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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, a biparametric perturbation method is proposed to solve the Foppl–von Karman equations of bimodular thin plates subjected to a single load. First, by using two small parameters, one describes the bimodular effect and another stands for the central deflection, we expanded the unknown deflection and stress in double power series with respect to the two parameters and obtained the approximate analytical solutions under various edge conditions. Due to the diversity of selection of parameters and its combination, by using the bimodular parameter and the load as two perturbation parameters, we elucidated further the application of this method. The use of two sets of parameter schemes both can obtain satisfactory perturbation solutions; the numerical simulations also verify this idea. The results indicate that in a biparametric perturbation method, the selection and its combination of parameters may reflect the combined effects introduced by nonlinear factors. The method proposed in this study may be used for solving other mathematical equations established in some application problems.

Orthotropic membrane structure is widely applied in construction buildings, mechanical engineering, electronic meters, space and aeronautics, etc. During their serving period, membrane structure is prone to vibrate stochastically and seriously under stochastic dynamic loads, which may lead to structural failure. For this purpose, this paper investigates the stochastic dynamic response and reliability analysis of membrane structure under impact load obeying Gaussian distribution. The equation of stochastic motion of membrane structure is established by Von Karman's large deformation theory. The results of stochastic dynamic response are obtained with perturbation method solving the equation. Then, reliability parameters of extreme value of dynamic response are calculated by Moment method based on first-passage probabilities of level crossing. Furthermore, the theoretical model proposed is validated by experimental study using Monte Carlo method. The effects of parameters including impact velocity, pretension force and radius on structural reliability are discussed in addition. The model proposed herein provides some theoretical basis for the stochastic vibration control and dynamic design of orthotropic membrane structure based on reliability theory.

In existing studies, the well-known Hencky problem, i.e. the large deflection problem of axisymmetric deformation of a circular membrane subjected to uniformly distributed loads, has been analyzed generally on small-rotation-angle assumption and solved by using the common power series method. In fact, the problem studied and the method adopted may be effectively expanded to meet the needs of larger deformation. In this study, the classical Hencky problem was extended to the problem without small-rotation-angle assumption and resolved by using the perturbation idea combining with power series method. First, the governing differential equations used for the solution of stress and deflection in the perturbed system were established. Taking the load as a perturbation parameter, the stress and deflection were expanded with respect to the parameter. By substituting the expansions into the governing equations and corresponding boundary conditions, the perturbation solution of all levels were obtained, in which the zero-order perturbation solution exactly corresponds to the small-rotation-angle solution, i.e. the solution of the unperturbed system. The results indicate that if the perturbed and unperturbed systems as well as the corresponding differential equations may be distinguished, the perturbation method proposed in this study can be extended to solve other nonlinear differential equations, as long as the differential equation of unperturbed system may be obtained by letting a certain parameter be zero in the corresponding equation of perturbed system.

The large deflection condition of a bimodular plate may yield a dual nonlinear problem where the superposition theorem is inapplicable. In this study, the bimodular Foppl–von Karman equations of a plate subjected to the combined action of a uniformly distributed load and a centrally concentrated force are solved using a biparametric perturbation method. First, the deflection and radial membrane stress were expanded in double power series with respect to the two types of loads. However, the biparametric perturbation solution obtained exhibited a relatively slow rate of convergence. Next, by introducing a generalized load and its corresponding generalized displacement, the solution is expanded in a single power series with respect to the generalized displacement parameter, thereby leading to the better convergence on the solution. A numerical simulation is also used to verify the correctness of the biparametric perturbation solution. The introduction of a bimodular effect will modify the stiffness of the plate to some extent. In particular, the bearing capacity of the plate will be strengthened further when the compressive modulus is greater than the tensile modulus.

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 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.

The large deflection problem for a thin circular plate with different moduli in tension and compression has dually non-linear characteristics. In this paper, we use perturbation technique to obtain a general analytical solution of thin circular plate with different moduli in tension and compression, in which four edge conditions including rigidly clamped, clamped but free to slip, simply hinged and simply supported are considered. Because the perturbation solution is expanded in ascending powers of a known perturbation parameter (central deflection, for example) and the unknown constants and functions in the solution are gradually determined by decomposing boundary conditions and governing equation, the constants and functions obtained in such a manner have an inherent consistency concerning material properties. The results show that via construction of some parameters reflecting materials properties, not only the solution based on bimodular elasticity theory may regress to that on classical theory with singular modulus, but also the solution obtained under simply hinged edge may serve as a general solution to describe other three edge conditions. Via the general solution, the relations of load vs. central deflection, the plate–membrane transition for bimodular problem and the radial membrane stresses and bending stresses at the center and edge of the plate, are also discussed. Moreover, the comparison between the analytical solutions and numerical results indicates that the perturbation solutions based on the central deflection are overall valid. This work will be helpful for analyzing the mechanical behaviors of flexible layer structures while considering large deformation and bimodular effect.

For beams with gradient, due to the combined influences introduced by loads and gradient, the first derivative item in Euler-Bernoulli equation can not be neglected thus making the solution of the problem be a nonlinear large deflection one. In this paper, we use a new perturbation method with two small parameters, one describes the loads effect and another describes the geometrical nature of the problem, to solve the nonlinear large deflection problem of beams with gradient under the two different boundary conditions. We derive the first and second order approximate analytical solution of the deflection, the rotation and the arc length of the beam, as well as the internal forces of the beam at the end. The results indicate that the choice of two independent parameters may describe comprehensively the nonlinear effects caused by loads and gradient, which enables the approximate solution to be precise enough to be used for the analysis of large-deflection beam with gradient.

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.

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.

Based on elastic theory of different tension-compression moduli, bending beam subjected to lateral force and bending-compression column with different moduli were solved by the equivalent section method. Formulas for the neutral axis, normal stress, shear stress and displacement were developed also. This equivalent section method can turn conveniently different moduli problems into the similar moduli ones, i.e., classical elasticity problems so the existent results aimed beams and columns with similar moduli both can be used indiscriminately without complicated derived process. Compared with the present derived method based on different moduli theory the applicability and efficiency of equivalent section method is demonstrated.