Elastic disk with isoperimetric Cosserat coating

Bifurcations of an elastic disc coated with an elastic inextensible rod

“…To satisfy the condition of inextensibility of the coating, additional relations for the complex coefficients A ±n can be obtained by using equation (99) 2 in [43] and the following relations [25]:…”

“…In the following, only the cases pertinent to equation (4.26) will be explicitely derived, while for the sake of brevity analogous treatment of equation (4.27) will not be reported. Using complex variables formalism, the bifurcation equation (4.7) can be rewritten by adopting the Fourier series representation introduced in §4b for the incremental boundary displacement and stress components at a point τ ∈ L. The first three terms on the left-hand side of equation 4.26) have been already derived in [25] and can now be adapted as…”

“…(where the superscripts 'c' and 'd' have been omitted) so that, using equations (43) reported in [25], equation (4.28) becomes…”

“…Equations ( 43) derived in [25] and the above equations (4.14), allow to rewrite equations (4.32) as…”

“…The present article employs the coating model for an elastic disc introduced in [25], which can be considered a specific case of the shell-coating model formulated in [26]. This model assumes that the elastic disc is coated with an elastic rod that is axially inextensible and unshearable, thereby introducing a Cosserat and isoperimetric constraint for the disc.…”