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Although it is often asserted that, in view of their reduced length, axially compressible beams have a higher buckling load than their inextensible counterpart, a detailed analysis demnstrates that this is not necessarily the case. The argument to arrive at this conclusion is made in terms of relatively straightforward concepts of elasticity and structural mechanics. It is shown that for certain classes of materials the reduced pre-buckling length is more than compensated by a softening of the elastic response, leading to a reduction of the Euler critical load.

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed in their weak and strong forms. A suitable finite element is used to accommodate the new degrees of freedom emanating from the theory and several numerical examples with large geometrical nonlinearities are displayed showing the relative influence of the strain gradient. The numerical apparatus is then applied to permanently magnetized bodies under the action of external magnetic fields.

The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various measures of misalignment and lack of uniformity that may arise when two individually perfectly uniform structures are combined are suggested, and the concept of coupled symmetries is proposed and illustrated.