Mechanical response of fabric sheets to three-dimensional bending,twisting, and stretching

A model for the mechanics of woven fabrics is developed in the framework of two-dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of appropriate constitutive equations. The model accounts for the strain of the fabric and additional effects associated with the normal bending, geodesic bending, and twisting of the constituent fibers.     

Nonlinear deformation and stability of reinforced elliptical cylindrical shells loaded by internal pressure under twisting and bending

The problem of stability of cylindrical shells with an elliptical cross-sectional contour reinforced by a set of stringers under combined loading by bending and twisting moments, transverse force, and internal pressure is studied with the use of the variational method of finite elements in displacements. The subcritical stress-strain state of the shells is assumed to be moment and nonlinear. The effect of nonlinearity of deformation of the shells and their ellipticity on the critical loads and buckling type is determined.     

Stability of nonlinear flexure waves in cylindrical shells

Translated from Prikiadnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 119–122, September–October, 1992.     

Nonlinear bending response and buckling of ring-stiffened cylindrical shells under pure bending

In this paper, the nonlinear bending response of finite length cylindrical shells with stiffening rings is investigated by using a modified Brazier approach. The basic assumptions for the present study are that the deformation of a shell subjected to pure bending can be simplified into a two-stage process. One is that the shell ovalizes but its axis remains straight; the other is that the bending of the shell is regarded as a beam with nonuniform ovalization. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding critical moment, associated with local buckling, is determined by employing the Seide–Weingarten approximation. Numerical results are shown and compared with those obtained from other methods, which demonstrates that the assumptions used in the present study are reasonable.     

Stability of long transversely-isotropic elastic cylindrical shells under bending

The present paper investigates buckling of cylindrical shells of transversely-isotropic elastic material subjected to bending, considering the nonlinear prebuckling ovalized configuration. A large-strain hypoelastic model is developed to simulate the anisotropic material behavior. The model is incorporated in a finite-element formulation that uses a special-purpose “tube element”. For comparison purposes, a hyperelastic model is also employed. Using an eigenvalue analysis, bifurcation on the prebuckling ovalization path to a uniform wrinkling state is detected. Subsequently, the postbuckling equilibrium path is traced through a continuation arc-length algorithm. The effects of anisotropy on the bifurcation moment, the corresponding curvature and the critical wavelength are examined, for a wide range of radius-to-thickness ratio values. The calculated values of bifurcation moment and curvature are also compared with analytical predictions, based on a heuristic argument. Finally, numerical results for the imperfection sensitivity of bent cylinders are obtained, which show good comparison with previously reported asymptotic expressions.     

Exact solutions of functionally graded piezoelectric shells under cylindrical bending

Within a framework of the three-dimensional (3D) piezoelectricity, we present asymptotic formulations of functionally graded (FG) piezoelectric cylindrical shells under cylindrical bending type of electromechanical loads using the method of perturbation. Without loss of generality, the material properties are regarded to be heterogeneous through the thickness coordinate. Afterwards, they are further specified to be constants in single-layer homogeneous shells and to obey an identical exponent-law in FG shells. The transverse normal load and normal electric displacement (or electric potential) are, respectively, applied on the lateral surfaces of the shells. The cylindrical shells are considered to be fully simple supports at the edges in the circumferential direction and with a large value of length in the axial direction. The present asymptotic formulations are applied to several benchmark problems. The coupled electro-elastic effect on the structural behavior of FG piezoelectric shells is evaluated. The influence of the material property gradient index on the variables of electric and mechanical fields is studied.     

On stability of orthotropic cylindrical shells

In contrast to [1–3], the present paper obtains a system of stability equations and the corresponding resolving equation for orthotropic cylindrical shells of any but very short length in the case where the precritical stress state cannot be treated as the zero-moment state. These equations are a generalization of the results obtained in [4]. On the basis of these equations, one can obtain both the well-known formulas [1–3] and, for medium-length shells, some new expressions of the critical load in longitudinal compression and that under the joint action of torsionalmoments, normal pressure, and longitudinal compression. Some estimates are performed and the determination of the domain of application of some formulas given in [2] and in the present paper is attempted. For an orthotropic shell, a relationship between the elastic parameters and the shear modulus is established for axisymmetric and nonaxisymmetric buckling mode shapes in longitudinal compression.     

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.     

Stability of reinforced cylindrical shells in bending by a moment with torsion

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 158–162, January–February, 1989.     

Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure

The stability problem of a cylindrical shell of oval cross section loaded by a bending moment and internal pressure is studied. The variational displacement finite-element method is used. For the prebuckling stress-strain state, the bending and nonlinearity are taken into account. The effects of the nonlinear nature of the deformation and the cross-sectional ovality of the shells on the critical loads and buckling modes are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 119–125, May–June, 2006.