Asymptotic analysis for periodic perforated shells

Asymptotic Analysis and Computation for Shells

Several examples are discussed of asymptotic results illustrating key features of thin shell behavior and possibly extending the benchmark problems for verification of direct numerical procedures. The basic nature of shell solutions for static loading usually can be categorized as membrane, inextensional, and edge effect. With different boundary conditions or geometry, different solution types ...

Asymptotic analysis of periodically-perforated nonlinear media

A well-known result on the asymptotic behaviour of Dirichlet problems in perforated domains shows the appearance of a ‘strange’ extra term as the period of the perforation tends to 0. In a paper by Cioranescu and Murat [10] (see also e.g. earlier work by Marchenko Khrushlov [17]) the following result (among others) is proved. Let Ω be a bounded open set in R, n ≥ 3 and for all δ > 0 let Ωδ be t...

Separation of scales and almost-periodic effects in the asymptotic behaviour of perforated periodic media

Homogenization of Thin Piezoelectric Perforated Shells

We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled....

Asymptotic Solutions for Shells with General Boundary

The influence of arbitrary edge loads on the stresses and deformations of thin, elastic shells with general boundaries is studied by means of asymptotic expansions of a general tensor equation. Expansions are made in terms of an exponential or an Airy function and a series in powers of a small-thickness parameter. Most of the steps in the procedure are effected by using the dyadic form of the t...