• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.381-387
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• 2016

In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1417-1425
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• 1990

In this paper, when the glass plate of fragile material is subjected to impact load, the fracture pattern and the generation phenomenon of cone crack were theoretically clarified by using the analysis method of impulsive stress in the first paper. The numerical analysis results of strain distribution at a distance of 0.1cm, from the impact loading point to 5cm, were compared with experimental results. The main conclusions obtained are as follows; (1) The generation phenomenon of cone crack at the impact fracture of the glass plate can be analytically confirmed by using the three dimensional dynamic theory of elasticity. And the numerical analysis results of strain distribution using this theory are relatively in close agreement with the crack size obtained from the impact fracture experiment. (2) After the stress wave generated at the impact point propagated to the spherical compressive wave, this stress wave reflected from the back surface and reached again at the surface of the plate to the spherical stress wave. Then the generation of cone crack can be confirmed along the stress wave surface. (3) The plate is the thicker, the more is the generation phenomenon of cone crack at the lower impact velocity range (20m/s-35m/s). Because the fracture generate before the maximum tensile stress acting to the glass plate, cone crack was rarely ever generated.