Elliptical Membrane Research Articles

Numerical approximation of the solution of Koiter’s model for an elliptic membrane shell in absence of friction subjected to an obstacle via the penalty method

Numerical approximation of the solution of Koiter’s model for an elliptic membrane shell in absence of friction subjected to an obstacle via the penalty method

Comparative investigation of exosome extraction from rat bone marrow mesenchymal stem cells using three different methodologies

AbstractExosomes have been identified as crucial mediators in numerous physiological and pathological processes, emerging as a focal point of scientific inquiry. This study aims to compare three methods for isolating exosomes from rat bone marrow mesenchymal stem cells: ultracentrifugation (UC), ultrafast separation system (EXODUS), and commercial precipitation kit (EXO‐kit). First, the investigation compared exosomal morphology, particle size distribution, and expression of marker proteins. Subsequently, the RNA content, protein concentration, and purity of exosomes were evaluated. Finally, the impact of these exosomes on cellular metabolic viability and migration capacity was assessed. Results indicated that exosomes exhibited spherical or elliptical membrane structures, and most of the exosomes extracted by the three methods were in the range of 30to 200 nm. UC‐extracted exosomes demonstrated the least impurities and clearest background, followed by EXODUS‐extracted exosomes, and lastly EXO‐kit‐extracted exosomes. The EXO‐kit‐extracted exosomes yielded the highest RNA and protein content, whereas those isolated through UC exhibited superior purity. Furthermore, exosomes extracted from EXODUS and EXO‐kit methods effectively enhanced the metabolic viability and migratory ability of osteoblast precursor cells compared to UC‐extracted exosomes. In conclusion, each of the three methodologies presents advantages and limitations. Therefore, the selection of an appropriate exosome extraction technique should be based on specific experimental objectives and requirements.

Numerical Approximation of the Solution of an Obstacle Problem Modelling the Displacement of Elliptic Membrane Shells via the Penalty Method

Numerical Approximation of the Solution of an Obstacle Problem Modelling the Displacement of Elliptic Membrane Shells via the Penalty Method

Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

Most of engineering and biological thin shell structures are characterized by non-axisymmetric and statically indeterminate configurations, which often require the knowledge of the constitutive material model to determine the stress state. In this work, a forward elastostatic method is introduced for the direct stress measurements in elastic homogeneous thin shells of arbitrary shape. The stress distribution is proven to be independent of the material properties for incompressible solids, while in compressible materials it depends only on the Poisson’s ratio, which is shown to have a negligible influence on the stress state. Hence, the proposed technique enables the direct assessment of the stress field in statically indeterminate thin shells without a known material model. The shell formulation is implemented using the finite difference method to independently measure the stresses during finite inflation of planar elliptical membranes and from the deformed shapes obtained through digital image correlation during bulge tests on a hyperelastic material, showing very good agreement with finite-element predictions and the applicability of the method to nonlinear elastic materials. Therefore, the procedure can be coupled with imaging techniques for the direct assessment of stresses in thin shell structures and in the identification of material parameters through non-axisymmetric bulge tests.

Asymptotic analysis of linearly elastic elliptic membrane shells subjected to an obstacle

In this paper we identify a set of two-dimensional variational inequalities that model the displacement of a linearly elastic elliptic membrane shell subjected to a confinement condition, expressing that all the points of the admissible deformed configurations remain in a given half-space.

Viscoelastic elliptic membrane shells on bilateral frictional contact: An asymptotic approach

Viscoelastic elliptic membrane shells on bilateral frictional contact: An asymptotic approach

On the improved interior regularity of a boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle

<p style='text-indent:20px;'>In this paper we show that the solution of an obstacle problem for linearly elastic elliptic membrane shells enjoys higher differentiability properties in the interior of the domain where it is defined.</p>

On the justification of the frictionless time-dependent Koiter's model for thermoelastic shells

Our first objective is to identify two-dimensional equations that model the displacement of a linearly elastic flexural shell subjected to the action of an external heat source. To this end, we embed the shell into a family of linearly elastic flexural shells, all sharing the same middle surface θ ( ω ‾ ) , where ω is a domain in R 2 and θ : ω ‾ → E 3 is a smooth enough immersion and whose thickness 2 ε > 0 is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as ε approaches zero, the corresponding “limit” two-dimensional variational problem. Our second objective is to identify and justify a set of two-dimensional equations that are meant to approximate the original three-dimensional model in the case where the shell under consideration is either an elliptic membrane shell or a flexural shell.

Manufacturing and Characterisation of Polymeric Membranes for Water Treatment and Numerical Investigation of Mechanics of Nanocomposite Membranes.

In this study, polyethersulfone (PES) and polyvinylidene fluoride (PVDF) microfiltration membranes containing polyvinylpyrrolidone (PVP) with and without support layers of 130 and 150 μm thickness are manufactured using the phase inversion method and then experimentally characterised. For the characterisation of membranes, Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and pore size analysis are performed, the contact angle and water content of membranes are measured and the tensile test is applied to membranes without support layers. Using the results obtained from the tensile tests, the mechanical properties of the halloysite nanotube (HNT) and nano-silicon dioxide (nano SiO2) reinforced nanocomposite membranes are approximately determined by the Mori–Tanaka homogenisation method without applying any further mechanical tests. Then, plain polymeric and PES and PVDF based nanocomposite membranes are modelled using the finite element method to determine the effect of the geometry of the membrane on the mechanical behaviour for fifteen different geometries. The modelled membranes compared in terms of three different criteria: equivalent stress (von Mises), displacement, and in-plane principal strain. Based on the data obtained from the characterisation part of the study and the numerical analysis, the membrane with the best performance is determined. The most appropriate shape and material for a membrane for water treatment is specified as a 1% HNT doped PVDF based elliptical membrane.

Asymptotic Analysis of Elliptic Membrane Shells in Thermoelastodynamics

In this paper we consider a family of three-dimensional problems in thermoelasticity for elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero. We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain is the common middle surface of the family of three-dimensional shells. The problems are dynamic and the constitutive thermoelastic law is given by the Duhamel-Neumann relation.

Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model

Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model

Manufacturing, Characterisation and Mechanical Analysis of Polyacrylonitrile Membranes.

To investigate the effect of polyvinylpyrrolidone (PVP) addition and consequently porosity, two different sets of membranes are manufactured, since PVP is a widely used poring agent which has an impact on the mechanical properties of the membrane material. The first set (PAN 1) includes polyacrylonitrile (PAN) and the necessary solvent while the second set (PAN 2) is made of PAN and PVP. These membranes are put through several characterisation processes including tensile testing. The obtained data are used to model the static behaviour of the membranes with different geometries but similar loading and boundary conditions that represent their operating conditions. This modelling process is undertaken by using the finite element method. The main idea is to investigate how geometry affects the load-carrying capacity of the membranes. Alongside membrane modelling, their materials are modelled with representative elements with hexagonal and rectangular pore arrays (RE) to understand the impact of porosity on the mechanical properties. Exploring the results, the best geometry is found as the elliptic membrane with the aspect ratio 4 and the better RE as the hexagonal array which can predict the elastic properties with an approximate error of 12%.

Numerical simulations for the dynamics of flexural shells

In this paper, we study a model describing the displacement of a linearly elastic flexural shell subjected to given dynamic loads from the computational point of view. The model under consideration takes the form of a set of hyperbolic variational equations posed over the space of admissible linearised inextensional displacements, and a set of initial conditions. Since the original model is not suitable for the implementation of a finite element method, we conduct the experiments on the corresponding penalised model. It was recently shown that the solution to such a penalised model is a good approximation of the solution to the original model. Numerical tests are therefore conducted on the the penalised model; the approximation of the solution to the penalised model is obtained via Newmark’s scheme, which is then implemented and tested for shells having the following middle surfaces: a portion of a cylinder and a portion of a cone. For the sake of completeness, we also present the results of the numerical tests related to a model describing the displacement of a linearly elastic elliptic membrane shell under the action of given dynamic loads.

Determination of parameters of plastic deformation of elliptic membranes

Introduction. Thin-walled structural elements, combining lightness with high strength, are widely used in all industries. Widespread round design elements. However, based on the functional purpose, thin-walled structural elements of various shapes in plan are becoming more and more common. Methods. A technique has been developed for the study of thin elliptic membranes for the case of plastic deformation under the action of uniform pressure. The deflections of the membranes in the experiment are more than ten thicknesses. In this regard, to solve the problem, the following are used: geometric nonlinear relations for the deformations of the middle surface (according to Kh.M. Mushtari and K. Z. Galimov), relations for finite displacements and deformations for curvature expressions (according to K.Z. Galimov), physical relations (according to the theory of plasticity A.A. Ilyushin). Due to the smallness of the membrane thickness, only tensile membrane strains and forces are taken into account. The problem is solved by the Bubnov - Galerkin method and reduced to solving a nonlinear system of three algebraic equations. The “shooting” algorithm for solving the resulting system of equations is described. Results. The work on the assessment of the reliability of the results. To estimate the error, the comparison of the calculation results with the experimental results of G.D. Golovlev was also performed. An example of the calculation of an elliptical membrane is considered.

Effect of adipose-derived stem cell derived exosomes on angiogenesis after skin flap transplantation in rats

To investigate the effect of adipose-derived stem cell derived exosomes (ADSC-Exos) on angiogenesis after skin flap transplantation in rats. ADSCs were isolated and cultured by enzymatic digestion from voluntary donated adipose tissue of patients undergoing liposuction. The 3rd generation cells were observed under microscopy and identified by flow cytometry and oil red O staining at 14 days after induction of adipogenesis. After cells were identified as ADSCs, ADSC-Exos was extracted by density gradient centrifugation. And the morphology was observed by transmission electron microscopy, the surface marker proteins (CD63, TSG101) were detected by Western blot, and particle size distribution was measured by nanoparticle size tracking analyzer. Twenty male Sprague Dawley rats, weighing 250-300 g, were randomly divided into ADSC-Exos group and PBS group with 10 rats in each group. ADSC-Exos (ADSC-Exos group) and PBS (PBS group) were injected into the proximal, middle, and distal regions of the dorsal free flaps with an area of 9 cm×3 cm along the long axis in the two groups. The survival rate of the flap was measured on the 7th day, and then the flap tissue was harvested. The tissue morphology was observed by HE staining, and mean blood vessel density (MVD) was measured by CD31 immunohistochemical staining. ADSCs were identified by microscopy, flow cytometry, and adipogenic induction culture. ADSC-Exos was a round or elliptical membrane vesicle with clear edge and uniform size. It has high expression of CD63 and TSG101, and its size distribution was 30-200 nm, which was in accordance with the size range of Exos. The distal necrosis of the flaps in the ADSC-Exos group was milder than that in the PBS group. On the 7th day, the survival rate of the flaps in the ADSC-Exos group was 64.2%±11.5%, which was significantly higher than that in the PBS group (31.0%±6.6%; t=7.945, P=0.000); the skin appendages in the middle region of the flap in the ADSC-Exos group were more complete, the edema in the proximal region was lighter and the vasodilation was more extensive. MVD of the ADSC-Exos group was (103.3±27.0) /field, which was significantly higher than that of the PBS group [(45.3±16.2)/field; t=3.190, P=0.011]. ADSC-Exos can improve the blood supply of skin flaps by promoting the formation of neovascularization after skin flap transplantation, thereby improve the survival rate of skin flaps in rats.

An existence and uniqueness theorem for the dynamics of flexural shells

In this paper, we define, a priori, a natural two-dimensional model for a time-dependent flexural shell. As expected, this model takes the form of a set of hyperbolic variational equations posed over the space of admissible linearized inextensional displacements, and a set of initial conditions. Using a classical argument, we prove that the model under consideration admits a unique strong solution. However, the latter strategy makes use of function spaces, which are not amenable for numerically approximating the solution. We thus provide an alternate formulation of the studied problem using a suitable penalty scheme, which is more suitable in the context of numerical approximations. For the sake of completeness, in the final part of the paper, we also provide an existence and uniqueness theorem for the case where the linearly elastic shell under consideration is an elliptic membrane shell.

The first clawed lobster virus Homarus gammarus nudivirus (HgNV n. sp.) expands the diversity of the Nudiviridae

Viral diseases of crustaceans are increasingly recognised as challenges to shellfish farms and fisheries. Here we describe the first naturally-occurring virus reported in any clawed lobster species. Hypertrophied nuclei with emarginated chromatin, characteristic histopathological lesions of DNA virus infection, were observed within the hepatopancreatic epithelial cells of juvenile European lobsters (Homarus gammarus). Transmission electron microscopy revealed infection with a bacilliform virus containing a rod shaped nucleocapsid enveloped in an elliptical membrane. Assembly of PCR-free shotgun metagenomic sequencing produced a circular genome of 107,063 bp containing 97 open reading frames, the majority of which share sequence similarity with a virus infecting the black tiger shrimp: Penaeus monodon nudivirus (PmNV). Multiple phylogenetic analyses confirm the new virus to be a novel member of the Nudiviridae: Homarus gammarus nudivirus (HgNV). Evidence of occlusion body formation, characteristic of PmNV and its closest relatives, was not observed, questioning the horizontal transmission strategy of HgNV outside of the host. We discuss the potential impacts of HgNV on juvenile lobster growth and mortality and present HgNV-specific primers to serve as a diagnostic tool for monitoring the virus in wild and farmed lobster stocks.

About calculation with the high accuracy of eigenvalues of the operator Laplace in the ellipse (with the regional condition of Neumann)

The method of the computing experiment investigates the task about fluctuations of the elliptic membrane with the regional condition of Neumann. It is shown that on the grid 40×61 it is possible to define up to 50 eigenvalues with several right significant figures for eccentricity e = 0.99999.

An obstacle problem for Koiter’s shells

In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ model.

A confinement problem for a linearly elastic Koiter's shell

In this Note, we propose a natural two-dimensional model of “Koiter's type” for a general linearly elastic shell confined in a half space. This model is governed by a set of variational inequalities posed over a non-empty closed and convex subset of the function space used for modeling the corresponding “unconstrained” Koiter's model. To study the limit behavior of the proposed model as the thickness of the shell, regarded as a small parameter, approaches zero, we perform a rigorous asymptotic analysis, distinguishing the cases where the shell is either an elliptic membrane shell, a generalized membrane shell of the first kind, or a flexural shell. Moreover, in the case where the shell is an elliptic membrane shell, we show that the limit model obtained via the asymptotic analysis of our proposed two-dimensional Koiter's model coincides with the limit model obtained via a rigorous asymptotic analysis of the corresponding three-dimensional “constrained” model.