Influence of transverse shift and compression on the value of critical load for curved rods

Abstract

The refined calculation formulae for determining the critical load for curved axis rods, which take into account the influence of transverse shear and compression deformations, are investigated. An analysis of these effects is given for cases when the ring of composite material is subjected to radial pressure and it loses its circular shape. It is known that composite materials have anisotropic properties by nature, and their strength and rigidity characteristics can differ significantly. Therefore, the calculation of elements from such materials requires more accurate models and calculation equations, as well as the use of more advanced mathematical methods. In contrast to the calculated equations, where the previous authors considered the transverse displacement only partially and the transverse compression was neglected, in this paper the transverse compression is accounted to the fourth exponent of the transverse coordinate, and the transverse displacement - to the third. Therefore, the calculated equations are more accurate, the results of the obtained calculations also have the corresponding accuracy.To convert the system of differential bending equations into differential equations for critical load calculation, the known substitutions used by H.S. Golovin and V.V. Bolotin for similar tasks were used. The numerical result obtained for the composite material ring is approximately 20% lower compared to the similar result if the ring material was isotropic. Calculations have shown that the effect of transverse compression deformation for a ring with a relative thickness h/R=0,1 is insignificant - within 1-2 %%, depending on the ratio of elasticity modulus. The acquired results are close to those obtained on the basis of plane elasticity theory problem, when the transverse modulus of elasticity approximates infinity.