Application of Short and Long (Enhanced Vlasov's) Solutions for Cylindrical Shell on Example of Concentrated Radial Force

Abstract

Abstract Analytical approaches for cylindrical shell are mostly based on expansion of all variables in Fourier series in circumferential direction. This leads to eighth-order differential equation with respect to axial coordinate. Here it is approximately treated as a sum of two fourth-order biquadratic equations. First one assumes that all variables change more quickly in circumferential direction than in axial one (long solution), while the second (short) one is based on opposite assumption. The accuracy and applicability of this approach were demonstrated (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032) on example of action of one or two concentrated radial forces and compared with finite element method results. This paper is an improvement of our previous work (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032). Two amendments are made. The first is insignificant one and use slightly modified expressions for bending strains, while the second one relates to the short solution. Here we do not consider any more that circumferential displacement is negligible as compared with radial one. Eventually this improves the accuracy of results, as compared with previous work. For example, for cylinder with radius, R, to wall thickness, h, ratio equal to 20, the maximal inaccuracy for radial displacement in point of force application decreases from 5% to 3%. For thinner cylinder with R/h = 100, this inaccuracy decreases from 2.5% to 1.25%. These inaccuracies are related to larger terms in Fourier expansion, the significance of which decrease when length or area of outer loading becomes greater. The last conclusion is demonstrated for the case of distributed concentrated force acting along short segment on axial line.