Heterogeneity of a material or construction can be caused by two main reasons.
Non-uniformity of certain physical characteristics (density, elastic modulus, con-
conductivity, etc.) is the first. Two- or multi-phase composites are typical examples of
this type of material. The second origin of heterogeneity is a geometrical one. Re-
Reinforcement of the shells and plates by stringers, discrete supports and other con-
constructive elements is widely used in numerous applications. Both reasons cause
heterogeneity of the stress-strain state and the descriptions of the mechanical re-
responses meet very similar mathematical difficulties. Therefore, it is natural to ana-
analyze and solve the corresponding boundary-value problems applying a similar and
in some cases identical technique.
Many problems in modern composites, heterogeneous plates and shells theory
are governed by partial differential equations with rapidly changing and mostly
discontinuous coefficients. Obviously, there are two opposite limits in which the
direct application of conventional technique is efficient.
The first limit is a small number of heterogeneities. It means that the scale, /, of
inhomogeneity (inclusion diameter, distance between stringers, etc.) is of the same
order as the typical outer size, L, of the structure, L <* /. Direct numerical methods
(finite elements, finite differences, etc.) should be applied in this case. The high
level of modern digital computing power provides precise results in numerous
complicated problems of composites, plates and shell mechanics.
However, even modern computers [65,71,158] cannot efficiently assist in solv-
solving the problems corresponding to the mechanics of heterogeneous media in the
opposite limit L » /. This is a reason for an application of certain kind of homog-
enization technique in this limit: effective media theory (EMT, the term used in
composite mechanics) or structurally orthotropic theory (SOT, the term used in
plate and shell mechanics) in particular. The replacement of heterogeneous media
by the homogeneous continuum, which is characterized by certain effective consti-
constitutive equations, is the basic instrument for both EMT and SOT. Four important
questions should be resolved in the context of homogenization of the media.