Noncircular Cylindrical Shells Research Articles

Free Vibration Behaviours of Thick Laminated Non-Circular Cylindrical Shells

In this paper the free vibration behaviours of thick laminated composite non-circular cylindrical shells are investigated using higher-order theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different order displacement terms. The strain-displacement relations are accurately accounted for in the formulation without neglecting/approximating the (I +z/R) terms. The solutions are obtained employing finite element procedure. Detailed study is made to highlight the influences of length and thickness ratios, eccentricity parameter, ply-angles and number of layers on the free vibration characteristics of non-circular shells.

Thermo-Elastic Stability Characteristics of Laminated Non-circular Cylindrical Shells Using Higher Order Theory

In this paper thermo-elastic stability characteristics of laminated noncircular cylindrical shells subjected to uniform temperature rise are studied using higher order kinematics which accounts for the transverse shear and transverse normal deformations, and incorporates realistic through the thickness approximations of the in-plane displacements. The governing equations obtained through the minimization of total potential energy are solved using finite element approach. The strain-displacement relations are accurately introduced in the formulation. The combined influence of higher-order shear deformation, shell geometry and non-circularity on the critical temperature parameter of oval shells as an example of non-circular shell is examined.

Analytical estimates of the contact zone area for a pressurized flat-oval cylindrical shell placed between two parallel rigid plates

The paper presents an analytical estimate for an area of contact for a thin-walled noncircular cylindrical shell placed between two parallel rigid plates with an initial gap and then pressurized hydrostatically up to the contact appearance. The Euler–Bernoulli beam is used to model the shell deformation under the plane strain assumption. Such a simplification allows one to obtain the simplest closed-form estimate for the contact zone area. The first approximation is obtained neglecting the deformation of the curvilinear segments of the flat oval shell cross-section while the solution for the curved beam loaded by the homogeneous pressure is considered as a second approximation. The accuracy of the proposed analytical solutions as well as their usability in the preliminary design of thin-walled elements of various cooling systems is validated by the results of both numerical simulations and experimental tests.

The Study of Natural Oscillations of Thin Elastic Shells of Complicated Shapes by the Energy Method

The problem of natural oscillations of an elastic thin non-circular cylindrical wavy shell of an open profile is considered. The problem is based on the Rayleigh-Ritz energy method. On the basis of the proposed method for determining the lowest frequencies and forms of natural vibrations of shells of complicated shape, the numerical convergence of the developed algorithm is investigated. The evaluation of the results of this numerical experiment is given.

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell Under Combined Loading with Bending and Twisting Moments

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress–strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell under Combined Loading with Bending and Twisting Moments

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell under Combined Loading with Bending and Twisting Moments

Analytical-Numerical Solution of Static Problems for Noncircular Cylindrical Shells of Variable Thickness

An analytical-numerical method of solving boundary-value static problems for transversally isotropic infinitely long noncircular cylindrical shells of variable thickness is formulated and developed. The system of basic equations is derived using the relations of the refined theory of deep shells with low shear stiffness. Expressions for internal power factors and generalized displacements of closed and open cylindrical shells with arbitrary cross-section acted upon by surface and linear forces are presented. The integrals appearing in these expressions are calculated with the method of trapezoids. The numerical results for a closed shell of elliptic cross-section under uniform internal pressure presented in the form of tables and plots are analyzed

Natural Frequencies and Modes of Noncircular Cylindrical Shells with Variable Thickness

The dynamic characteristics of thin cylindrical isotropic shells with variable thickness are determined using numerical and experimental approaches. Numerical calculations are performed by the finite-element method with FEMAR software. In experimental study, stroboscopic holographic interferometry is used which makes it possible to observe interferential patterns of vibrations of the shell surface in real time. The results obtained by two different methods are compared

Точні розв’язки деяких задач статики для некругових циліндричних оболонок з врахуванням деформацій поперечного зсуву

Точні розв’язки деяких задач статики для некругових циліндричних оболонок з врахуванням деформацій поперечного зсуву

Exact Solutions of Boundary-Value Problems for Noncircular Cylindrical Shells

Boundary-values problems for transversely isotropic infinitely long noncircular cylindrical shells under static loads are formulated and solved analytically. The system of basic equations is derived from a refined theory of deep shells with low shear stiffness. Expressions of the internal forces and generalized displacements for closed and open oval cylindrical shells under internal pressure and transverse force are derived. The effect of the aspect ratio and transverse-shear strains on the stress–strain state of these shells is analyzed

Dynamic Analysis of Partially Filled Non-circular Cylindrical Shells with Liquid Sloshing

The paper investigates the dynamic behavior of thin-walled reservoirs containing an ideal liquid taking into account the effects of hydroelastic interaction and sloshing. A mathematical statement of the problem is based on the principle of virtual displacements, which accounts for the pre-stressed non-deformed state of the shell caused by various force factors. The behavior of compressible liquid is described by linearized Euler equations, which are transformed by the Bubnov–Galerkin method. The dynamics of partially filled circular and elliptical cylindrical reservoirs are investigated numerically using a finite element procedure. It has been shown that allowing for sloshing considerably reduces eigenfrequencies of vibrations of the examined systems but has inessential effect on the displacements of the structure under non-stationary loads. Based on the modal analysis we present a classification of eigenmodes of free surface oscillations of a liquid in vertical tanks. It has been found that due to consideration of the sloshing effect, the frequency spectrum of the system can split into two parts in the case when the vibration frequencies of liquid differ from the vibration frequencies of an empty shell. Moreover, under harmonic excitation consideration of liquid sloshing leads to a more complicated amplitude-frequency curve characterized by displacement jumps.

Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure

A finite element formulation of solving the stability problems for the discretely reinforced noncircular cylindrical shells is presented taking into account that their subcritical stress strain state is instantaneous and nonlinear. The author-developed finite elements for a natural-curved shell and the beam elements of reinforcements are used. A numerical algorithm to study the nonlinear deformation and stability of shells was developed. The stability of a stringer-stiffened cylindrical shell with an elliptical cross-sectional contour under transverse bending and internal pressure is examined. We also investigate the effect of internal pressure, ellipticity and nonlinearity of deformation, as well as of reinforcement discreteness and heterogeneity.

Natural vibrations of non-circular cylindrical shells partially filled with fluid with sloshing of free surface

Natural vibrations of non-circular cylindrical shells partially filled with fluid with sloshing of free surface

Investigation of free vibrations of noncircular cylindrical shells by the spline-collocation method

We consider free vibrations of thin isotropic elliptic shells of constant thickness on the basis of the spline-collocation method. It is established that, in the case of conservation of mass of elliptic and circular cylindrical shells, the frequencies of free vibrations of noncircular cylindrical shells decrease with increase in eccentricity of the cross section of the shell.

Studies of nonlinear deformation and stability of stiffened oval cylindrical shells under combined loading by bending moment and boundary transverse force

The finite-element statement of stability problems for stiffened oval cylindrical shells is presented with the moments and the nonlinearity of their subcritical stress-strain state taken into account. Explicit expressions for the displacements of elements of noncircular cylindrical shells as solids are obtained by integration of the equations derived by equating the linear deformation components with zero. These expressions are used to construct the shape functions of the effective quadrangular finite element of natural curvature, and an efficient algorithm for studying the shell nonlinear deformation and stability is developed. The stability of stiffened oval cylindrical shells is studied in the case of combined loading by a boundary transverse force and a bending moment. The influence of the shell ovality and the deformation nonlinearity on the shell stability is investigated.

Studies of nonlinear deformation and stability of noncircular cylindrical shells in transverse bending

The variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined.

Study of nonlinear deformation and stability of discretely reinforced elliptic cylindrical shells in transverse bending

A finite-element method for solving problems of nonlinear deformation and stability of nonuniformly discretely reinforced noncircular cylindrical shells is considered. An effective computer algorithm for the study of shells is developed. Stability of stringer cylindrical shells with an elliptical cross section in transverse bending is examined. The effect of ellipticity, nonlinearity of shell deformation at the subcritical stage, reinforcement discreteness, and heterogeneity on shell stability is determined.

810 伝達マトリックス法に基づく非円筒シェル構造物の点加振応答解析

810 伝達マトリックス法に基づく非円筒シェル構造物の点加振応答解析

Study of nonlinear deformation and stability of reinforced shells under combined loading by a bending moment and a transverse boundary force

We present a finite-element statement for the solution of stability problems for reinforced elliptic cylindrical shells with moment properties and nonlinearity in their precritical stressstrain state taken into account. Integrating the equations obtained by equating the linear strain components with zero, we find explicit expressions for the displacements of elements of noncircular cylindrical shells as rigid bodies. Using these expressions, we construct the shape functions of a fourangle finite element of natural curvature and develop an effective algorithm for studying nonlinear deformation and stability of shells. We study the stability of reinforced elliptic cylindrical shells under combined loading by a transverse boundary force and a bending moment and investigate how the ellipticity of the shells and the nonlinearity of deformation at the precritical stage affect the shell stability.

Analysis of nonlinear deformation and stability of reinforced elliptic cylindrical shells under bending with internal pressure

A finite element statement of solving problems on stability of reinforced elliptic cylindrical shells taking into account momentness and nonlinearity of their subcritical stress strain state is presented. The explicit expressions for displacements of noncircular cylindrical shell elements as rigid bodies are determined by integrating the equations obtained by equating the components of linear strains to zero. These expressions were used to construct the form functions for an efficient quadrilateral finite element of natural curvature. An efficient numerical algorithm of nonlinear deformation and stability of shells was developed. The stability of reinforced elliptic cylindrical shells under combined loading by bending moment, transverse boundary force and internal pressure is analyzed. We also examine how the critical loads are affected by the strain nonlinearity and ellipticity of shell deformation at the subcritical stage.