Effective Bending Rigidity Research Articles

The equivalence of a jointed shield-driven tunnel lining to a continuous ring structure

This paper presents a new method of determining the correction factor to approximate a jointed, shield-driven tunnel lining as a continuous ring structure under plane strain conditions. An earth pressure distribution pattern is proposed which is developed based on the long-term behavior of shallow tunnels constructed in soft clays as observed in the field. The "force method" was used to determine the internal forces and displacements of jointed, shield-driven tunnels. Either the vertical or the horizontal displacement of the tunnel lining can be used as a common matching parameter. Factors such as joint stiffness, soil resistance, joint distribution, number of joints, and tunnel geometry can be considered by the proposed method. Simplified design equations for the estimation of equivalence factors are also proposed for the typical tunnel lining geometry of urban subway tunnels. The proposed equivalence method was evaluated by comparing it with the results of laboratory tests.Key words: shield-driven tunnel, jointed segmental lining, effective bending rigidity ratio, equivalence factor, lining internal force, earth pressure distribution.

The equivalence of a jointed shield-driven tunnel lining to a continuous ring structure

This paper presents a new method of determining the correction factor to approximate a jointed, shield-driven tunnel lining as a continuous ring structure under plane strain conditions. An earth pressure distribution pattern is proposed which is developed based on the long-term behavior of shallow tunnels constructed in soft clays as observed in the field. The "force method" was used to determine the internal forces and displacements of jointed, shield-driven tunnels. Either the vertical or the horizontal displacement of the tunnel lining can be used as a common matching parameter. Factors such as joint stiffness, soil resistance, joint distribution, number of joints, and tunnel geometry can be considered by the proposed method. Simplified design equations for the estimation of equivalence factors are also proposed for the typical tunnel lining geometry of urban subway tunnels. The proposed equivalence method was evaluated by comparing it with the results of laboratory tests.Key words: shield-driven tunnel, jointed segmental lining, effective bending rigidity ratio, equivalence factor, lining internal force, earth pressure distribution.

Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes

We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchanged.

Adsorption of Semiflexible Polyelectrolytes on Charged Planar Surfaces: Charge Compensation, Charge Reversal, and Multilayer Formation

We study theoretically the adsorption of semiflexible charged polymers on an oppositely charged flat substrate. We restrict ourselves to polymers with relatively high line charge density τ and bare bending stiffness 𝓁0, such as DNA or fully charged synthetic polyelectrolytes, for which the condition τ2𝓁B𝓁0 > 1 (with 𝓁B = e2/4πεkBT denoting the Bjerrum length) is satisfied. In this case the effective bending rigidity (which includes chain stiffening due to electrostatic monomer−monomer repulsion) is always larger than the screening length, and we obtain very thin adsorption layers, where the polymers essentially lie flat on the surface and can be considered as a two-dimensional layer. We distinguish different adsorbed phases, including a two-dimensional lamellar phase where the polymers run parallel and do not overlap and a disordered phase where the polymers form a random network with multiple crossings. By explicitly including lateral correlations within the adsorbed layer, we find a regime of strong charge reversal, where the adsorbed phase exhibits a much higher surface charge density than the substrate and thus reverses the charge of the substrate by a factor much larger than unity. This charge-reversed regime is characterized by a typical distance between polymers larger than the screening length. We explicitly take image charge effects due to a dielectric jump at the substrate surface and the impenetrability of the substrate for salt ions into account. These effects lead to an increase of the electrostatic persistence length close to the substrate and inhibit adsorption for strongly charged polymers and low-dielectric substrates. At the end, we present some scaling arguments for the formation of charge-oscillating multilayers.

Inversion of pack ice elastic wave data to obtain ice physical properties

Geophones mounted on floating ice sheets can potentially provide data for a robust method to monitor mechanical properties of the ice. The technique relies on the measurement and inversion of low‐frequency elastic waves propagating in the ice. To test this hypothesis, several geophone systems were deployed on the Arctic ice as part of the Office of Naval Research Sea Ice Mechanics Initiative (SIMI), including a winter‐over system of 20 triaxial geophones at the fall 1993 SIMI camp. An inversion technique is discussed here through references to the literature and by analysis of geophone data, specifically those data collected on “clean” first‐year ice off Resolute Bay, Canada, and on highly irregular multiyear ice found at the fall SIMI camp. For undeformed first‐year ice, the inversion technique gave an estimate of ice properties that agreed well with known values, although extensive work remains to determine the effects of anisotropy and inhomogeneity. The geophone data for the nonuniform ice at the SIMI camp were very complex and difficult to analyze. The inversion yielded only trends in what can, at best, be termed effective ice thickness and bending rigidity; it is uncertain how these relate to actual ice properties. The SIMI geophone system demonstrated the feasibility of performing autonomous measurements of the characteristics of propagating waves in the Arctic ice; with continued study, it seems evident that such systems can be used in clean first‐year ice to monitor ice properties. However, extensive research is required to make this technique useful in multiyear or complex first‐year ice.

Stiffening of fluid membranes and entropy loss of membrane closure: Two effects of thermal undulations

The problem of membrane softening by thermal undulations is revisited. In contrast to general belief, fluid membranes are predicted to be stiffened, not softened, by their undulations. Equal values of the effective bending rigidity are calculated from the interplay of local mean curvature modes (hats) on the basically flat membrane and from the coupling of spherical harmonic modes with spherical curvature. In addition, a conjecture is made on the entropy of membrane closure. It relies on a similarity of membrane closure to periodic boundary conditions.

Inhomogeneous fluid membranes: Segregation, ordering, and effective rigidity.

Fluid membranes with spatially varying distributions of bending rigidity and spontaneous curvature are considered, which are applicable to inhomogeneous membranes consisting of different components and membranes with inclusions (such as proteins) or adsorbed colloidal particles. Thermally activated shape fluctuations of the membrane induce rather long-ranged interactions between these inhomogeneities, which are free to diffuse laterally and to organize into spatial structures. As a consequence of these interactions, one finds two ordered phases in addition to the disordered phase in which the inhomogeneities are randomly mixed: a segregated phase, where the inclusions tend to aggregate, and a hexagonal phase, where the inclusions maximize their mutual separation. The phase behavior depends crucially on the lateral correlation length within the membrane. Also, the effective bending rigidity of the membrane is calculated for all different phases; in general, the inhomogeneities in the elastic moduli considered here lead to a characteristic softening of the membrane. These results, which are obtained using perturbation theory, are confirmed by Monte Carlo simulations. Experimental applications comprise proteins or adsorbed colloidal particles in vesicular bilayers and lamellar stacks and membranes consisting of lipid mixtures.

From monolayers to bilayers: Effective rigidity and compressibility in asymmetric ternary amphiphilic systems.

Fluctuation effects in lamellar phases of ternary asymmetric amphiphilic systems are considered. These systems are characterized by two length scales corresponding to the thickness of the oil and water layers. For large separations between the amphiphilic layers, the dominant contribution to the free energy can be written in the Helfrich form if an effective bending rigidity is introduced that is allowed to depend on the water and oil layer thicknesses. The scaling form of this effective rigidity is determined from Monte Carlo simulations of an asymmetric three-layer system. An expression for the effective layer compressibility is derived, which can be expressed in terms of the effective bending rigidity. These effects lead to pronounced corrections of the scattering exponents ${\mathrm{\ensuremath{\eta}}}_{\mathit{m}}$, which can be measured in scattering experiments.

The conformation of fluid membranes: Monte Carlo simulations.

The conformation and scaling properties of self-avoiding fluid membranes with an extrinsic bending rigidity kappa were studied with the use of Monte Carlo methods. For kappa = 0, the results are consistent with branched polymer behavior at large length scales. There is a smooth crossover from a crumpled to an extended state with increasing kappa, with a peak in the specific heat when the persistence length reaches the system size. The scale-dependent effective bending rigidity is a decreasing function of system size for all bare rigidities. These results indicate that fluid membranes are always crumpled at sufficiently long length scales.

Shear-Lag Effect in Sandwich Panels With Stiffeners Under Three-Point Bending

In this paper, a modified theory based upon Reissner’s procedure for the shear-lag effect of the sandwich panel is presented, which includes the effects of the anisotropy of the faces and the shearing rigidity of the core. In order to verify this theory, bending experiments were performed with sandwich panels composed of a soft core, stiffeners, and orthotropic faces. It was found that the effective bending rigidity calculated from this theory was lower than that derived from the classical bending theory and that the theoretical strain distribution on the faces agreed well with the experimental results.