Stability and initial postbuckling behavior of anisotropic cylindrical shells subject to torsion

Abstract

The paper presents an analytical solution describing the stability and postbuckling behavior of a cylindrical shell made of an anisotropic material with one plane of symmetry and subjected to torques at the ends. The solution is found using Koiter's buckling theory and the Donnell-Mushtari-Vlasov theory of anisotropic shells. The force and deflection functions are approximated by trigonometric series that satisfy hinged boundary conditions. The system of algebraic equations to which the problem is reduced at the main stage of solution is analyzed. Specific results on stability and sensitivity to imperfections of boron-plastic shells consisting of layers with different reinforcement directions are obtained Keywords: cylindrical shells, stability, postbuckling behavior, anisotropic materials, one plane of elastic symmetry, torsion, Koiter's buckling theory, Donnell-Mushtari-Vlasov shell theory Introduction.Recently, there has been much attention focused on the stability and postbuckling behavior of composite cylindrical shells subject to torsion [6,[11][12][13][14][15][16][17][18][19][20]. Traditional design models are improved, profound experimental research is conducted, and attempts are made to refuse formulations based on previous experience [4,6,11,12]. A very important issue for cylindrical shells made of fibrous composites is the applicability of an orthotropic model in the case of many types of layups [15,16,19]. Anisotropic shells, unlike isotropic and orthotropic ones, under torsion have two critical loads depending on the torque direction. Since this direction is constant in some structures, the load-bearing capacity of the shell can significantly be increased by choosing an appropriate layup. If the torsion direction is unknown, then it is necessary to be guided by the lower of the two critical loads and to tend to choose the number and orientation of layers so as to minimize the difference among them.The purpose of the present study is to develop a method to analyze the stability and initial postbuckling behavior of anisotropic shells subject to end torques. The solution will be represented in the form of trigonometric series as in similar problems for isotropic shells [1][2][3]. The method is based on the Donnell-Mushtari-Vlasov (DMV) theory of anisotropic shells [5,7] and Budiansky modification of Koiter's asymptotic theory of buckling [1,2,8,10].1. DMV Equations for Anisotropic Shells. Consider shells of constant thickness t consisting of N layers of thickness t k each. Each layer is an anisotropic body with one symmetry plane coinciding with its midsurface. The elastic relations for layered anisotropic shells can be written with accuracy sufficient for the engineering theory of shells [1]:

Nonlinear axisymmetric deformation of anisotropic spherical shells

“…The single-layer shell is advantageous over the two-layer shells, which seems strange at first sight. The reason will become clear if we compare this result with the relationship between the critical loads and the laminate structure in cylindrical shells [17,18]: in the elastic relations, the stiffnesses C 16 , C 26 , D 16 , and D 26 are nonzero when N = 1, whereas they are zero and the stiffnesses K 16 and K 26 are nonzero when N = 2.…”

“…Although system (16) is of the eighth order, the general solution (18) includes only four vectors, three being solutions of the homogeneous system and one being the solution of the inhomogeneous system. This is because solution (18) at a a 1 10 = , satisfies the boundary conditions irrespective of the value of C i .…”

Stability of shallow anisotropic shells of revolution

“…The equilibrium equations of such shells differ from those for cylindrical shells only by terms multiplied by 1 1 / R , where R 1 is the meridian radius [2, 5, 6]. Solving these equations, we obtain new mechanical results though the method is very similar to that outlined in [8][9][10][11]. However, the chief result of the present study is the conformation that complex series can be used to reduce the number of governing equations.…”

“…The stability of anisotropic cylindrical shells under loading of various types was analyzed in [8][9][10][11][12][13]. Stability problems were solved using the Donnell-Mushtari-Vlasov theory (DMV).…”

“…Problem Solving. In [8][9][10][11], the unknown functions w and f were approximated by Fourier series of …”