Aleksandrov and Pogorelov used bending fields (the velocity fields of continuous isometric deformations) to show infinitesimal rigidity of some classes of surfaces ([2] and [12]). Bending fields (and the rigidity matrix) were also successfully employed in the study of infinitesimal rigidity of polyhedra and tensegrity frameworks (see [7]). We will use these tools to re-derive a previously known...

The article shows the effect of torsional rigidity of beam elements onto spatial work of bridges, floorings and other plate-ribbed systems It is shown that, in determining the torsional rigidity using existing methods it is necessary to have spatial spiral cracks, but torsional rigidity when normal cracks is not researched. A method is described for determining the torsional rigidity of reinfor...

The bilayer bending rigidities were measured for the same spherical vesicles with two methods, fluctuation mode analysis and electric deformation. In some of the sample cells the glue sealing the cell was in direct contact with the sample, in others the sample was shielded from the glue by a silicone grease. The values of the rigidity, wlfile being lowest and practically equal for the unshielde...

We propose a new micromechanical approach to probe bending rigidity at molecular scale. Long flexible filaments made of magnetic colloids and linkers are shown to adopt under magnetic field a hairpin configuration. Measuring the hairpin curvature as a function of the field intensity and the linker length from diffracted light allows us to deduce the linker bending rigidity kappa. The technique ...

We study the spontaneous symmetry breaking of the bending rigidity of lipid membranes in two principal directions by a Landau mean-field theory. When the temperature is below the tilting temperature (T(c)), the coupling between molecular orientation and membrane local curvature square leads to an increase of the bending rigidity in the tilting direction and therefore a spontaneous symmetry brea...

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes o...

The joints between segmental rings can withstand a certain amount of bending moment as well as axial and shear forces. Generally, in the structural analysis of tunnel segmental lining, the joints can be modeled as elastic hinges or rotational springs, and their rigidity should be demonstrated in terms of the rigidity of the joints or their rotational stiffness. Therefore, the bending moment act...

We give a rigorous proof of the approximability of the so-called Helfrich’s functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity.

The ease with which a cell membrane can bend and deform is important for a wide range of biological functions. Peripheral proteins that induce curvature in membranes (e.g. BAR domains) have been studied for a number of years. Little is known, however, about the effect of integral membrane proteins on the stiffness of a membrane (characterised by the bending rigidity, Kc). We demonstrate by comp...