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In the design of cantilevered balconies of buildings, many stability problems exist concerning vertical plates, in which reaching a critical load plays an important role during the stability analysis of the plate. At the same time, the concrete forming vertical plate, as a typical brittle material, has larger compressive strength but lower tensile strength, which means the tensile and compression properties of concrete are different. However, due to the complexities of such analyses, this difference has not been considered. In this study, the variational method is used to analyze stability problems of cantilever vertical plates with bimodular effect, in which different loading conditions and plate shapes are also taken into account. For the effective implementation of a variational method, the bending strain energy based on bimodular theory is established first, and critical loads of four stability problems are obtained. The results indicate that the bimodular effect, as well as different loading types and plate shapes, have influences on the final critical loads, resulting in varying degrees of buckling. In particular, if the average value of the tensile modulus and compressive modulus remain unchanged, the introduction of the bimodular effect will weaken, to some extent, the bending stiffness of the plate. Among the four stability problems, a rectangular plate with its top and bottom loaded is most likely to buckle; next is a rectangular plate with its top loaded, followed by a triangular plate with its bottom loaded. A rectangular plate with its bottom loaded is least likely to buckle. This work may serve as a theoretical reference for the refined analysis of vertical plates. Plates are made of concrete or similar material whose bimodular effect is relatively obvious and cannot be ignored arbitrarily; otherwise the greater inaccuracies will be encountered in building designs.

The closed-form solution of circular membranes subjected to gas pressure loading plays an extremely important role in technical applications such as characterization of mechanical properties for freestanding thin films or thin-film/substrate systems based on pressured bulge or blister tests. However, the only two relevant closed-form solutions available in the literature are suitable only for the case where the rotation angle of membrane is relatively small, because they are derived with the small-rotation-angle assumption of membrane, that is, the rotation angle θ of membrane is assumed to be small so that “sinθ = 1/(1 + 1/tan2θ)1/2” can be approximated by “sinθ = tanθ”. Therefore, the two closed-form solutions with small-rotation-angle assumption cannot meet the requirements of these technical applications. Such a bottleneck to these technical applications is solved in this study, and a new and more refined closed-form solution without small-rotation-angle assumption is given in power series form, which is derived with “sinθ = 1/(1 + 1/tan2θ)1/2”, rather than “sinθ = tanθ”, thus being suitable for the case where the rotation angle of membrane is relatively large. This closed-form solution without small-rotation-angle assumption can naturally satisfy the remaining unused boundary condition, and numerically shows satisfactory convergence, agrees well with the closed-form solution with small-rotation-angle assumption for lightly loaded membranes with small rotation angles, and diverges distinctly for heavily loaded membranes with large rotation angles. The confirmatory experiment conducted shows that the closed-form solution without small-rotation-angle assumption is reliable and has a satisfactory calculation accuracy in comparison with the closed-form solution with small-rotation-angle assumption, particularly for heavily loaded membranes with large rotation angles.

In this study, we obtained analytical solutions for functionally graded curved beams with different properties in tension and compression, in which the moduli of elasticity in tension and compression are assumed as two different exponential functions. First, by determining the unknown neutral layer, we established a simplified mechanical model concerning tension and compression subzone and derived the one-dimensional solution (i.e., the solution in the scope of mechanics of materials). Given that the one-dimensional solution is a relatively simplified one, thus a comprehensive understanding of this problem is still needed. For this purpose, we established the consistency equation expressed in terms of stress function under two-dimensional theory of elasticity. Combining boundary conditions of inner and outer edges with continuity conditions of the neutral layer, we applied power series method for the solution of stress components under pure bending. The variations of radial and circumferential stresses in different cases of bimodular functionally graded parameters are comprehensively analyzed with numerical examples. Results indicate that the position of the neutral layer is generally related to the elastic modulus and the functionally graded coefficients of the materials. Moreover, the maximum tensile or compressive bending stress may not take place at the outer or inner edges of the curved beam but inside the beam, which should be given more attention in the analysis and design of functionally graded curved beams with different properties in tension and compression.

The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.

In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.

This study is devoted to the design of an elastic polymer thin film-based capacitive wind-pressure sensor to meet the anticipated use for real-time monitoring of structural wind pressure in civil engineering. This sensor is composed of four basic units: lateral elastic deflection unit of a wind-driven circular polymer thin film, parallel plate capacitor with a movable circular electrode plate, spring-driven return unit of the movable electrode plate, and dielectric materials between electrode plates. The capacitance of the capacitor varies with the parallel move of the movable electrode plate which is first driven by the lateral elastic deflection of the wind-driven film and then is, after the wind pressure is reduced or eliminated, returned quickly by the drive springs. The closed-form solution for the contact problem between the wind-driven thin film and the spring-driven movable electrode plate is presented, and its reliability is proved by the experiment conducted. The numerical examples conducted show that it is workable that by using the numerical calibration based on the presented closed-form solution the proposed sensor is designed into a nonlinear sensor with larger pressure-monitoring range and faster response speed than the linear sensor usually based on experimental calibration.

Piezoelectric materials have been found to have many electromechanical applications in intelligent devices, generally in the form of the flexible cantilever element, thus, the analysis to the corresponding cantilever is of importance, especially when advanced mechanical properties of piezoelectric materials should be taken into account. In this study, the vibration problem of a piezoelectric cantilever beam with bimodular functionally-graded properties is solved via analytical and numerical methods. First, based on the equivalent modulus of elasticity, the analytical solution for vibration of the cantilever beam is easily derived. By the simplified mechanical model based on subarea in tension and compression, as well as on the layer-wise theory, the bimodular functionally-graded materials are numerically simulated, thus, the numerical solution of the problem studied is obtained. The comparison between the theoretical solution and numerical study is carried out, showing that the result is reliable. This study shows that the bimodular functionally-graded properties may change, to some extent, the dynamic response of the piezoelectric cantilever beam, however, the influence could be relatively small and unobvious.

Adhesion between coatings and substrates is an important parameter determining the integrity and reliability of film/substrate systems. In this paper, a new and more refined theory for characterizing adhesion between elastic coatings and rigid substrates is developed based on a previously proposed pressurized blister method. A compressed air driven by liquid potential energy is applied to the suspended circular coating film through a circular hole in the substrate, forcing the suspended film to bulge, and then to debond slowly from the edge of the hole as the air pressure intensifies, and finally to form a blister with a certain circular delamination area. The problem from the initially flat coating to the stable blistering film under a prescribed pressure is simplified as a problem of axisymmetric deformation of peripherally fixed and transversely uniformly loaded circular membranes. The adhesion strength depends on the delamination area and is quantified in terms of the energy released on per unit delamination area, the so-called energy release rate. In the present work, the problem of axisymmetric deformation is reformulated with out-of-plane and in-plane equilibrium equations and geometric equations, simultaneously improved, and a new closed-form solution is presented, resulting in the new and more refined adhesion characterization theory.

In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such that it comes into contact with a frictionless rigid plate, resulting in a restriction on the maximum deflection of the deflected circular membrane. The power series method was employed to solve the boundary value problem of the resulting nonlinear differential equation, and a closed-form solution of the problem addressed here was presented. The difference between the axisymmetric deformation caused by gas pressure loading and that caused by gravity loading was investigated. In order to compare the presented solution applying to gas pressure loading with the existing solution applying to gravity loading, a numerical example was conducted. The result of the conducted numerical example shows that the two solutions agree basically closely for membranes lightly loaded and diverge as the external loads intensify.

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

A typical characteristic of bimodular material beams is that when bending, the neutral layer of the beam does not coincide with its geometric middle surface since the mechanical properties of materials in tension and compression are different. In the classical theory of elasticity, however, this characteristic has not been considered. In this study, a bimodular simply-supported beam under the combination action of thermal and mechanical loads is theoretically analyzed. First, a simplified mechanical model concerning the neutral layer is established. Based on this mechanical model, Duhamel’s theorem is used to transform the thermoelastical problem into a pure elasticity problem with imaginary body force and surface force. In solving the governing equation expressed in terms of displacement, a special solution of the displacement equation is found first, and then by utilizing the stress function method based on subarea in tension and compression, a supplement solution for the displacement governing equation without the thermal effect is derived. Lastly, the special solution and supplement solution are superimposed to satisfy boundary conditions, thus obtaining a two-dimensional thermoelasticity solution. In addition, the bimodular effect and temperature effect on the thermoelasticity solution are illustrated by computational examples.

In this study, we derived an electroelastic solution of functionally graded piezoelectric beams with bimodular effect under the combined action of uniformly distributed loads, concentrated loads, a...

In this study, the conductive diaphragm in conventional capacitive pressure sensors with dual function (the deformable element and the upper electrode plate of a non-parallel plate capacitor) was modified into a non-conductive elastic annular thin-film (as the deformable element) centrally connected with a conductive rigid circular plate or alternatively with a non-conductive rigid circular plate adhered by a conductive thin-film (as the upper electrode plate of a parallel plate capacitor). This modification brings two advantages: the parallel plate capacitor is more convenient in the accurate calculation of capacitance than a non-parallel plate capacitor; it is easier to select a deformable element with good elastic behavior in non-conductive elastic thin-films than to select such a deformable element in conductive diaphragms. These advantages could provide convenience for further improving the performance of sensors. The presented closed-form solution can meet the needs of the research and development of this improved capacitive pressure sensor.

In this study, we obtained an electroelastic solution for functionally graded piezoelectric circular plates under the action of combined mechanical loads which include the uniformly distributed loads on the upper surface of the plate and the radial force and bending moment at the periphery of the plate. All electroelastic materials parameters are assumed to vary according to the same gradient function along the thickness direction. The influence of different functionally graded parameters on the elastic displacement and elastic stress, as well as the electric displacement and electric potential, was discussed by a numerical example. The solution presented in this study is not only applicable to the case of combined loads, but also to the case of a single mechanical load. In addition, this solution reflects the influence of the function gradient on the pure piezoelectric plate, which is helpful to the refined analysis and optimization design of similar structures.

The well-known Hencky solution is only applicable to the problem of deformation of the elastic circular membrane without initial stress under transverse uniformly-distributed loads. The problem considered here is a more general case: an initial tensile or compressive stress has been present in the initially flat circular membrane before the membrane is subjected to the transverse loads. The closed-form solution of the considered problem was presented and all the expressions obtained here for displacements, strains and stresses have the same form as those in the well-known Hencky solution. The initial stress plays an important role in the determination of numerical value of the integral constant controlling membrane equation. The solution obtained here can be regressed into the well-known Hencky solution when the initial stress is equal to zero, and it is therefore called extended Hencky solution.

In this study, based on the pressure blister test technique, a theoretical study on the synchronous characterization of surface and interfacial mechanical properties of thin-film/substrate systems with residual stress was presented, where the problem of axisymmetric deformation of a blistering film with initial stress was analytically solved and its closed-form solution was presented. The expressions to determine Poisson’s ratios, Young’s modulus, and residual stress of surface thin films were derived; the work done by the applied external load and the elastic energy stored in the blistering thin film were analyzed in detail and their expressions were derived; and the interfacial adhesion energy released per unit delamination area of thin-film/substrate (i.e., energy release rate) was finally presented. The synchronous characterization technique presented here has theoretically made a big step forward, due to the consideration for the residual stress in surface thin films.

When materials that exhibit different mechanical behaviors in tension and compression must be analyzed, Ambartsumyan's bimodular model for isotropic materials can be adopted. It deals with the principal stress state in a point, which is particularly important in the analysis and design of structures. In this article, an equivalent section method is used to transform the bimodular curved beam into a classical one with singular modulus; consequently, the simplified solution for bending stresses may be easily determined only by changing a few parameters relating to section characteristics. For the determination of the unknown neutral layer, a perturbation method is used to obtain the explicit expression. Based on the known neutral layer, a stress function method is used to obtain the elasticity solution for stresses and displacements via boundary conditions and continuity conditions. Based on the elasticity solution, an initial stresses problem in a bimodular multiply-connected body is considered. The compar...

In this paper, the existing shaft-loaded blister test technique was improved and a theoretical study on synchronous characterization of mechanical properties of coating thin-film and film/substrate interface was presented. Problems considered include the exact analytical solution to the problem of axisymmetric deformation of a blistering film and the theoretical derivation of expressions to determine Poisson׳s ratios, Young׳s modulus, the work done by the applied external load, the elastic energy stored in a blistering film, and energy release rate. Some relative issues such as how to control the blistering film as free as possible from plastic yielding and the influence of changing the loading-shaft radius on the membrane stress distribution were discussed. Moreover, an experiment was conducted to verify the presented theoretical work.

In this work, electrospinning was used to fabricate core–shell nanofibers containing acid–base pairs. Quercetin was used as a model active ingredient. To exploit its solubility in basic conditions, a solution of quercetin, polyvinylpyrrolidone (PVP) and sodium hydroxide was used as the core fluid, and one consisting of citric acid and PVP as the shell fluid. Scanning and transmission electron microscopy demonstrated that core–shell nanofibers with linear morphologies were obtained, without beads or spindles. X-ray diffraction showed that quercetin was present in the fibers in an amorphous state; Fourier transform infrared spectroscopy indicated this may be a result of hydrogen bonding between the drug and the polymer matrix. In in vitro dissolution tests the drug was found to be released immediately when the fibers encountered an aqueous medium. There was no change in the pH of the medium after dissolution, as a result of the presence of the acid–base pair. This provides a new strategy for improving the dissolution behavior of poorly water-soluble drugs using polymeric nanostructures.

In this paper, a new loading method able to subtly control the crack driving force for pressurized blister test was proposed. A theoretical study of the adhesion energy measurement for film/substrate interface using this loading method was presented. Problems considered include solving the exact volume under a circular blister and the elastic strain energy stored in a thin blistering film, determining the work done by the poured colored liquid as external force to the system and the elastic strain energy stored in the compressed air. A new formula of energy release rate was finally presented. A comparison between the work presented here and the existing work was made.

Ambartsumyan's bimodular model for isotropic materials deals with the principal stress state in a point, which is particularly useful in the analysis and design of structures. In this paper, based on the known flexural stiffness for a bimodular thin plate in small-deflection bending, we establish the von Karman equations with different moduli in tension and compression and then use the perturbation method and the displacement variation method to solve the problem, respectively. The comparison shows that the perturbation solution based on the central deflection is valid. The analytical result shows that the bimodularity of the material will have an effect on the relation of load vs. deflection to a certain extent. We also investigate the yield conditions for a bimodular thin plate in large-deflection bending. It is concluded that this introduction of materials nonlinearity will eventually influence the yield stress at the edge and center of the plate, however, it does not change the yield order that when loading further, the edge of the plate will firstly yield and then the center of the plate. Moreover, during the transition from plate to membrane, the bimodular plate will gradually regress to the classical one. This work will be helpful for analyzing the mechanical behaviors of thin film materials with obvious bimodularity and with moderate thickness or hardness.

In this paper we reviewed the research on the dynamic response of forced vibrations of orthotropic membranes, which applies in the membrane structural engineering. We applied the large deflection theory of membranes, the D’Alembert’s principle and the momentum theorem to derive the fundamental equations of forced vibrations of orthotropic membranes, which we solved according to the Lindstedt Poincare Perturbation Method, and obtained the formula of impact load and nonlinear forced vibration deflection of rectangular membranes with four edges fixed. Then a numerical computation method for the equation was applied. The results of practical examples are shown and discussed in the paper. This paper provide a method for analyzing some practical engineering problems and furthermore the nonlinear governing equations of forced vibration and the solving method provide some theoretical foundation for the .research relating to the solving of membrane structures under dynamic loads by comprehensively conside...

Based on the numerically iterative technique, we introduce the shear modulus pattern used for accelerating convergence and rebuild the iterative program. Using this program, we analyze the bending problem of a bimodular deep beam under the action of uniformly distributed loads, in which the different ratios of span length to height of the beam, and of elastic modulus in compression to that in tension, are considered. The results show that the bimodularity have great influences on the bending stress and the deflection of deep beam.

In this paper, based on the exact analytical solution of axisymmetric deformation of the circular membrane fixed at its edge under the action of uniformly-distributed loads, we propose a new method to be able to simultaneously determine Poisson’s ratio and Young’s modulus of elasticity for thin films. We also present a set of exact formulas used for simultaneously determining Poisson’s ratio and Young’s modulus of elasticity for free-standing thin films or coating thin films without residual stresses or pre-tension. This method has the advantages of simplicity and reliability, and it doesn’t involve the substrate effect.

Using an exact analytical solution of axisymmetric deformation of a circular membrane centrally connected to a rigid plate under the action of concentrated load at its center, we present an exact formula for the energy release rate applicable to ultrathin film–substrate systems without residual stresses or with small residual stresses. Also, a closed-form solution of axisymmetric deformation of circular membrane under the action of concentrated load at its center is presented.

Materials which exhibit different elastic moduli in tension and compression are known as bimodular materials. The bimodular materials model, which is founded on the criterion of positive-negative signs of principal stress, is important for the structural analysis and design. However, due to the inherent complexity of the constitutive relation, it is difficult to obtain an analytical solution of a bimodular bending components except in particular simple problems. Based on the existent simplified model, this paper solves analytically bending thin plates with different moduli in tension and compression. By using the continuity conditions of stress components in unknown neutral layer, we determine the location of the neutral layer, and derive the governing differential equation for deflection, the flexural rigidity, and the internal forces in the thin plate. We also use a circular thin plate with bimodulus to illustrate the application of this solution derived in this paper. The results show that the introduction of different moduli has influences on the flexural stiffness of the bending thin plate.

Based on Foppl–von Karman membrane theory, we theoretically study an axisymmetric deformation problem of a clamped punch-loaded blister configuration, a circular membrane centrally connected with a rigid plate under the action of the centrally concentrated load. With the uses of an intermediate parameter and a controlled parameter, we present an exact analytical solution of the quantitative relation (load vs. deflection) of the membrane without any hypotheses adopted in existent work.

In this study, a set of Föppl–von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of equilibrium of the plate is established on the existence of the neutral layer when considering different properties in tension and compression. During the derivation of the consistency equation, the tensile effect in the thin plate with bimodular effect is fully taken into account. The perturbation method is used to solve the set of governing equations under different edge constraints, in which the central deflection and the load of the plate are taken as a perturbation parameter, respectively. The results indicate that the two selections for perturbation parameters are valid and consistent, and the two solutions are convenient for engineering application. This study also shows that the bimodular effect will modify the relation of load versus central deflection of the plate to some extent, and under the same edge constraint, the capacities resisting deformation in different cases of moduli depend on the relative magnitudes among the tensile modulus, the neutral layer modulus, and the compressive modulus.