Membrane Theory Research Articles

Mechanical study on initial profile solution for inflatable reflector made of orthotropic material

The woven fabric membrane materials are widely used in space and terrestrial inflatable reflectors. However the material׳s anisotropy makes the design analysis more complex. The deviation from the desired shape, so-called “W-profile error”, influences the precision of the membrane surface significantly. In this study, a model of an axisymmetric paraboloid surface using membrane theory is established for the purpose of facilitating the surface precision optimization. Analytical solutions for displacements of the reflector are derived. An iteration method of initial reflector profile solution is stated and a finite element (FE) software employed in the solution is presented. A case study is illustrated to make a comparison between numerical and theoretical analyses. Finally, the conclusions are drawn that the analytical method and the FE iterative method for initial profile solution are feasible and efficient.

Role of atomic vacancies and boundary conditions on ballistic thermal transport in graphene nanoribbons

Quantum thermal transport in armchair and zigzag graphene nanoribbons is investigated in the presence of single atomic vacancies and subject to different boundary conditions. We start with a full comparison of the phonon polarizations and energy dispersions as given by a fifth-nearest-neighbor force-constant model (5NNFCM) and by elasticity theory of continuum membranes (ETCM). For free-edge ribbons, we discuss the behavior of an additional acoustic edge-localized flexural mode, known as fourth acoustic branch (4ZA), which has a small gap when it is obtained by the 5NNFCM. Then, we show that ribbons with supported edges have a sample-size dependent energy gap in the phonon spectrum which is particularly large for in-plane modes. Irrespective to the calculation method and the boundary condition, the dependence of the energy gap for the low-energy optical phonon modes against the ribbon width $W$ is found to be proportional to $1/W$ for in-plane, and $1/{W}^{2}$ for out-of-plane phonon modes. Using the 5NNFCM, the ballistic thermal conductance and its contributions from every single phonon mode are then obtained by the nonequilibrium Green's function technique. We found that, while edge and central localized single atomic vacancies do not affect the low-energy transmission function of in-plane phonon modes, they reduce considerably the contributions of the flexural modes. On the other hand, in-plane modes contributions are strongly dependent on the boundary conditions and at low temperatures can be highly reduced in supported-edge samples. These findings could open a route to engineer graphene based devices where it is possible to discriminate the relative contribution of polarized phonons and to tune the thermal transport on the nanoscale.

Higher dimensional quantum Hall effect as A-class topological insulator

We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.

Anisotropic spontaneous curvatures in lipid membranes.

Symmetry restrictions due to fluidity require the strain energy in the Helfrich theory of lipid membranes to be locally isotropic in nature. Although this framework is suitable for modeling the interaction of membranes with proteins that generate spherical curvature such as clathrin, there are other important membrane-bending proteins such as BIN-amphiphysin-Rvs proteins that form a cylindrical coat with different curvatures in the longitudinal and the circumferential directions. In this work, we present a detailed mathematical treatment of the theory of lipid membranes incorporating anisotropic spontaneous curvatures. We derive the associated Euler-Lagrange equations and the edge conditions in a generalized setting that allows spatial heterogeneities in the properties of the membrane-protein system. We employ this theory to model the constriction of a membrane tubule by a cylindrical scaffold. In particular, we highlight the role of the equilibrium equation in the tangential plane in regulating the spatial variation of the surface tension field.

Inverse problem for shape control of flexible space reflectors using distributed solar pressure

This paper investigates controlled elastic deflection of thin circular space reflectors using an inverse problem approach to non-linear thin membrane theory. When changing the surface reflectivity across the membrane, the distributed loads due to ambient solar radiation pressure can be manipulated optically, thus controlling the surface shape without using mechanical or piezo-electric systems. The surface reflectivity can in principle be modulated using uniformly distributed thin-film electro-chromic coatings. We present an analytic solution to the inverse problem of finding the necessary reflectivity distribution that creates a specific membrane deflection, for example that of a parabolic reflector. Importantly, the reflectivity distribution across the surface is found to be independent of membrane size, thickness and solar distance, enabling engineering of the reflectivity distribution directly during the manufacture of the membrane.

Integrable structure in discrete shell membrane theory

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Mechanics of filled jute bag

A simplified model of a filled-in jute bag in the form of composite shell of three segments, each of which is generated by surface of revolution, is assumed. The development and distribution of stresses in the different portions of the composite shell under the action of uniform internal pressure is calculated using membrane theory. The portion subjected to maximum stress and the controlling factors in the failure of bag, such as bag dimension and width/length ratio of bag, are identified. These findings corroborate the observations related to failure of filled jute bags in actual use.

A New Way to Simulate the Fluid Structure Interaction between the Bioprosthetic Heart Valve and Blood: FE-SPH Method

The object of this study is to utilize FE-SPH method to simulate the dynamic behavior of bioprosthetic heart valve during systole. Two kind of bioprosthetic heart valve numerical models are designed based on membrane theory, and they are represented by FE mesh, the blood is modelled as SPH particles. The interaction between the blood and bioprosthetic heart valve is carried out with contact algorithms. Results show that: when the valve leaflets are opening, compared with that of spherical valve, the stress and strain states of cylindrical valve are unstable, and the peak Von Mises is also higher, which high peak stress and its instability may induce the fatigue of valve. The valve opening time of columnar valve leaflets is longer than that of spherical ones, which reduces the blood ejection time. Above results indicate that spherical valve is superior to cylindrical valve. The FE-SPH method is capable of simulating the fluid structure interaction between the bioprosthetic heart valve and blood during the systole.

Free Vibration Analysis of Inflatable Space Structure

This paper present the modal analysis for the predicating the behavior of inflatable membrane structure of general square shape with a thickness in millimeter using the various smart material which optimally within structural member subjected to edge- constrained rather than applying bending or moments. A numerical solution for membranes may also be found using the finite element method. In this paper flat thin membrane choose to analysis the behavioral effect of the multi-layered membranes using the properties of different smart material and compare their results in terms of frequency and out plane deflection with mode shape. This analysis makes more effective to select the smart materials in the space technology. Vibration analysis of arbitrary square shape membrane is also done using a finite element package, ANSYS APDL. The analysis shows good agreement in finite element solutions. Keywords: Boundary condition, finite element, material property, membrane, mode shape, natural frequency, out plane displacement. I. Introduction In the field of Engineering and Architecture, membrane structures play a vital role in many ways. Examples include textile covers and roofs, aircraft and space structures, parachutes, automobile airbags, sails, windmills, human tissues and long span structures. They are typically built with very light materials which are optimally used. These structures are characterized because they are only subjected to in-plane axial forces. Even in the field of architectures and civil engineering, both pre-stressed membranes and cable networks constitute a very remarkable group. A membrane is essentially a thin shell with no flexural stiffness. Consequently a membrane cannot resist any compression at all. However, membrane theory accounts for tension and compression stresses, and the need for a computational procedure that takes into account tension stresses only is needed. In membrane theory only the in-plane stress resultants are taken into account. A numerical solution for membranes may be found using the finite element method (1-3). The deployable space structures consist of thin polymer films that offer a wider range of packaging configurations than structures with traditional deployment mechanisms. Due to the flexibility of such deployable structure like shell or membrane shows greater importance for space application and hold great promise. The material constitutive behavior and the analytical tools to analyze them are required to make advances in building cheaper, lighter and more reliable structures. Many structures are in the developing stage and the materials that are meant to serve to make these applications possible are not yet within reach. Future missions depend much on new discoveries, mainly in material manufacturing. There are several different space applications in which the use of thin membrane structures are used or being considered. Due to their light weight, high strength-to-weight ratio and ease of stowing and deploying, membranes are especially attractive for space applications. Inflatable reflectors, space-based radar, space based communication systems such as antennae and solar power collection panels on spacecraft, etc are the examples included. (4-5). The membrane material used in the numerical analysis was assumed inextensible and its weight was neglected in the determination of the equilibrium shape. They found that the membrane's mass density is of little influence on the computed natural frequencies. Other researchers used finite elements and boundary elements to model and compute natural frequencies and mode shapes of a single-anchor inflatable dam (6). This study makes impact on finding the vibration aspect on the flat membrane using the various smart materials. The pressure in an inflatable structure can also play a critical role in the suppression of vibration (7). Literature that exists on pure structural membrane components has concentrated mostly on inflated components such as beams (8), torus (Main), and inflated lenticular concentrators (9). The dynamics of the membrane themselves are of great interest though, as it is the membrane itself that is performing the useful work, and in some applications they could be attached to more traditional aerospace structures. Therefore improving understanding the behavior of the membranes appears to be important. A membrane is essentially a thin shell with no flexural stiffness. Consequently a membrane cannot resist any Compression at all. However, membrane theory accounts for tension and compression stresses. In membrane theory only the in-plane stress resultants are taken into account (10). This paper present the modal analysis for the predicating the behavior of various inflatable membrane structure of general square shape with a thickness in millimeter using the various smart materials. A numerical solution for membranes may be found using the finite element method. Finite element analysis of membrane structures for small deformations can be found in (11) but

Phenomenological Elasticity Theory Approach to Bolalipid Membranes

Extremophilic bacteria reveal exceptional stability and vitality under the high temperature, pressure and environment acidity. Such features are considerably provided by properties of their membranes composed of bolalipids. Therefore bolalipids appears to be very intriguing and promising object for the investigations. As opposed to “conventional” lipids bolalipids are composed of two polar head connected by two hydrocarbonic tails. As a rule they pierce through the whole membrane. At present the investigation of bolalipids is at its opening stage of the gathering of the various experimental and computer simulations data. However, for the effective progress in the investigation of the bolalipid membranes the elasticity theory should be developed. Similar theory applied to the conventional lipid membranes gives results that are in an excellent agreement with the experimental data. That is why we have chosen the way of the adaptation of the effective elasticity theory of lipid membranes to the case of bolalipids.In the present work we constructed the phenomenological elasticity theory of the bolalipid membranes. The set of all feasible types of deformations are found and the number of the possible experiments for the determining of the elastic moduli are suggested. Theory takes into account the presence of the two configurations of bolalipids in the membrane: U-shape and O-shape configurations. The way of the experimental determination of the ratio of these configurations is proposed.

Single Part Influence on Assemblies for a Cycle Time Able Quality Control as well as a Suitable Toleration

The complex interrelations of force and stiffness during the clamping process of freeform shaped parts in car body fixtures cannot be described in a universal valid way by membrane theory. So calculations with FEM are used for this. However due to the long calculating time FEM is not suitable for fast quality decisions during the process. The paper presents a new method that is able to calculate adjustments and combination possibilities of different part failure classes within sub-second range. In addition the new method, that is based on a systematic analyze of the single part influences to the assembly, gives an understanding of the interrelations of all components of an assembly. So a suitable toleration is possible. The method is shown by means of an assembly example.

円筒から切り出されたシェルの片持ち支持条件下における膜応力的特徴

A cantilever-supported shell that is cut out from a circular cylinder is investigated. It is found that the shell with the specified boundary shape has a membrane stress field, which is obtained by solving analytically the differential equations. In order to confirm the results, typical examples are solved numerically using FEM based on Galerkin type weak form. Then, the effect of the plate bending neglected by membrane theory is investigated. Furthermore, it is verified that the influence caused by difference between the idealized boundary condition of the membrane theory and the exact fixed boundary condition of FEM is very small. Therefore, this shell is said mostly in membrane stress state, and has shell-like advantage on shape, space and ecomomy.

A Simplified Method for Analysis of Geosynthetic Reinforcement Used in Pile Supported Embankments

The inclusion of geosynthetic reinforcement in the piled embankment can help transfer loads to the piles and reduce total and differential settlements. In order to select the appropriate reinforcement material, the reasonable calculation of the deflection and tension is very important. Current design methods usually do not represent the true three-dimensional (3D) nature of the displacements, strains, and stresses of the geosynthetics, and the resulting error may be large and cannot be neglected in some cases. In this study, two- and three-dimensional finite element analyses were conducted to identify the behavior of geosynthetic reinforcement and investigate the accuracy of the assumptions made in the current design methods. Based on the numerical results, a new 3D deflected shape of the geosynthetic reinforcement was suggested, and then the corresponding governing equation was derived and solved based on the membrane theory. To investigate the validity of the proposed method, the predicted maximum deflection, deflection shape, and the developed tensile force of the geosynthetics have been compared with the experimental data collected from the literatures and finite element analysis results.

Hybrid and Nonhybrid Lipids Exert Common Effects on Membrane Raft Size and Morphology

Cell membranes perform multiple functions that may be facilitated by the lateral organization of lipids and proteins into nanoscale compartments, termed membrane rafts. Understanding the origins of raft domains and the physicochemical mechanisms that control their finite small size is important for elucidating their functional significance and manipulating their properties. However, it has proven difficult to characterize rafts in cells due to the chemical complexity of biological membranes, and various models have been advanced based on theory and experiments of representative model membranes. In one popular model, a special role in the domains existence and properties has been postulated for chain-asymmetric or hybrid lipids having a saturated sn-1 chain and an unsaturated sn-2 chain. It was proposed that these lipids align in a preferred orientation at the boundary of ordered and disordered phases, lowering the interfacial energy and thus reducing domain size. Such a unique "line-active" role for hybrid lipids is an appealing explanation for nanoscopic rafts, as animal cell membranes contain few symmetric low-melting lipids but an abundance of hybrid lipids. We present data from small-angle neutron scattering and fluorescence techniques demonstrating the existence of nanoscopic and modulated liquid phase domains in a mixture composed entirely of nonhybrid lipids and cholesterol. Our results are indistinguishable from those obtained previously for mixtures containing hybrid lipids, conclusively showing that hybrid lipids are not required for the formation of nanoscopic liquid domains. These findings present new challenges for current theoretical descriptions of nanodomains.

Resonant Frequency and Phase Noise of Nanoelectromechanical Oscillators Based on Two-dimensional Crystal Resonators

Abstract This study presents a theoretical analysis of one of the most promising nanoelectromechanical (NEMS) components – a NEMS oscillator. The analyzed oscillator contains a stretched circular plate, fabricated of two-dimensional crystals (graphene, bBN, MoS2 etc.), as a resonator. The calculation of resonant frequency based on the classical continuum theory of plates and membranes is presented, and then the phase noise theory of the oscillators using a circular plate as a frequency determining element. We assume that thermal and 1/f noise are present in the oscillator circuit. A satisfactory agreement is obtained between our calculations and recent experimental literature data for graphene.

Wetting transitions within membrane compartments.

A biomimetic membrane in contact with several aqueous phases is theoretically studied using a combination of Helfrich curvature elasticity theory for fluid membranes and self-consistent field theory for polymers in solutions. Two phases that are thermodynamically formed by phase separation of aqueous solutions, as well as stable and metastable shapes of fluid vesicles, have been observed. The wetting transitions from complete to partial wetting and to complete dewetting are identified within a membrane compartment. The dependences of wetting transitions on material parameters, such as the intrinsic contact angles θin, the interaction strengths between the polymers χαβ and between the membrane and the polymer ηp, and impermeability of the membrane to the enclosed polymers ζp, are investigated. For a given χαβ, impermeability ζp and affinity to the membrane ηp, θin is found to be a constant and independent of the reduced volume of vesicles and the volume fraction of two phases.

Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition

This paper presents the nonlinear free vibration analysis of axisymmetric polar orthotropic circular membrane, based on the large deflection theory of membrane and the principle of virtual displacement. We have derived the governing equations of nonlinear free vibration of circular membrane and solved them by the Galerkin method and the Bessel function to obtain the generally exact formula of nonlinear vibration frequency of circular membrane with outer edges fixed. The formula could be degraded into the solution from small deflection vibration; thus, its correctness has been verified. Finally, the paper gives the computational examples and comparative analysis with the other solution. The frequency is enlarged with the increase of the initial displacement, and the larger the initial displacement is, the larger the effect on the frequency is, and vice versa. When the initial displacement approaches zero, the result is consistent with that obtained on the basis of the small deflection theory. Results obtained from this paper provide the accurate theory for the measurement of the pretension of polar orthotropic composite materials by frequency method and some theoretical basis for the research of the dynamic response of membrane structure.

Furrow Constriction in Animal Cell Cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles’ surface tension.

Conceptual thoughts on continuum damage mechanics for shallow ice shelves

AbstractWe consider a theory for shallow ice shelves that includes an isotropic damage variable. A zeroth-order shallow-shelf approximation allows a simple yet consistent treatment of both ice dynamics and damage evolution. We find that the damage variable (like temperature) has, in general, to vary with depth; a purely two-dimensional membrane theory can only be considered a rough approximation for isothermal ice shelves.

Shapes of vesicles encapsulating two aqueous phases

Motivated by recent experiments, vesicles encapsulating two aqueous phases are theoretically explored using a combination of Helfrich curvature elasticity theory for fluid membranes and self-consistent field theory for polymers. The spatial distributions of two polymers, α and β, have been obtained, and two thermodynamic phases occur, as expected. Stable or metastable shapes of fluid and closed vesicles have also been achieved. Due to the impenetrability of the membrane to polymer, the available spaces of polymers α and β are limited and the conformational entropies for the polymers are reduced. Different chain segments that possess different permeability to the membrane would induce different inhomogeneous entropic pressures on the membrane, thereby leading to shape transformations of the vesicles. In the present study, the typical shapes of vesicles encapsulating two phases are studied as functions of the concentrations of polymers α and β, and the interactions between the chain segments and the membrane. The two phases formed by polymers α and β are also found to be altered and have been discussed in detail. In addition, morphological phase diagrams are presented as a function of the reduced volume, v. The phase boundaries between oblates and prolates, and oblates and stomatocytes of vesicles encapsulating two phases are found to move toward the higher reduced volume, and oblates occupy a much wider range of the reduced volume compared with 'neat' vesicles.