Geometry-Induced Rigidity in Elastic Torus from Circular to Oblique Elliptic Cross-Section

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

Stress Analysis in Damaged Pipeline with Composite Coating

This paper studied the distribution of stresses near damage in the form of axial surface cracks in a pipeline reinforced with a spiral-wound composite coating. The authors applied the homogenization method to determine the effective elastic characteristics of a structurally anisotropic layered package. By means of the classical momentless theory of shells, it was established that the stress state of the coated intact pipe under the pressure of the pumped product depends on the parameters of the geometry of the capacity strip, as well as on the component composition of the heterogeneous coating. The finite element method was applied to solve the problem of plane deformation of a piecewise homogeneous ring with an internal crack perpendicular to the interface. This problem assumes the linearity of the materials and the ideal mechanical contact with the layers. The effect of the composite coating and the size of the damage on the magnitudes of the energy flow into the crack tip, and on the stress intensity factor, was studied in detail. Various variants of the coating were considered, namely, winding of the coating on an unloaded pipe and reinforcement of the pipe under repair pressure.

Calculation of the stress state of a noncircular helicoidal tube based on the tensor theory of shells

The purpose of the study was to develop an algorithm for calculating helical-symmetric shells with a closed contour in oblique Gaussian coordinates. The twist and length of the shell were taken unchanged. The method is based on the representation of the generating contour of the helicoidal surface by a discrete set of points with the replacement of differentiation along the angular coordinate by finite differences. The unknown were the displacement vectors at the indicated points of the contour. Due to the helicoidal symmetry, the differentiation of vector quantities with respect to the helical coordinate was replaced by vector multiplication. The tensor of deformations and the tensor of the parameters of the change in curvature were calculated using the nabla operator, represented in oblique Gaussian coordinates. Integration over the contour coordinate was replaced by summation over discrete points. The tensors found, which characterize the deformed state, were used to calculate the strain energy of one period of the helicoidal shell, and then the total potential of the mechanical system was compiled. The unknown displacements were determined by minimizing the total potential, taking into account the constraints that prohibit the displacement of the shell as a rigid whole. The study gives a numerical example of the application of the developed approach.

Geometry-Induced Rigidity in Elastic Torus from Circular to Oblique Elliptic Cross-Section

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

Behavior of Polygonal Shells of Complex Geometry, Taking into Account the History of a High Level of Loading

The paper presents the results of the study of the stress-strain state of polygonal shells of positive and negative curvature with different geometric shape of the plan, taking into account the influence of the prehistory of a high loading level. To derive the resolving equation, equation, a mixed-type equation of the moment theory of shells was used. The calculation of the investigated out according to the moment theory, taking into account the influence of a complex stress state edge effect. The numerical implementation of this solution is carried out in relation to hinged and restrained shells. The bearing capacity of short-term and long-term loaded reinforced concrete polygonal shells was investigated by the method of limiting equilibrium.

Gol'denveizer Problem of Elastic Torus

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

A Cylindrical Superelement for Thermo-Mechanical Analysis of Thin Composite Vessels

In this study, a new cylindrical shell superelement with trigonometric shape functions is developed. This element is formulated based on the classical theory of shells, and it is especially designed for coupled-field analysis of thin cylindrical vessels or tubes made of composite materials. As a case study, a thermo-mechanical analysis of a thin composite cylinder is conducted. By invoking to the uniform and non-uniform meshing, the deformation and the stress results are calculated and compared with the analytical solutions. At the end, the efficiency and accuracy of the proposed superelement is also depicted via comparison of the corresponding results with the ones which are calculated by means of shell elements and via a commercial software package.

Forced vibrations of multilayered cylindrical shells taking into account the discresibility of the ribs with non-steady loads

This work considers the problem of nonstationary behavior of multilayered discretely reinforced cylindrical shells.By the way the problem is very important. Multiplayed shells with allowance for discrete ribs are widely used in engineering, industrial and public building, aviation and space technology, shipbuilding. In the framework of the Timoshenko type non – linear theory of shells and ribs nonstationary vibrations multilayered shells of revolution with allowance for discrete ribs are investigated. Reissner’s variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance for discrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers, as well as bringing their solutions to receiving concrete numerical results in wide diapason of geometrical, physico–mechanical parameters of structures are elaborated. In particular three-layer discretely reinforced cylindrical shells were investigated.

Nonlinear resultant theory of shells accounting for thermodiffusion

The complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells are discussed in more detail. They are formulated from restrictions imposed by the resultant 2D entropy imbalance according to Coleman–Noll procedure extended by a set of 2D constitutive equations based on heuristic assumptions.