Heterogeneous Cylinder Research Articles

Minimum Weight Design of Stiffened Fiber Composite Cylinders

Abstract : A structural synthesis capability for stiffened fiber composite cylindrical shells has been developed. The design variables are the configuration and material parameters. The material parameters considered are the fiber volume content and the ply orientations in the skin. Both longitudinal and circumferential stiffeners are assumed to have hat cross-sections. The instability loads of the heterogeneous anisotropic cylinder under combined axial, radial, and torsional loading are calculated with smeared stiffener theory. In the synthesis scheme, multiple load conditions on the cylinder are permissible. The optimal design problem is cast into a model of a nonlinear mathematical programming problem which is solved with the penalty function technique of Fiacco-McCormick. Since weight is independent of the ply orientations there exist alternative optima. Special modifications on the iteration procedure are made, so that the ply angles tend to move in such a way that the overall strength of the cylinder is improved. Numerical examples are discussed. (Author-PL)

The State of Stress and Strain in an Orthotropic Heterogeneous Viscoelastic Cylinder with Burning Inner Boundary

The analysis of stress and strain in an orthotropic heterogeneous linear viscoelastic cylinder which has a burning inner boundary and which is subjected to a time-dependent internal pressure, has been worked out. The assumptions of isothermal conditions and infinitesimal strains are consistently made and the conditions of a quasistatic plane strain are adopted. Numerical solution for an orthotropic heterogeneous viscoelastic cylinder is established and which was anticipated to be quite stable. The established solution can be reduced to that of a homogeneous orthotropic cylinder. As special cases from the general problem, solutions for an isotropic compressible cylinder and an isotropic incompressible cylinder can also be derived. Numerical examples have been worked out to illustrate the influence of anisotropy, heterogeneity, and viscosity on the deformation of a burning cylindrical grain in a solid propellant rocket. The results for both short-time and long-time behavior are presented for a relaxation function of a form similar to that obtainable from a seven-parameter Maxwell model which has been shown to represent the rheological behavior of a filled elastomer fairly well.

XLIV On the potentials of uniform and heterogeneous elliptic cylinders at an external point

XLIV <i>On the potentials of uniform and heterogeneous elliptic cylinders at an external point</i>

On the rolling motion of a cylinder

The time occupied by a heterogeneous cylinder in oscillating upon a horizontal plane through a small arc has been investigated by Euler; and he has determined the pressure of the cylinder upon the plane when oscillating through any arc, applying the formula he has arrived at to find the pressure upon the plane at the highest and lowest points of oscillation. It is the object of the present paper to endeavour to extend this investigation to the continuous rolling of the cylinder, under which more general form its oscillation is obviously included as a particular case. In the first part of the paper, the time of rolling through any angle, and therefore of completing any given number of revolutions, is investigated ; and in the second, the conditions of the pressure upon the plane at any period of a revolution.

XXIII. On the rolling motion of a cylinder

The oscillatory motion of a heterogeneous cylinder rolling on a horizontal plane has been investigated by Euler. He has determined the pressure of the cylinder on the plane at any period of the oscillation, and the time of completing an oscillation when the arcs of oscillation are small . The forms under which the cylinder enters into the composition of machinery are so various and its uses so important, that I have thought it desirable to extend this inquiry, and in the following paper I have sought to include in the discussion the case of the continuous rolling of the cylinder, and to determine— 1st. The time occupied by a heterogeneous cylinder in rolling continuously through any given space. 2ndly. The time occupied in its oscillation through any given arc. 3rdly. Its pressure, when thus rolling continuously, on the horizontal plane on which it rolls.