dhabi, United Arab Emirates
Abstract
This investigation concerns the determination of the scaling laws based on the similitude theory for beams and plates cases when
loaded statically and with low velocity impact, respectively. Understanding the relationship between model and prototype
behaviour is essential in scaled down models designs. The similarity conditions are established directly from the system field
equations. Theoretical predictions of the model were projected with each scaling law and compared with the prototype theoretical
predictions. Both finite element analysis and experimental tests were compiled for studied cases. The results obtained, using the
similitude theory, were in good agreement with the experimental and numerical results. The scaling laws, which produced good
predictions, were identified. The prediction depended on the scaling variables range used to stay within acceptable accuracy.
Keywords: similitude; scaling; low velocity impact
Conclusions
This investigation considered the determination of the scaling laws for beams and plates loaded statically and
with low-velocity impact, based on similitude theory. The similarity conditions were established directly from the
field equations of the system for both described cases. Similarity FEA results were compared with theoretical values
for the case of the beam. Experimental tests were compared to theoretical results for the case of the plates impacted
by a mass. The results obtained using the similitude theory were in good agreement with the experimental and
numerical results and highly depend on the selection of the scaling variables. In case of the plate impact, it was
possible to scale the velocity and still achieve results within the acceptable error range Further investigations will be
needed to fully describe the ranges at which the distorted models will accurately predict the prototype behaviour.

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