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A theoretical and computational study is reported of the effect of cylinder yaw angle on the vorticity and velocity field in the cylinder wake. Previous experimental studies for yawed cylinder flows conclude that, sufficiently far away from the cylinder ends and for small and moderate values of the yaw angle, the near-wake region is dominated by vortex structures aligned parallel to the cylinder. Associated with this observation, experimentalists have proposed the so-called Independence Principle, which asserts that the forces and vortex shedding frequency of a yawed cylinder are the same as for a cylinder with no yaw using only the component of the freestream flow oriented normal to the cylinder axis. The current paper examines the structure, consequences and validity for yawed cylinder flows of a quasi-two-dimensional approximation in which the velocity and vorticity have three nonzero components, but have vanishing gradient in the direction of the cylinder axis. In this approximation, the cross-stream velocity field is independent of the axial velocity component, thus reproducing the Independence Principle. Both the axial vorticity and axial velocity components are governed by an advection-diffusion equation. The governing equations for vorticity and velocity in the quasi-two-dimensional theory can be nondimensionalized to eliminate dependence on yaw angle, such that the cross-stream Reynolds number is the only dimensionless parameter. A perturbation argument is used to justify the quasi-two-dimensional approximation and to develop approximate conditions for validity of the quasi-two-dimensional approximation for finite-length cylinder flows. Computations using the quasi-two-dimensional theory are performed to examine the evolution of the cross-stream vorticity and associated axial velocity field. The cross-stream vorticity is observed to shed from the cylinder as thin sheets and to wrap around the Karman vortex structures, which in turn induces an axial velocity deficit within the wake vortex cores. The computational results indicate two physical mechanisms, associated with instability of the quasi-two-dimensional flow, that might explain the experimentally observed breakdown of the Independence Principle for large yaw angles. [DOI: 10.1115/1.1523069]

An exact solution for stress distributions within a finite transversely isotropic cylinder for the axial point load strength test (PLST) is analytically derived. Lekhnitskii's stress function is first used to uncouple the equations of equilibrium. Two different kinds of solutions corresponding to the real and the complex characteristic roots of the governing equation of the stress function are derived. The solution type to be used for stress analysis depends on the anisotropic parameters of the cylinder. The solution for isotropic cylinders under the axial PLST is recovered as a special case. Numerical results show that the pattern of stress distribution along the line joining the point loads does not depend on the degree of anisotropy of the cylinder, but the magnitude of the stress distributions does. In particular, the local maximum tensile stress, which is located near the point loads, may be either larger or smaller than that of isotropic cylinders. In general, the maximum tensile stress inside the cylinder increases with the ratio of Young's moduli, but decreases with both the ratio of Poisson's ratio and the ratio of the shear moduli. If anisotropy of the cylinder is ignored, the point load strength index may be overestimated when the ratio of Young's moduli is greater than one, or when the ratios of Poisson's ratio or of the shear moduli is smaller than one. DOI: 10.1061/(ASCE)0733-9399(2002)128:2(209) CE Database keywords: Axial loads; Cylinders; Isotropy; Poisson ratio.

The unsteady wake of a long square cylinder has been numerically analyzed in the present study. Velocity signals at selected locations in the near-wake and the instantaneous forces on the cylinder have been recorded from the numerical model at various Reynolds numbers. These form the basis of investigating the dynamic behavior of the flow system. Results of the present work show the following. Flow past a square cylinder undergoes a sequence of transitions from a steady pattern up to a Reynolds number of 40 to a chaotic one around a Reynolds number of 600. The transition to chaos is manifested through a quasi-periodic route that includes the frequency-locking phenomenon. The quasi-periodicity is seen to set in with two or more Hopf bifurcations. The transition to chaos in the wake of a bluff object is related to the three-dimensionality of the flow. In a 2D simulation, this appears in the form of new harmonics in the velocity traces. The quasi-periodic route to chaos has been established through different characterization tools, such as the spectra, autocorrelation function, time-delay reconstruction, and the Poincare section. Chaotic behavior is quantified through the calculation of Lyapunov exponent and fractal dimension.

A simple analytical solution for the bifurcation buckling of a cylinder under axial loading is provided including finite-strain effects. Thus, the small strain theory result of Batterman is generalized. In addition to the thin shell theory solution (excluding shear deformations), a solution including shear deformation effects is also given. All solutions can be evaluated for either the flow or deformation theory of plasticity. The finite-strain constitutive theory used is one in which small strain type relationships apply between the Jauman rate of the Kirchhoff stress tensor and the deformation rate tensor. The analytical results are compared to finite-element analyses to test the validity of the assumptions made. The solutions are explicit. Starting with a point on the stress-strain curve, one calculates explicitly the diameter-to-thickness ratio D/t for a cylinder that will buckle at that level of stress and strain (repeating this as necessary to generate a plot of wrinkling strains as a function of D/t). Unless the tangent modulus at bifurcation is large compared to the stress, the results clearly indicate that finite strains have an important stabilizing effect, leading to higher bifurcation strains.

The bifurcation of elastoplastic pressure-sensitive hollow cylinders under radial surface loads has been studied. The flow and deformation theories of Drucker-Prager are used in modeling material response. Results indicate that flow theory failed to detect any bifurcation points. The dominant bifurcation mode for thick-walled cylinders is a circumferential surface instability based on deformation theory. It has also been found that values derived by deformation theory are impervious to deviations from associativity.

The classical St. Venant problems of simple tension, pure bending and flexure by a transverse force have been examined in circular bars with elastic moduli that is a function of the radial coordinate. Ordinary differential equations have been derived and are used in solving for a specific modulus of elasticity. The solutions are then used in determining the homogeneous effective moduli for inhomogeneous cylinders. It has been observed that uniform distribution of the reinforcement leads to a minimum of the Young's modulus in the class of spatial variations in the concentration examined.

An exact elastic-plastic analytical solution for an arbitrarily laminated metal matrix composite tube subjected to axisymmetric thermo-mechanical and torsional loading is presented. First, exact solutions for transversely isotropic and monoclinic (off-axis) elastoplastic cylindrical shells are developed which are then reformulated in terms of the interfacial displacements as the fundamental unknowns by constructing a local stiffness matrix for the shell. Assembly of the local stiffness matrices into a global stiffness matrix in a particular manner ensures satisfaction of interfacial traction and displacement continuity conditions, as well as the external boundary conditions. Due to the lack of a general macroscopic constitutive theory for the elastic-plastic response of unidirectional metal matrix composites, the micromechanics method of cells model is employed to calculate the effective elastic-plastic properties of the individual layers used in determining the elements of the local and thus global stiffness matrices. The resulting system of equations is then solved using Mendelson's iterative method of successive elastic solutions developed for elastoplastic boundary-value problems. Part I of the paper outlines the aforementioned solution strategy. In Part II (Salzar et al., 1996), this solution strategy is first validated by comparison with available closed-form solutions, as well as with results obtained using the finite-element approach. Subsequently, examples are presented that illustrate the utility of the developed solution methodology in predicting the elastic-plastic response of arbitrarily laminated metal matrix composite tubes. In particular, optimization of the response of composite tubes under internal pressure is considered through the use of functionally graded architectures.

Part I (Salzar et al., 1996) of the paper presented an exact elastic-plastic analytical solution for an arbitrarily laminated metal matrix composite tube subjected to axisymmetric thermo-mechanical and torsional loading. In Part II, this solution strategy is first validated by comparison with available closed-form solutions, as well as with results obtained using the finite-element approach. Subsequently, examples are presented that illustrate the utility of the developed solution methodology in predicting the elastic-plastic response of arbitrarily layered metal matrix composite tubes. In particular, optimization of the response of composite tubes under internal pressure is considered through the use of functionally graded architectures.

A fracture mechanics-based fatigue life analysis was developed for overstrained, pressurized thick-wall cylinders with one or several semi-elliptical-shaped axial grooves at the inner diameter. The fatigue life for a crack initiating at the root of the groove was calculated for various cylinder, groove, and crack configurations and for different material yielding conditions. Comparisons were made with fatigue crack growth and laboratory life results from A723 thick-wall cylinders, in which cannon firing tests were first performed to produce axial erosion grooves, followed by cyclic hydraulic pressurization to failure in the laboratory. The life analysis, with an initial crack size based on the expected pre-existing defects, gave a good description of the crack growth and fatigue life of the tests for cylinders with and without grooves. General fatigue life calculations summarized important material and configurational effects on the fatigue life design of overstrained cylinders, including effects of material yield strength, cylinder diameter ratio, stress concentration factor, and initial crack size.

The add-on method utilizes previously acquired solutions for sub-problems, comprising portions of a scatterer, as a part of the analysis. The process of adding the remainder of the solution is a relatively efficient one, assuming that the initial stage of the sub-problem has been performed. The 'add on' method is based on two basic principles: A. Superposition is used to break up the unknown current into two components, the first one being a readily computable solution to a simple short circuited problem, and the second one is excited by a current source over the aperture area, and is the only one requiring computation. B. A gradual algorithm is used for the computation of the second current component for many sub-problems. Principle A leads to a purely algebraic algorithm of principle B, with no integral operators. In this work, this formulation is extended to the cylindrical case. In this case the aperture region is a portion of a circle complementing the circular conducting shell, thus it shrinks as the conductor increases in size and no truncation is needed. The short circuit current for the closed circular cylinder is computed rapidly using the FFT. The cylindrical problem is solved for large cylinders in three ways: 1. A direct Moment Method solution, 2. A direct spatial decomposition solution based on the MoM matrix and invoking the matrix partitioning technique, 3. The cylindrical add-on scheme. All solutions are identical, however, the computational advantage of the add-on technique is quite apparent, as seen from the analysis of the operation count as well as from numerical examples.

The buckling of orthotropic cylindrical shells under torsion has been solved as a three-dimensional elasticity problem. The constitutive differential equations have been solved by using a mixed form of the Galerkin method with a series of Legendre polynomials in the thickness coordinate. Results show that solutions based on the Donnell shell theory lead to nonconservative values for the critical loads for isotropic cylinders. Solutions derived from the shell theory results in higher critical loads for orthotropic cylinders. Shear deformation theories have been found to generate values that are similar to the elasticity solutions.