Membrane Theory Research Articles

Bending theory of composite pressure vessels: A closed-form analytical approach

Composite pressure vessels are strategic for the present and future of the aerospace, transportation, and energy industries. These shell structures are utilized to store and transport liquids and gases and are principally composed of a cylindrical shell and two elliptical heads. The current rules for the structural design of composite pressure vessels make use of the membrane theory that excludes the bending of the structure. Nevertheless, the cylindrical shell and the elliptical heads present different curvature radii. These changes generate a localized bending deformation that determines an increase in the stress state as an effect of a local bending moment and shear force distributions that arise in the geometric transition zone. The stresses related to the bending effects die out rapidly, moving away from the junction plane, but they are sensibly higher than the membrane stress and, therefore, cannot be neglected in the mechanical assessment. Here, a closed-form analytical solution for the bending theory of composite shells is proposed. It can assist in the design of composite pressure vessels and drive the design towards reliable configurations for structural integrity. Using the Donnell–Mustari–Vlasov theory for thin-walled composite shells, the governing fourth-order differential equation is deduced and solved to obtain the displacements and stresses acting in the junction. The analytical results are successfully compared with those of reference finite element models for validation; their accuracy is proved considering different thicknesses, lay-ups, and flattening factors of the vessel

Kinematic analysis of a finger-mimicking pneumatic network actuator consisting of parallelogram-shaped chambers

Fast pneumatic network (fast Pneu-Net, fPN) actuators made of silicone materials have aroused increasing attention these years for their promising applications in soft robotics. To enrich current research, we present a novel fPN actuator that consists of parallelogram-shaped chambers and aluminum endoskeleton that takes the shape of human finger. The proposed actuator can bend at multi-positions when inflated, bringing about more degrees of freedom controllability. Additionally, the performed finite element analysis indicates that the parallelogram-shaped chamber that tilts 30° towards the distal end exhibits an increase in deformation for about 11 % compared to the rectangle-shaped counterpart, offering an improved bending performance. An analytical model that based on the pressurized hyperelastic membrane theory is developed to estimate the actuator’s bending angles/profiles at varied pressures. Geometric relation of the chamber interactions upon deformation is discussed depending on whether the lateral walls are contact or not. The stress-strain relation of the elastomer is described using 3-term Yeoh constitutive model. Experimental validations on the theoretical calculations are carried out, from which the coefficient of proportionality that takes into account the effect on deformation caused by the embedded endoskeleton is determined. Furthermore, the Modified Denavit-Hartenberg (MDH) notation is employed to establish the forward kinematics of the actuator, and the numerical calculations are compared with the physical actuator.

Elastometry of Complex Fluid Pendant Capsules.

Oil/water interfaces are ubiquitous in nature. Opposing polarities at these interfaces attract surface-active molecules, which can seed complex viscoelastic or even solid interfacial structure. Biorelevant proteins such as hydrophobin, polymers such as PNIPAM, and the asphaltenes in crude oil (CRO) are examples of some systems where such layers can occur. When a pendant drop of CRO is aged in brine, it can form an interfacial elastic membrane of asphaltenes so stiff that it wrinkles and crumples upon retraction. Most of the work studying CRO/brine interfaces focuses on the viscoelastic liquid regime, leaving a wide range of fully solidified, elastic interfaces largely unexplored. In this work, we quantitatively measure elasticity in all phases of drop retraction. In early retraction, the interface shows a fluid viscoelasticity measurable using a Gibbs isotherm or dilatational rheology. Further retraction causes a phase transition to a 2D elastic solid with nonisotropic, nonhomogeneous surface stresses. In this regime, we use new techniques in the elastic membrane theory to fit for the elasticities of these solid capsules. These elastic measurements can help us develop a deeper understanding not only of CRO interfaces but also of the myriad fluid systems with solid interfacial layers.

Integral Method for Determining the Stress State of an Anisotropic Reinforced Concrete Shell

The article deals with the issue of estimating the strength and stress-strain state of a reinforced concrete shell by the method of membrane theory and the theory of infinitesimal bending. A brief description of the methodology consists in the fact that the ground stress state of the shell is allocated to an independent problem, when, without introducing boundary effects, two of the four boundary conditions of the general moment theory are distinguished, which, together with the equations of the momentless theory, determine the ground stress state, and then boundary effects are superimposed. The equilibrium equations of the moment theory in forces and moments, geometric equations, components of tangential deformation and displacement, and the physical equations of state connecting them, expressing forces and moments through the components of deformation, are presented, since the characteristics of the stress-strain state of the shell depend not only on the variability of external influences and forces, but also on the length of the structure. The provisions laid down in the article shall be retained in the case of casings made of anisotropic material, provided that the presented elastic ratio is met. A system of equations of the generalized semi-membrane (semi-bending) state of an arbitrary shell of zero curvature, which determines the accuracy of this approach, is solved. The equations of the semi-torque theory for a circular cylindrical shell are presented, as well as describing the semi-membrane stress state of a long shell of zero curvature. The most important result of the study is the method of constructing integrals of the ground stress state of the shell based on the method of simple iterations, which expands the possibilities of the reliability theory, which makes it possible to build the foundations for the practical calculation of reinforced concrete shells according to the membrane theory and the theory of infinitesimal bending.

Bubble-Induced Strong Thermal Contraction for Graphene

Abstract The thermal expansion coefficient (TEC) of van der Waals (vdW) layered structures is of crucial importance in governing the dependability and longevity of advanced optoelectronic equipment. Bubbles are commonly found within layered structures, yet their impact on the thermal expansion coefficient of the structure is still not well understood. We derive an analytical formula that describes the influence of bubbles on the variation in length, utilizing both the elastic membrane theory and the improved van der Waals gas state equation. The results demonstrate that as the temperature increases, bubbles can induce significant thermal contraction in few-layer graphene structures. The analytical predictions are validated through molecular dynamic (MD) simulations, confirming the accuracy and reliability of the proposed model. These findings hold significant value in enhancing our understanding of the dependability and durability of functional equipment that relies on van der Waals layered structures.

DESIGN OF SHELL CONJUNCTION ZONES IN PRESSURE VESSELS

Separation forces occur in shell junctions of fuel tanks due to the change in its geometry. To compensate the forces, thrust rings are placed in these zones. Moreover, there is a necessity to determine a form and dimensions of the trust ring cross section with consideration of the operation conditions. Welding is used to join trust rings with a shell in case of conventional manufacturing. Nowadays, additive manufacturing technology is constantly being developed. Additive method allows to create objects with various geometry, in a layer-by-layer way of addition of the material in accordance with a computer model. These new technological capabilities make the task of determining of the geometry of the fuel tank in the shell’s junctions zone actual. 
 The following work provides a consideration of two approaches to the determination of the conversion geometry of shells in-between area instead of trust ring. The first approach is based on determination of a median surface with the use of rational cubic splines and membrane theory of shells. The second approach is based on the use of topology optimization of the initial design. The choice of the first approach relates to the fact that standard energy functional like potential energy of uniform bent rod or uniform sheet can be described with cubic splines. In the following work the use of rational cubical splines for build-up a transitive area in a junction zone of the spherical-conical vessel is considered. Spline parameters are determined based on the condition of median surface propagation of the transitive zone in its probable location. Thickness of the shell in the transitive area was evaluated due to the membrane theory of shells with the use of Huber von Mises Hencky theory of failure. Obtained solutions are tested in numerical models of spherical-conical vessel. Comparison of two approaches is carried out and practical recommendations are given.

Effect of Bending Rigidity and Nonlinear Strains on Free Vibration of Hemi-Ellipsoidal Shells

Abstract This paper focuses on free vibration of hemi-ellipsoidal shells with the consideration of the bending rigidity and nonlinear terms in strain energy. The appropriate form of the energy functional is formulated based on the principle of virtual work and the fundamental form of surfaces. Natural frequencies and their corresponding mode shapes are determined using the modified direct iteration method. The obtained results, which show a close agreement with previous research, are compared with those obtained based on the membrane theory. The effect of the support condition, thickness, size ratio, and volume constraint condition on frequency parameters and mode shapes is demonstrated. With the bending rigidity, shell thickness has a significant impact on the frequency, especially in higher vibration modes and in shells with a considerable thickness but the frequency parameter converges to that determined by using the membrane theory while the reference radius-to-thickness ratio is increasing. In addition, accounting for the bending rigidity solves the issue of determining natural frequencies and mode shapes of the shells using the membrane theory without the volume constraint condition. The obtained results also indicate that the free vibration analysis with bending is essential for the hemi-ellipsoidal shell with a base radius-to-thickness ratio of less than 100, which gives over 2.84% difference compared with that of the shell derived by membrane theory, and this allows engineers to perform the analysis in more applications.

Hierarchical shape optimization for large deployable membrane reflector with spatial skirt cable

In the shape optimization analysis of electrostatically controlled deployable membrane reflector (ECDMR), the poor balance of the membrane with spatial skirt cable is the main reason for the degradation of the reflector surface precision. At the same time, while in the optimization of the pre-stress of large deployable reflectors, the membrane structure has strong geometric nonlinearity, and the lack of necessary gradient information leads to low efficiency of the calculation. Therefore, according to the structural characteristics of the cable-membrane reflector, the two optimization objectives of the highest surface precision and the most uniform stress distribution is considered, and a hierarchical shape optimization method is proposed based on membrane theory and unbalance force analysis, which realizes the solution of the multi-objective optimization problem when the three optimization objectives have different priorities. The interior effective membrane reflective surface is analyzed using membrane theory, and the external membrane with spatial skirt cable is analyzed using nonlinear finite element method. The gradient information required for optimization is also obtained by unbalance force analysis, which ensures better optimization efficiency and can solve large-scale optimization problems. Therefore, the node positions and element equilibrium stresses of the structure can be optimized simultaneously, which further expands the search space of the equilibrium state and reduces the possibility of falling into local optimal solutions. Finally, a numerical example of a 30 m aperture ECDMR is calculated and analyzed, and the results show that the proposed method can obtain a high surface precision with a fast solution speed.

Nonlinear dynamics of ionic liquid enhanced soft composite membrane under electro-mechanical loading

The incorporation of ionic liquids (ILs) into dielectric elastomer composites has attracted significant interest due to their potential applications in soft actuators and optical devices. Their soft and hyperelastic nature make them a distinct dynamic. In this paper, nonlinear dynamics of IL enhanced soft composite (ILESC) dielectric membrane subjected to electro-mechanical loading is investigated. A mixed micromechanical model with the incorporation of an electric double layer (EDL) and Maxwell-Wagner-Sillars (MWS) polarization is developed to estimate mechanical and electrical properties of the ILESC. Governing equations are derived via an energy method with the framework of the hyperelastic membrane theory, Neo-Hookean constitutive model and the couple dielectric theory. These equations are discretized by Taylor series expansion (TSE) and differential quadrature (DQ) methods and are solved by incremental harmonic balance (IHB) method combined with arc-length technique. The developed model and results are verified by comparing to experimental data and previous results. The influence of volume fraction, shape and size of IL fillers, static and dynamic applied electric field and excitation amplitude on forced vibration and resonant response of the ILESC membrane are comprehensively analyzed. It is found that ILESC membrane with slender ellipsoidal ILs displays larger amplitude, lower peak amplitude frequency and more obvious softening behavior.

Semi-Analytical Methods for the Joint Strength and Sealing Performance in the Failure Process of the Subsea Pipeline Compression Connector

Radial seals are sensitive to axial overload failure and may cause leaks. This paper presents two semi-analytical methods for the joint strength and sealing performance of the subsea pipeline compression connector under axial overload failure. The method for the joint strength consists of two parts: One is the analytical model for the joint strength of the connection and seal under axial tension and compression conditions. The models are based on membrane theory, considering the hardening and bending effects. The other is a two-dimensional, axisymmetric finite element model for the joint strength of the radial metal seal. The semi-analytical method for the overload sealing performance is derived using a finite element model and the Reynolds equation of the laminar flow. The effects of critical parameters on the joint strength and the overload sealing performance are analyzed. The experiments are carried out with specimens and prototypes to evaluate the evolution of the sealing interface and the joint strength. The results show that both the internally turned sealing surface and the deflection of the pipe can improve the joint strength. In addition, the compression-type connector can remain sealed under the maximum axial overload. The proposed methods allow the prediction and identification of the overload joint strength and the sealing condition of the compression-type connector and provide a better understanding of the radial metal seal under the axial overload condition.

Application of membrane anatomy in hepatopancreatobiliary and splenic surgery

Understanding of a variety of membranous structures throughout the body,such as the fascia,the serous membrane,is of great importance to surgeons. This is especially valuable in abdominal surgery. With the rise of membrane theory in recent years,membrane anatomy has been widely recognized in the treatment of abdominal tumors,especially of gastrointestinal tumors. In clinical practice. The appropriate choice of intramembranous or extramembranous anatomy is appropriate to achieve precision surgery. Based on the current research results,this article described the application of membrane anatomy in the field of hepatobiliary surgery,pancreatic surgery,and splenic surgery,with the aim of blazed the path from modest beginnings.

Analytical Solution and Buckling of Hemi-Ellipsoidal Shell Structures of Revolution under Uniformly Distributed Load

This paper focuses on the analytical procedure for determining novel exact expressions for internal forces and displacements of hemi-ellipsoidal shells formed as an axisymmetric shell of revolution under uniformly distributed load such as imposed loads. The simplest form of expressions for solutions is derived based on the linear membrane theory under symmetrical loading that is formed as a shell of revolution. The results have been validated and have a good consistency with numerical solutions from the finite-element method (FEM) which are derived based on the principle of virtual work and differential geometry. The obtained analytical exact solution is only valid for small displacements or if the response does not exceed the linearity limit. In cases of large displacements, geometrical nonlinear finite-element analysis is recommended to determine the solution. The linearity limit determination is demonstrated, and the effects of shells’ geometry, thickness, and magnitude of applied loads are presented. Additionally, the linear buckling analysis has been performed. The study found that the size ratio, thickness, and support condition have a significant effect on the critical load of the first mode, and the hemispherical shells have the highest buckling resistance due to the geometry.

Frequency calculation method and wind-induced dynamic response of cable net façades considering the façade stiffness

In this study, a frequency formula for cable net façades that considers façade stiffness is proposed, and the effect of the façade stiffness on the dynamic behavior is analyzed. Initially, a theoretical formula based on membrane theory is derived for calculating the frequency of cable net façades while neglecting façade stiffness. Moreover, a total of 720 detailed finite element (FE) models of cable net façades with various parameters are established in ANSYS finite element software. The effects of glass thickness, cable spacing and cable force on frequency are analyzed with the detailed FE models. Based on the theoretical formula and detailed FE models, a fitted frequency formula that includes the façade stiffness is further proposed to calculate the first-order mode, which is the prominent mode. Furthermore, the effect of the façade stiffness on the dynamic response of the structure, including the cable force and displacement, is researched under excitation by wind loads based on time history analysis. The results show that the influence of façade stiffness on the frequency and dynamic response gradually decreases as the number of cable net grids increases. When the grid number is above 10, the impact can be ignored. In addition, the fitted formula can be used when the grid number is under 10, and when the number of grids exceeds 10, the theoretical formula can be applied. Considering this simplification, a simplified FE model is proposed in engineering design for grid numbers exceeding 10. When the grid number is less than 10, it is recommended to adopt a detailed FE model designed to avoid errors in structural design.

A theoretical solution for metal-FRP hybrid toroidal pressure vessel based on membrane approach

Metal-FRP (fiber reinforced polymer) hybrid circular toroidal pressure vessel (TPV) can withstand higher internal fluid pressure compared to a metal TPV of the same thickness. The design of hybrid metal-FRP TPV needs prediction of the stresses and strains induced in the base metal and FRP layers. Existing predictive models for metal TPV based on linear membrane theory are inadequate in obtaining non-singular displacements at the apex in the meridian of the TPV. Further, they are not applicable for metal-FRP TPV. Therefore, a theoretical solution based on a modified linear membrane approach is proposed for a metal-FRP hybrid circular TPV subjected to an internal pressure. The proposed solution is validated through numerical simulations based on three-dimensional finite element analysis (FEA). Subsequently, a parametric study is conducted to understand the effect of the CFRP’s modulus and number of layers, thickness of base metal and R/r ratio (radius of the toroid to its cross-section) on the behavior of the aluminium-CFRP hybrid TPV. The comparison of results in an illustrative case and parametric studies show that the predictions from the proposed model are in good agreement with FEA results.

Method based on the membrane theory for equivalence between arbitrarily shaped pressure pulse applied on circular plate and rectangular pressure pulse

Obtaining a theoretical solution for the response of plate structures to arbitrarily shaped pressure pulses is often difficult. For engineering purposes, arbitrarily shaped pressure pulses are often simplified to equivalent rectangular pressure pulses to calculate the theoretical responses of the plate structures. Therefore, the semi-empirical method proposed by Youngdahl is often used. Although the effectiveness of Youngdahl's method has been verified in small deformation cases, the method lacks a theoretical explanation of the equivalence basis for cases of large deformation. In this paper, a method based on the membrane theory (MEM) is established for equivalence between arbitrarily shaped pressure pulse applied on circular plate and rectangular pressure pulse, and the differences and similarities between the MEM and the Youngdahl's equivalent method (YEM) are analyzed. Using the membrane theory, the responses of five different pressure pulses are compared, revealing that the pulse shape has a significant influence on the theoretical deformation obtained by the membrane theory. Then, a load equivalent method based on the membrane theory is proposed. In particular, for a linearly decaying pressure pulse, an analytical solution of the equivalent load is provided, and the equivalent pressure and pulse duration of the MEM and YEM are calculated. Notably, the pressure and pulse duration obtained by the MEM under the large deformation theory significantly differ from those obtained by the YEM. A numerical simulation indicates that the response errors of the equivalent load relative to the original linearly decaying pressure pulse of the two methods are close, both within the acceptable range of engineering. The theoretical analysis shows that the product of the characteristic frequency of the membrane response and pulse duration — a dimensionless number — affects the relative magnitude of the equivalent pressure of the YEM and MEM. When the final deformation time occurs after the duration of the linearly decaying pressure pulse, the deformation of the circular plate under the equivalent load obtained by the YEM is greater than that obtained by the MEM.

A Rate-Dependent Cell Microinjection Model Based on Membrane Theory.

As an effective method to deliver external materials into biological cells, microinjection has been widely applied in the biomedical field. However, the knowledge of cell mechanical property is still inadequate, which greatly limits the efficiency and success rate of injection. Thus, a new rate-dependent mechanical model based on membrane theory is proposed for the first time. In this model, an analytical equilibrium equation between the injection force and cell deformation is established by considering the speed effect of microinjection. Different from the traditional membrane-theory-based model, the elastic coefficient of the constitutive material in the proposed model is modified as a function of the injection velocity and acceleration, effectively simulating the influence of speeds on the mechanical responses and providing a more generalized and practical model. Using this model, other mechanical responses at different speeds can be also accurately predicted, including the distribution of membrane tension and stress and the deformed shape. To verify the validity of the model, numerical simulations and experiments were carried out. The results show that the proposed model can match the real mechanical responses well at different injection speeds up to 2 mm/s. The model presented in this paper will be promising in the application of automatic batch cell microinjection with high efficiency.

Application and accuracy of shell theory in the analysis of stress and deformations in cylindrical pressure vessels

The presented study focusses on the application of the analytical shell theory to the problems of stresses and deformations in cylindrical pressure vessels. Two standard types of dished ends are investigated, torispherical and ellipsoidal. To solve the problem the membrane theory and edge effect theory is applied. The equations of deformations are formulated to calculate the forces in the shells junction. The orthotropic material model is taken into account. Two known solutions of the homogeneous Reissner– Meissner differential equations are studied. The resolved stress and deformation are compared with the numerical results of the finite element method. The accuracy of the analytical solution is highly dependent on the thickness of the pressure vessel, as well as on the shape of the dished end. According to the results discussed, the solution for the structure with torispherical dished ends is accurate only for exceptionally small thickness, beyond the typical values for industrial pressure vessels. This shortcoming has been proven to be the result of the limitations of the membrane theory, despite the thin-walled nature of the shells studied.

Geometric and strain behaviour of full-scale geotextile tubes for dewatering sludge

Geotextile tubes have been presented as a viable alternative for dewatering sludge generated in different industries, characterised by having fine grain and high moisture content. The material commonly used to develop this system is woven geotextile due to its high strength properties. However, nonwoven geotextile tubes are a possible underexplored alternative that have good cost benefits. This paper presents the geometric and strain behaviour of two full-scale nonwoven geotextile tubes used for dewatering water treatment plant (WTP) sludge. Four technologies were used to monitor the full-scale tests: ultrasonic sensor (US), perspective laser tracking (PLT), light detection and ranging (LIDAR) and draw wire sensor (DWS). The geometric parameters of a quarter of the cross-section and the strains in the geotextile were obtained during sequential fills. These data were compared with results obtained from an analytical method based on membrane theory that considers the non-linear-elastic behaviour of the geotextile. The DWS and LIDAR technologies were the most suitable for monitoring the strains and shapes of the tubes, respectively. Good agreement was found between analytical and experimental results, indicating the applicability of the adopted method to the design of the first filling cycle of the monitored nonwoven geotextile tubes.

A Semi-Analytical Method for the Sealing Performance Prediction of Subsea Pipeline Compression Connector

To predict the sealing performance of the subsea pipeline compression connector, a semi-analytical method is proposed and verified. The leakage condition is obtained as a function of the minimum radial deflection. The semi-analytical method consists of three parts: a macroscopic analytical model for the interference process deduced based on the membrane theory, a mesoscopic two-dimensional finite element analysis of the internally turned sealing surface according to scanning electron microscope observation, and a formulation of the leakage ratio according to the Abbott–Firestone curve. The influences of the geometry parameters are analyzed. The prediction and identification of the leakage condition near the minimum preloaded deflection are investigated. Experimental tests are also carried out to verify the proposed method. The results show that, within five times the pipeline threshold of the thin wall thickness, compression connectors designed by the proposed method can create a reliable seal with a rough internally turned surface, saving 57% of the design time while reducing the machining time and costs.

On the Construction of Mathematical Models of the Membrane Theory of Convex Shells

Introduction. The paper considers the issues of constructing mathematical models of the momentless equilibrium stress state of elastic convex shells using methods of the complex analysis. At the same time, shells with a piecewise smooth (ribbed) lateral surface were considered for the first time. The work objective was to find classes of shells for which it is possible to build meaningful mathematical models.Materials and Methods. Using the methods of the theory of the discontinuous Riemann-Hilbert problem for generalized analytic functions, a criterion for the unconditional solvability of the corresponding static problem for the equilibrium equation of a convex shell with a ribbed lateral surface has been obtained. This criterion, combined with the methods of the theory of generalized analytical functions, is a tool for constructing mathematical models of the state of momentless stress equilibrium of elastic convex shells.Results. A method has been developed for constructing mathematical models of the momentless equilibrium stress state of a convex shell under the action of a variable external load and the condition of stress concentration at the corner points of the median surface. The introduction of a vector parameter, as well as the concepts of “order of quasi-correctness” and “quasi-stability”, into the boundary condition provided both quantitative and qualitative comparison of mathematical models. Classes of shells have been found for which the description of mathematical models is given in terms of the geometry of the boundary in the vicinity of the corner points of the median surface. The obtained result, when applied to shallow convex shells, provides a geometric criterion of quasi-stability. It is established that for a shallow shell, which is not quasi-stable, the only adequate mathematical model is a probabilistic one.Discussion and Conclusions. The proposed method for constructing a two-parameter family of problems with a modified boundary condition makes it possible to simulate the momentless equilibrium stress state for fairly wide classes of convex shells with a piecewise-smooth lateral surface under a sleeve connection. At the same time, the developed algorithm for calculating the boundary condition index allowed us to answer the question of the existence of an adequate mathematical model for a shell with a side surface of an arbitrary configuration, and for shells of a special type (specifically, shallow or shells of revolution), to formulate a geometric criterion for the existence of a mathematical model.