Abstract:
Theory of three dimensional (3D) elasticity is utilized here in this paper for
boundary value problems (BVPs) of finite length cylinders. A diaphragm
supported cylinder under mechanical sinusoidal and uniformly distributed
pressure loads is considered as a two dimensional (2D) generalized plane
strain problem of elasticity in (r, z) direction. The 2D problem is reduced to a
one dimensional (1D) one by assuming an analytical solution in longitudinal
direction (z) in terms of Fourier series expansion which satisfies the simply
(diaphragm) supported boundary conditions exactly at the two ends z = 0, l.
Fundamental (basic) dependent variables are chosen in the radial direction of
the cylinder. The resulting first order simultaneous ordinary differential
equations are integrated through an effective numerical integration technique
by first transforming the BVP as a set of initial value problems (IVPs).
Numerical solutions for isotropic cylinders are first validated for their
accuracy with available 1D solution of an infinitely long cylinder. Stresses and
displacements in axial and radial directions in cylinders having various l/R and
h/R ratios are presented for future reference.
