A closed-form solution for stress analysis of hollow circular cylinder structure under non-uniform external load and its engineering application

Hollow circular cylinder structures are widely used in industry for their high bearing capacity. In some engineering cases, these structures are always subjected to complicated non-uniform external loads. For example, casings used for oil production are subjected to non-uniform ground stresses. In this study, a generalized closed-form analytical solution for stress analysis of hollow circular cylinder under non-uniform external load was derived. The common non-uniform external load was decomposed by Fourier series under the principle of superposition by theory of elasticity. Analytical solutions for stress results of sine or cosine series external load problems were obtained by the semi-inverse method. A baseline analysis of a casing under non-uniform ground stress was presented using the proposed analytical method and the finite element method to validate the accuracy of the proposed analytical model. A parametric analysis was conducted finally to discuss the effects of non-uniform coefficients on the stress results. Results show that, the hollow circular cylinder structure’s anti-collapse capacity will be strongly weakened, when the non-uniform coefficient increases. This proposed analytical model can be referenced in strength verification of hollow circular cylinder structures in engineering practice.

Mathematical modeling and computer simulation of the three-dimensional pattern formation of honeycombs

We present a mathematical model, a numerical scheme, and computer simulations of the three-dimensional pattern formation of a honeycomb structure by using the immersed boundary method. In our model, we assume that initially the honeycomb cells have a hollow hemisphere mounted by a hollow circular cylinder shape at their birth and there is force acting upon the entire side of the cell. The net force from the individual cells is a key factor in their transformation from a hollow hemisphere mounted by a hollow circular cylinder shape to a rounded rhombohedral surfaces mounted by a hexagonal cylinder shape. Numerical simulations of the proposed mathematical model equation produce the rounded rhombohedral surfaces mounted by a hexagonal cylinder patterns observed in honeybee colonies.

Estimation of Effective Thermal Conductivity of Two-Phase Material for Hollow Circular Model

Two-phase materials are commonly used in engineering application because of its various properties like strength, thermal conductivity, durability and toughness etc. Effective thermal conductivity (ETC) of two-phase material is the fundamental property to predict its thermal performance. Various geometry (spheres, cylinders, irregular particles) have been considered by researchers for calculating ETC of two-phase materials. Due to complex structure, hollow circular cylinder geometry is not reported yet. In this paper, two-dimensional periodic two-phase system, with hollow circular cylinder shape is considered for calculating ETC. In present work unit cell approach method is used to derive collocated parameters model for estimation of ETC. Hollow circular cylinder model with Ψ = 0.2 gives good result for estimating ETC with average percentage error of 6.46%.

Overall Heat Transfer Coefficient of Functionally Graded Hollow Cylinder

This paper presents how to calculate the overall heat transfer coefficient of a very long functionally graded hollow circular cylinder subjected to steady state heat transfer. Thermal conductivity coefficient of the functionally graded cylinder (FGC) vary radially and continuously according to an exponential form, which is supposed to be independent of the temperature. Overall heat transfer coefficient is found analytically in terms of the radial coordinate, thermal conductivity, material parameter, inner surface and outer surface temperatures of the cylinder. Once the overall heat transfer coefficient is found, calculation of the heat transfer rate across the cylinder wall is quite straightforward. The equation derived for the overall heat transfer coefficient can be applied to any type of functionally graded hollow circular cylinder playing with the material parameter term.