Gj. Ruddock et Ajm. Spencer, A NEW APPROACH TO STRESS-ANALYSIS OF ANISOTROPIC LAMINATED ELASTIC CYLINDERS, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 453(1960), 1997, pp. 1067-1082
Citations number
24
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
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.