Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

Calculation of the spherical elements of non-uniform thickness for structures with holes based on the variational RVR-method

“…By using the RVR-method, we have demonstrated the numerical calculations that are of interest to engineer-ing practice when assessing the effect of the heterogeneity of the spherical shell's material on its stressed-strained state. The analysis of these results confirms the effective use of the RVR-method [13,15] in solving complex spatial problems on the heterogeneous shells with holes, the concentration of stresses near which could significantly affect the carrying capacity of structures. The new numerical-analytical RVR-method for calculating non-thin homogeneous and continuously heterogeneous shells with holes could be used in the design of responsible shell-type elements of structures in the various sectors of modern industry.…”

“…It is important to note that the effectiveness of the proposed RVR method for deriving reliable results was tested in resolving a large number of technical tasks studied by other authors. In particular, paper [13] shows a satisfactory match between the RVR-based numerical values of the stress concentration factor and the experimental data reported in the scientific literature for an isotropic cylinder with an elliptical hole.…”

“…Similarly to works [13,15], in structures (5), the numbers l 1 , l ii (i = 1,2), l 13 , l 33 of the approximations of the desired displacements and stresses for the shell thickness determine its shift model when setting a combination of quantities (l 1 , l 3 , l ii , l 13 , l 33 ). In this case, l 1 is the number of terms held in expanding, along the z coordinate, the meridian displacement u 1 ; l 3 -the normal displacement u 3 ; l ij -tangential stresses σ ij ; l 13 -the transverse tangential stresses σ 13 and l 33 -the transverse normal stress σ 33 .…”

“…In particular, the Vekua method [12] was applied in [10] to derive equations of the equilibrium of the heterogeneous isotropic spherical shell of constant thickness; [11] investigated the strained state of a sloping transversal-isotropic spherical shell with a circular opening. It should be noted that the presence of holes in the designed anisotropic article leads to the need to take into consideration the significant impact of stress concentrators on the carrying capacity of the examined shell-type structure [13]. In particular, the results of work [14] show that that the exact three-dimensional characteristic of tense states is important for assessing the structural integrity and predicting the fatigue growth of end-to-end cracks emanating from the hole.…”

Investigation of the Dynamic Strength of a Tank With a Fluid Under Non-Uniform Motion of a Refueler

“…У цих працях має місце фрагментарне дослідження умов безпечної експлуатації автоцистерн, але в жодній з них не визначено найбільш вразливого за умовами міцності елемента конструкції, яким є вузол з'єднання корпусу цистерни з її днищами. Разом з тим можна послатися на праці [5][6][7][8], в яких пропонується досліджувати міцність пружних оболонкових конструкцій ефективним чисельно-аналітичним RVR-методом для крайових задач у випадку статичного навантаження.…”