Bending Of Cylindrical Shells Research Articles

Influence of Mean Pressure and Fixing Stiffness on Cylindrical Shell Bending

Influence of Mean Pressure and Fixing Stiffness on Cylindrical Shell Bending

The Exact Solution of the Bending Moment in the Folding Process of Negative Poisson’s Ratio Honeycomb Tape Spring and Multi-Objective Optimization Design

The tape spring is a crucial component used in the deployment mechanism of spacecraft, and the lightweight design of the deployment mechanism is currently one of the critical issues that need to be addressed. This paper explores the substitution effect of two different negative Poisson’s ratio honeycomb-corrugated spring structures for use in space-deployable structures. Theoretical and finite element methods demonstrated that the negative Poisson’s ratio honeycomb structure could be equivalent to an orthotropic structure. The cylindrical shell bending theory was adopted, taking into account the nonlinearity of the geometric equation, the influence of cross-sectional deformation and cross-sectional position on the internal force expression, and the influence of the geometric equation to derive expressions for the bending moment and curvature radius during the folding and bending process. Numerical methods were used for comparative analysis. The NSGA-II algorithm optimized the geometric parameters of the negative Poisson’s ratio honeycomb, resulting in the optimal solution under given constraints. The results showed that the Auxetic re-entrant honeycomb structure performed better in bending moment capacity than the Star-shaped honeycomb, and the bending moment capacity of the Auxetic re-entrant honeycomb structure per unit mass was superior to that of the traditional tape spring.

Nonlinear bending of cylindrical shells subjected to transverse loads

This technical note presents an analytical solution of the nonlinear bending of cylindrical shells subjected to transverse bending loads, induced by the flattening of cross-section. The bending equation, representing the nonlinear relationship between beam bending curvature and externally applied load, is derived on the framework of a flattened cylindrical shell. Numerical examples of cylindrical-shell beams subjected to pure bending and uniformly distributed transverse bending loads are provided to demonstrate the rationality of the present analytical model.

Exploring photo-deformation of polydomain liquid crystal polymers by homogenization

ABSTRACTThis article explores photo-deformation of polydomain liquid crystal polymers. Photo-isomerization-driven stimuli differ from thermal ones in mechanical response in that domains deform in differing amounts according to their relative alignment with respect to light polarization, by contracting along their liquid crystal orientation by an amount maximized at parallel alignment, and therefore polydomains’ response to light is complicated. Theoretical analysis of polydomain deformation with random domain alignments can be greatly simplified by applying homogenization method to obtain effective overall deformation. Not only is polydomain photo deformation very different from monodomain, but domain distributions enable very different photo responses. Anticlastic, syn-clastic and cylindrical-shell bending modes will be predicted, dictated by order parameter and material thickness. This work serves as a guide to theoretical analysis of composite materials with microstructure and to controlling their morphing shapes experimentally.

Аналітична модель деформування фланця з приєднаною обичайкою під дією внутрішнього тиску

The rings torsion theory that is based on the assumption about flat rigid cross-section was suggested by the authors in the previous papers. The analytical expressions of torsional stiffness have been derived for different kind of loads: pure moment, shear force and surface pressure. In the present paper the analytical model of flange with attached cylindrical shell deforming under internal pressure is suggested. The mechanical system is split into two parts (flange and shell) with the help of imaginary section method. An unknown shear force and bending moments are applied to both parts according to this method. Therefore flange is loaded under internal pressure, shear force and bending moments. As mentioned above, for all these loads the angle of flange cross-section rotation can be presented in analytical form based on the rings torsion theory. Full rotation angle is presented as a sum of these angles. The radial displacement of imaginary section was determined on the basis of the assumption about flat rigid cross-section. On another hand, the rotation angle and radial displacement of imaginary section are determined on the base of the cylindrical shell bending theory too. Two linear equations in the unknown shear force and bending moment were derived by equating corresponding expressions. In such а way the analytical model of flange with attached shell deforming was built. The comparison calculations by finite element methods confirmed the adequacy of proposed model.

To the solution of the problem of bending of a cylindrical shell by the boundary elements method

The solution of the problem of the long cylindrical shell bending by a numerical and analytical boundary elements method is considered. The method is based on the analytical construction of a fundamental system of solutions and Green’s functions for the differential equation of the problem under consideration. This paper is devoted to the determination of these expressions. The semi-moment theory of the cylindrical shell calculation, proposed by V.Z. Vlasov, which for the problem under consideration leads to one eighth-order partial differential equation is used. The problem of the bending of a cylindrical shell is twodimensional, and in the numerical and analytical boundary elements method, plates and shells are considered as generalized one-dimensional modules, so the variational method of Kantorovich-Vlasov was applied to this equation to obtain an ordinary differential equation of the eighth order. Sixty-four expressions of all the fundamental functions of the problem are constructed, as well as an analytic expression for the Green’s function, which makes it possible to construct a load vector (without any restrictions on the nature of its application), and then proceed to the solution of boundary-value problems for the bending of long cylindrical shells under various boundary conditions.

Cylindrical shell bending theory for orthotropic shells under general axisymmetric pressure distributions

The axisymmetric linear bending theory of shells is treated for thin-walled orthotropic cylindrical shells under any smooth axial distribution of normal and shear pressures. The equations are developed, solved and explored in this paper. The derivation is presented in terms of a generalised Hooke’s Law with coupling between the axial membrane stress resultant and axial bending moment. This formulation permits the shell to be alternatively treated as a composite isotropic cylinder with axial stiffeners, rendering it useful for many practical problems. A linear kinematic relationship is assumed between the generalised strains and displacements. Expressions for the linear axial bending half-wavelength are presented for special cases of the stiffness matrix.The equations developed here are simple enough to be applied to the analysis of anisotropic thin-walled cylindrical shells using basic spreadsheet tools, removing the need to perform an onerous finite element analysis. Engineering applications potentially include corrugated metal, axially-stiffened or reinforced concrete silos under granular solid pressures, tanks under hydrostatic pressures, tubular piles under earth pressures, gas-filled cisterns and chimneys.

Uniqueness in some higher order elliptic boundary value problems in n dimensional domains

We develop maximum principles for several P functions which are defined on solutions to equations of fourth and sixth order (including a equation which arises in plate theory and bending of cylindrical shells). As a consequence, we obtain uniqueness results for fourth and sixth order boundary value problems in arbitrary n dimensional domains.

The bending vibration response and approximate calculation of elastic cylindrical shell

Useful structure characteristics of elastic cylindrical shells have led them to being widely applied in virtual projects, so it is important to conduct vibration research on the shells and find it’s a simpler corresponding compact calculation method. Utilising the input and transfer point mobility of a thin plate structure, a theoretical expression of the cylindrical shell's bending vibration responsewas deduced and numerical simulations were done to simplify the theoretical expression within an acceptable error margin, greatly reducing the amount of computations. Furthermore, whole vibration response distributions of the cylindrical shell were analyzed. It was found thathe vibration energy propagates in helical form under mono-frequency excitation, while under bandwidth frequency excitation, it attenuates around in term of fluctuation. The axial attenuation rate of the vibration energy is larger than the circumferential attenuation rate.

On composite shell models with a piecewise linear warping function

A multilayered shell model accounting for a piecewise linear (i.e. zig-zag) distribution of displacements through the laminate thickness is discussed. The model has seven unknown kinematic variables: three displacements of the middle surface, two rotations of the shell director and two displacements associated with the wrinkling of the laminate cross-sections. The initial transverse shear stress field is introduced, and the constitutive relations are then relaxed in the framework of the variational principle. Finite element solutions obtained with this kind of model are compared with the analytical solutions for the case of cylindrical shell bending.

Effectiveness of Wear Plate at the Saddle Support

A theory is presented to analyze the effectiveness of incorporating a wear plate at the saddle support of a cylindrical pressure vessel. The wear plate can be either welded to the vessel or of loose fitting. The theory is based on a contact stress formulation together with the use of a cylindrical shell bending theory for simply supported cylinder. The effectiveness of the wear plate in reducing the peak circumferential saddle-horn stress is quantified by definition of a stress reduction factor. Parametric data are carried out for the saddle angle of 120 deg. From the study, the optimum thickness of the wear plate for three different angular extensions, are obtained.

Experimental investigation of bending of cylindrical shells under conditions of creep and small vibrations

The article describes an installation worked out and built at the Institute of Mechanics of the Moscow State University for bending tests of cylindrical shells under conditions of creep and the joint effect of constant and variable stresses. The authors also investigated the dependence of creep of long cylindrical shells of aluminum alloy subjected to bending versus the additional effect of small bending and torsional vibrations. The amplitude of the variable periodic stress components does not exceed 2–3% of the maximal static value. Curves are presented plotted according to the test results and characterizing the change of curvature of the axis of the shell vs. time. It was established that the superposition of small vibrations on the basic static load considerably increases the creep rate (on an average doubling it).

Nonaxisymmetrical longitudinal ? Transverse bending of cylindrical shells under the combined influence of pure bending and pressure

Nonaxisymmetrical longitudinal ? Transverse bending of cylindrical shells under the combined influence of pure bending and pressure

Deformation of a thin cylindrical shell due to an axisymmetrical distribution of temperature

When a narrow heating element is wrapped around a short section of a cylindrical shell bending stresses occur. Such a situation arises when a circumferential weld is stress relieved locally. The paper develops a method of obtaining the deflected shape of such a thin cylindrical shell in terms of a series of eigenfunctions of the problem. Experimental results compare well with theoretical values.

Bending of Cylindrical Shells by Initial Parameter Method

The initial parameter method, in the form proposed by V. Z. Vlasov, is presented and extended to the case of symmetric bending of cylindrical shells. It is shown that the method can be used efficiently for the solution of shells with and without intermediate supports. The loads applied to the shell can be arbitrarily distributed and discontinuous in the axial direction of the shell. The problem formulation has the distinct advantage that the complete solution contains at most two unknown “initial parameters.” These unknown parameters are determined from the boundary conditions. For shells on many supports the solution contains additional unknowns which can be determined from the support conditions. In any case, the solution consists of solving only two sets of algebraic equations. Tables of influence coefficients and loading functions for some common load cases are given in the paper. Some examples are worked out to illustrate the application of the method of initial parameters.

Linear Strain Hardening of Cylindrical Shells

The load-deformation characteristics of circular cylindrical shells, made of linear isotropic strain hardening material, simply supported at both ends, and subjected to axisymmetric loading, is studied. The shell material is assumed to obey a square approximation to the exact Tresca yield curve for the axisymmetrical bending of cylindrical shells with zero end load. Depending on the value of the shell parameter and toe magnitude of the internal pressure, shells are found to deform under six different types of stress profile. The development of the stress profiles with increasing pressure and the corresponding load-deformation fields are presented for the entire range of the shell parameter, encompassing short, medium, long, and very long shells.

Limit Analysis of Cylindrical Shells

The load carrying capacity of circular cylindrical shells simply supported at both ends and subjected to axisymmetric hydrostatic load is examined. The shell material is assumed to obey an inscribing hexagonal approximation to the Tresca yield curve for axisymmetrical bending of cylindrical shells with zero end load. The results of this analysis, together with those obtained on the assumption that the shell material obeys a circumscribing square approximation to the Tresca yield curve, bound the limit loads associated with the Tresca yield conditions. The values of the limit loads are plotted against a wide range of the shell parameter. For long shells, it is demonstrated that the curve is asymptotic to the limit load given by the membrane analysis. The stress profiles, as well as the corresponding statically admissible stress fields and kinematically admissible velocity fields, are also demonstrated for particular values of the shell parameter.

Solution of Problems of Elasticity by the Framework Method

Abstract Because of mathematical difficulties which make the solution of differential equations of the theory of elasticity impossible in many cases, the author has been impelled to seek some other method of approach than one of pure mathematical analysis. The method outlined in this paper is of this character and may with some qualifications be applied to problems of two-dimensional stress, bending of plates, bending of cylindrical shells, the general case of three-dimensional stress, and a great variety of others. Essentially, the method consists in replacing the continuous material of the elastic body being studied by a framework of bars arranged according to a definite pattern, the elements of which are endowed with elastic properties suitable to the type of problem. This framework is then analyzed, according to the procedure outlined in the paper for various types of elastic problems. Examples of the application of the principles involved are also given.