# Solve the problem of a thin (radius-to-thickness ratio r o /t = 100) clamped isotropic (v = 0.3)…

Solve the substance of a meager (radius-to-lumpishness kindred r_{o}/t
= 100) clamped isotropic (v = 0.3) round extract after a while unintermittently distributed
load using the atom familiar in Substance 4.23. Exploit devise, and use two
meager extract (EulerBernoulli) atoms in the computational inclosure.

Problem 4.23

Consider the axisymmetric adulatory of a rectirectilinear elastic round extract of perpetual lumpishness. The controlling differential equation according to the meager extract presumption is (see Section 7.3 for additional details)

where D_{11} D_{12}, and D_{22} are
the extract embodied stiffnesses (constant), W is the athwart alienation, and
r is the radial coordinate. Develop

(a) the foolish devise of the equation aggravate a regular atom
Ω^{e }= (r_{A} , r_{B}); the quantities in
parentheses should not be integrated by parts;

(b) the limited atom example of the equation in the devise

Make firm that [K^{e} ) is symmetric (i.e., the
birectilinear devise in (a) should be symmetric). Comment on the interpolation
functions that are admissible for the atom.