A NEW APPROACH TO STRESS-ANALYSIS OF ANISOTROPIC LAMINATED ELASTIC CYLINDERS

We propose a new numerical method for the determination of stress and deformation in laminated and inhomogeneous, anisotropic, elastic and t hermoelastic plates and shells. The method determines numerical soluti ons of the three-dimensional elasticity equations, without recourse to any thin plate or shell approximations. It is based on a transfer mat rix formulation of the elasticity equations and proceeds by using fini te-difference approximations to derivatives in the in-surface coordina te directions, while retaining the derivatives in the through-thicknes s direction. This leads to a system of linear first-order differential equations, for the through-thickness values at the gridpoints, of the relevant stress and displacement variables. These equations are solve d numerically by standard methods. In this paper we consider the speci fic problem of an anisotropic laminated circular thermoelastic cylinde r in plane strain, but various other problems may be formulated in a s imilar way. We present numerical solutions to four test problems for a laminated circular cylinder under: (i) sinusoidally varying internal pressure; (ii) mixed boundary conditions with a through-thickness temp erature variation; (iii) a spatially discontinuous internal pressure, and (iv) both angular and radial temperature variation. For problems ( i), (ii) and (iv) analytical solutions are also derived, and excellent agreement between the numerical and analytical solutions is obtained.