A Refined Theory for Characterizing Adhesion of Elastic Coatings on Rigid Substrates Based on Pressurized Blister Test Methods: Closed-Form Solution and Energy Release Rate

Polymer Conductive Membrane-Based Circular Capacitive Pressure Sensors from Non-Touch Mode of Operation to Touch Mode of Operation: An Analytical Solution-Based Method for Design and Numerical Calibration

Polymer-based conductive membranes play an important role in the development of elastic deflection-based pressure sensors. In this paper, an analytical solution-based method is presented for the design and numerical calibration of polymer conductive membrane-based circular capacitive pressure sensors from non-touch mode of operation to touch mode of operation. The contact problem of a circular membrane in frictionless contact with a rigid flat plate under pressure is analytically solved, and its analytical solution is used for the design of touch mode circular capacitive pressure sensors for the first time. The analytical relationship with input pressure as independent variable and output capacitance as dependent variable is precisely derived and is used for the numerical calibrations of the analytical relationships with input capacitance as the independent variable and output pressure as the dependent variable in order to meet the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance. For the first time, an example showing the design and numerical calibration of a given (given design parameters) polymer conductive membrane-based circular capacitive pressure sensor from non-touch mode of operation to touch mode of operation is provided. Then, the influence of changing several important design parameters on input capacitance–output pressure relationships is comprehensively investigated in order to clarify the desired input–output relationships when changing design parameters.

Polymer Conductive Membrane-Based Non-Touch Mode Circular Capacitive Pressure Sensors: An Analytical Solution-Based Method for Design and Numerical Calibration

In this paper, an analytical solution-based method for the design and numerical calibration of polymer conductive membrane-based non-touch mode circular capacitive pressure sensors is presented. The accurate analytical relationship between the capacitance and applied pressure of the sensors is derived by using the analytical solution for the elastic behavior of the circular polymer conductive membranes under pressure. Based on numerical calculations using the accurate analytical relationship and the analytical solution, the analytical relationship between the pressure as output and the capacitance as input, which is necessary to achieve the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance, is accurately established by least-squares data fitting. An example of how to arrive at the design and numerical calibration of a non-touch mode circular capacitive pressure sensor is first given. Then, the influence of changing design parameters such as membrane thickness and Young’s modulus of elasticity on input–output relationships is investigated, thus clarifying the direction of approaching the desired input–output relationships by changing design parameters.

Revisiting the Boundary Value Problem for Uniformly Transversely Loaded Hollow Annular Membrane Structures: Improvement of the Out-of-Plane Equilibrium Equation

In a previous work by the same authors, a hollow annular membrane structure loaded transversely and uniformly was proposed, and its closed-form solution was presented; its anticipated use is for designing elastic shells of revolution. Since the height–span ratio of shells of revolution is generally desired to be as large as possible, to meet the need for high interior space, especially for the as-small-as-possible horizontal thrust at the base of shells of revolution, the closed-form solution should be able to cover annular membranes with a large deflection–outer radius ratio. However, the previously presented closed-form solution cannot meet such an ability requirement, because the previous out-of-plane equilibrium equation used the assumption of a small deflection–outer radius ratio. In this study, the out-of-plane equilibrium equation is re-established without the assumption of a small deflection–outer radius ratio, and a new and more refined closed-form solution is presented. The new closed-form solution is numerically discussed regarding its convergence and effectiveness, and compared with the old one. The new and old closed-form solutions agree quite closely for lightly loaded cases but diverge as the load intensifies. Differences in deflections, especially in stresses, are very significant when the deflection–outer radius ratio exceeds 1/4, indicating that, in this case, the new closed-form solution should be adopted in preference to the old one.

A Further Theoretical Study of Capacitive Pressure Sensors Based on Thin Film Elastic Deflection and Parallel Plate Capacitor: Refined Closed-Form Solution and Numerical Calibration

The capacitive pressure sensor based on thin film elastic deflection and a parallel plate capacitor uses a non-conductive elastic annular thin film centrally connected to a conductive, rigid, flat, concentric-circular thin plate as a pressure sensing unit. On application of pressure, the non-conductive thin film deflects elastically, which in turn moves the conductive thin plate (as a movable upper electrode plate of the parallel plate capacitor) towards the lower electrode plate, resulting in a change in the capacitance of the capacitor. Therefore, the applied pressure can be determined by measuring the capacitance change, based on the closed-form solution for the elastic behavior of the annular thin film under pressure. Such capacitive pressure sensors are more suitable for large-sized sensors such as those used for building-facade wind pressure measurements, etc. In this paper, a further theoretical study of such capacitive pressure sensors is presented. The newly presented, more refined closed-form solution can greatly reduce the output pressure error under the same input capacitance, in comparison with the previously presented closed-form solution. A numerical example of how to use the resulting closed-form solution to numerically calibrate input-output characteristics is given for the first time. The variation trend of pressure operation ranges and input-output characteristics with important parametric variations, which can be used for guiding the design of such capacitive pressure sensors, is investigated.

Large Deflection Analysis of Peripherally Fixed Circular Membranes Subjected to Liquid Weight Loading: A Refined Design Theory of Membrane Deflection-Based Rain Gauges

The anticipated use of elastic membranes for deflection-based rain gauges has provided an impetus for this paper to revisit the large deflection problem of a peripherally fixed circular membrane subjected to liquid weight loading, a statics problem when the fluid–structure interaction of membrane and liquid reaches static equilibrium. The closed-form solution of this statics problem of fluid–structure interaction is necessary for the design of such membrane deflection-based rain gauges, while the existing closed-form solution, due to the use of the small rotation angle assumption of the membrane, cannot meet the design requirements for computational accuracy. In this paper, the problem under consideration is reformulated by giving up the small rotation angle assumption, which gives rise to a new and somewhat intractable nonlinear integro-differential equation of the governing out-of-plane equilibrium. The power series method has played an irreplaceable role in analytically solving membrane equations involving both integral and differential operations, and a new and more refined closed-form solution without the small rotation angle assumption is finally presented. Numerical examples conducted show that the new and more refined closed-form solution presented has satisfactory convergence, and the effect of giving up the small rotation angle assumption is also investigated numerically. The application of the closed-form solution presented in designing such membrane deflection-based rain gauges is illustrated, and the reliability of the new and more refined closed-form solution presented was confirmed by conducting a confirmatory experiment.

Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

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.

Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading

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.

Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations

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.

Optimization of Adhesion Strength and Microstructure Properties by Using Response Surface Methodology in Enhancing the Rice Husk Ash-Based Geopolymer Composite Coating

As a result of their significant importance and applications in vast areas, including oil and gas, building construction, offshore structures, ships, and bridges, coating materials are regularly exposed to harsh environments which leads to coating delamination. Therefore, optimum interfacial bonding between coating and substrate, and the reason behind excellent adhesion strength is of utmost importance. However, the majority of studies on polymer coatings have used a one-factor-at-a-time (OFAT) approach. The main objective of this study was to implement statistical analysis in optimizing the factors to provide the optimum adhesion strength and to study the microstructure of a rice husk ash (RHA)-based geopolymer composite coating (GCC). Response surface methodology was used to design experiments and perform analyses. RHA/alkali activated (AA) ratio and curing temperature were chosen as factors. Adhesion tests were carried out using an Elcometer and a scanning electron microscope was used to observe the microstructure. Results showed that an optimum adhesion strength of 4.7 MPa could be achieved with the combination of RHA/AA ratio of 0.25 and curing temperature at 75 °C. The microstructure analysis revealed that coating with high adhesion strength had good interfacial bonding with the substrate. This coating had good wetting ability in which the coating penetrated the valleys of the profiles, thus wetting the entire substrate surface. A large portion of dense gel matrix also contributed to the high adhesion strength. Conversely, a large quantity of unreacted or partially reacted particles may result in low adhesion strength.