Stability and initial postbuckling behavior of anisotropic cylindrical shells under external pressure

Abstract

A solution is obtained to describe the stability and initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry. The solution is based on the Donnell-Mushtari-Vlasov nonlinear theory of anisotropic shells and Koiter's theory of buckling and postbuckling behavior. Calculated results are presented for boron plastic shells with reinforcement of different types under external pressure. It is shown that the conventional model of a composite as an orthotropic material is erroneous for many types of reinforcement Keywords: stability, initial postbuckling behavior, composite material, cylindrical shell, different types of reinforcement, external pressureIntroduction. Most studies on the stability of shells made of composite materials modeled a composite as an orthotropic material [2,3,5]. This model is justified for the most popular shell making techniques; however, there are cases where it was not proved to be applicable [4]. One example is a fiber-reinforced composite layer that, being orthotropic within its own layers, deforms as an anisotropic body with one symmetry plane when the reinforcement directions are not aligned with the coordinate axes of the shell. Analytic and numerical methods of stability analysis of shells with a similar kind of anisotropy were developed in [6][7][8][15][16][17][18][19]. Note that all results on the initial postcritical behavior of composite shells apply only to orthotropic materials [3].In what follows, we will study the relationship of the initial postcritical behavior and sensitivity of shells to geometrical imperfections and deviations of composites from orthotropy. To this end, we will use the above-mentioned technique, which is based on the Donnell-Mushtari-Vlasov (DMV) theory of anisotropic shells [1] and Budiansky's version [12] of Koiter's asymptotic theory of buckling and postbuckling behavior.1. DMV Equations. Consider shells of constant thickness t consisting of N layers, also of constant thickness t k . Each layer is an anisotropic body with one symmetry plane coinciding with the mid-surface. The elastic relations for laminated anisotropic shells can be written in the following form accurate to an extent sufficient for the engineering theory of shells:

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.…”

Stability of shallow anisotropic shells of revolution

“…Using the formulas for the evaluation of determinants [4], we find These formulas coincide with those in [8][9][10]. This proves that complete trigonometric series or complex Fourier series are equivalent here since the final formulas coincide, though the intermediate formulas are different.…”

“…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 …”