Optimum Structure Design of a Multilayer Piezo-Composite Disk for Control of Thermal Stress

This article deals with a control problem of a thermal stress in a composite circular disk consisting of a transversely isotropic structural layer onto which multiple piezoelectric layers with concentrically arranged electrodes are perfectly bonded. When a prescribed heating temperature distribution acts on the structural layer surface, the optimum structure design of the composite disk is performed so that the maximum thermal stress in the structural layer is minimized subject to constraints on stresses in the piezoelectric layers. A hybrid optimization technique combining the particle swarm optimization with the simplex method is employed for solving the optimum design problem. To resolve the difficulty in solving the problem with many optimization variables, three improvements are added to the hybrid optimization technique and an efficient design method is introduced. For a composite disk constructed of a CFRP layer and cadmium selenide layers, the layer thicknesses, the electrode dimensions, and the voltages applied to the electrodes are determined and the numerical results are presented in tabular and graphical forms. Finally, it is shown from the optimum design results that the highest suppression ratio of the maximum thermal stress reaches 40.8% in the case of a five-layer composite disk and is considered to be almost saturated.     

Control of Thermal Stress in a Piezo-Composite Disk

This article deals with a stress control problem of a composite circular disk consisting of a structural layer onto which piezoceramic layers are bonded. When a heating temperature distribution acts on the bottom free surface, the maximum thermal stress in the structural layer can be controlled by applying electric potentials to electrodes concentrically arranged on each piezoceramic layer. The applied electric potentials are determined by solving an optimization problem so that the maximum thermal stress in the structural layer is minimized subject to constraints on the stresses in the piezoceramic layers. Finally, numerical results are presented.     

INVERSE TRANSIENT THERMOELASTIC PROBLEM FOR A COMPOSITE CIRCULAR DISK

The present article deals with the application of a piezoelectric material as a sensor of thermomechanical disturbance. We consider a composite circular disk constructed of a transversely isotropic layer onto which a piezoceramic layer of crystal class 6mm is perfectly bonded. An inverse transient thermoelastic problem is solved to determine the unknown transient heating temperature distribution on the surface of the transversely isotropic layer, when the distribution of the electric potential difference across the piezoceramic layer is known. A finite difference method with respect to the time variable is employed to solve this inverse problem. The thermoelastic fields in the transversely isotropic and piezoceramic layers are analyzed by means of a transversely isotropic potential function method and a piezothermoelastic potential function method, respectively. Numerical results are presented for the time variation of the inferred heating temperature distribution and the corresponding distributions of temperature, displacements, stresses, and electric displacements.     

Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock

Abstract

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated.     

Thermal Buckling of Piezoelectric Functionally Graded Material Beams

Buckling analysis of functionally graded material (FGM) beams with surface-bonded piezoelectric layers which are subjected to both thermal loading and constant voltage is studied. The material nonhomogeneous properties are assumed to vary smoothly by distribution of power law through the beam thickness. The Euler-Bernoulli beam theory and nonlinear strain-displacement relation are used to obtain the governing equations of piezoelectric FGM beam. Beam is assumed under three types of thermal loading and various types of boundary conditions. For each case of thermal loading and boundary conditions, closed-form solutions are obtained. The effects of the applied actuator voltage, beam geometry, boundary conditions, and power law index of functionally graded material on the buckling temperature are investigated.     

CONTROL OF TRANSIENT THERMOELASTIC DISPLACEMENT IN A COMPOSITE DISK

Control of displacement in a composite disk subjected to axisymmetric heating is investigated. The disk consists of a transversely isotropic structural layer to which is bonded a layer of piezoceramic material of crystal class 6mm. First, a solution procedure based on potential functions is used to analyze the elastic and electric fields induced in the disk when a transient ambient temperature acts on the free surface of the structural layer. Then a transient distribution of electric potential across the piezo-electric layer is determined such that the resultant displacement at the surface of the structural layer has a prescribed distribution. Numerical results are obtained for the resulting thermal, elastic, and electric fields.     

Control of Dynamic Deformation of a Piezothermoelastic Beam with a Closed-Loop Control System Subjected to Thermal Disturbance

Control of dynamic deformation of a piezothermoelastic beam with a closed-loop control system subjected to thermal disturbance is studied. To suppress the deformation due to the disturbance, the beam is subjected to the closed-loop control procedure where one of the piezoelectric layers serves as a sensor to detect the deformation due to the disturbance and the other as an actuator to suppress it. The analytical solution of the dynamic deflection is formulated based on the classical laminate theory. Using numerical examples, suppression of the transient oscillation due to thermal disturbance by a series of pulses of electric voltage is examined.     

A FINITE DIFFERENCE SCHEME FOR INVERSE TRANSIENT PIEZOTHERMOELASTICITY PROBLEMS

A finite difference formulation is developed to determine the time-varying, axisymmetric, ambient temperature on the face of a piezoelectric circular disk based on knowledge of the distribution of the induced electric potential difference across the disk thickness. The disk, or “sensor, ”possesses hexagonal material symmetry properties of class 6mm and is constrained by a rigid, thermally insulated, and charge-free ring. The inverse problem is solved by means of potential functions. Numerical results for a cadmium selenide disk illustrate the effects of the surface heat transfer coefficient and radial variations of the measured electric potential difference on the temperature, stress, and electric displacement fields. The finite difference results are compared with an exact solution for the special case of steady-state heat conduction     

Thermal Buckling of Piezolaminated Plates Subjected to Different Loading Conditions

A thermal buckling analysis is presented for simply supported rectangular laminated composite plates that are covered with top and bottom piezoelectric actuators, and subjected to the combined action of thermal load and constant applied actuator voltage. The thermomechanical properties of composite and piezoelectric materials are assumed to be linear functions of the temperature. The formulations of the equations are based on the higher-order laminated plate theory of Reddy and using the Sanders nonlinear kinematic relations. The closed-form solutions for the buckling temperature are obtained through the Galerkin procedure and solving the resultant eigenvalue problem, which are convenient to be used in engineering design applications. Numerical examples are presented to verify the proposed method. The effects of the plate geometry, fiber orientation in composite layers, lay-up configuration, different utilized piezoelectric materials, temperature dependency of material properties, thermal conductivity, and energy generation on the buckling load are investigated.     

Inverse Problem of a Piezothermoelastic Cylinder Subject to Transient Heating

An inverse problem of a radially polarized piezoelectric hollow circular cylinder of crystal class 6 mm is investigated. It is assumed that a voltage induced by the action of a time-varying temperature applied to the inner surface of the cylinder is measured on the outer surface. The inverse problem entails a determination of the heating temperature from knowledge of the measured voltage. First, an exact solution to the problem is found by solving the equations of equilibrium and electrostatics for the cylinder subject to the prescribed boundary conditions. Then a least-squares residual method that incorporates Lagrange multipliers for satisfaction of the boundary equations is employed to derive an approximate analytic solution. Both formulations are utilized in order to calculate the unknown heating temperature, and the corresponding temperature, displacement and stress fields in a cylinder of cadmium selenide. Numerical results based upon the least-squares residual formulation are found to compare favorably with those obtained by the exact analysis.     

Effect of actively managed thermal-loading in optimal design of an aeroengine turbine disk

The effect of actively managed thermal loading for optimal design of turbine disk was investigated to seek the better balance between strength demand and minimum weight/volume. An integrated process of design was developed to achieve automatic iteration for this multi-objective optimization problem. Under equal consumption of heating energy and cooling air conditions, two types of actively managed thermal loading with different allocation ratios of heating energy (ϕ = 0.1 and ϕ = 0.2) in the outer and inner surface of disk were considered in the process of optimization. As a comparison, the disk at conventional thermal loading conditions (ϕ = 0) was also optimized at the same design conditions. Results showed that the better structure of disk with smaller weight/volume and lower maximum stress level was obtained due to thermal loading management. Through actively managing the thermal loading to reorganize the temperature distribution of disk, the optimized weight/volume and maximum hub stress fallen 2.24% and 12.16% respectively to compare with the conventional thermal loading condition. The reason for the preceding effect could be explained that an artificial V-shaped temperature distribution was built in the disk through actively managing thermal loading, and correspondingly, the reverse temperature gradient between hub and web produced a pulling effect and counteracted parts of stress from rotating.     

Thermal buckling and postbuckling analysis of piezoelectric FGM beams based on high-order shear deformation theory

This article deals with the thermal buckling and postbuckling of functionally graded material (FGM) beams with surface-bonded piezoelectric actuators based on physical neutral surface concept and high-order shear deformation theory including von Kármán strain–displacement relationships. The beams are exposed to a uniform temperature field and electric field, the material properties of FGM layers are temperature-dependent and vary in the thickness direction. The approximate solutions of piezoelectric FGM beams for thermal buckling and postbuckling are obtained by a two-step perturbation method, meanwhile, the analytical solutions of Timoshenko beam model and Euler beam model are also presented. The validity of the present work can be confirmed by comparisons with previous results. The effects of the applied actuator voltage, beam geometry as well as volume fraction index of FGM beam on the critical buckling temperature, and postbuckling load–deflection relationships are investigated.     

Dynamic Thermal Postbuckling Analysis of Piezoelectric Functionally Graded Cylindrical Shells

Dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage is analyzed using an incremental numerical technique. The shell is graded across the thickness according to a power law form function. The material properties of the functionally graded cylindrical shells are considered to be temperature dependent. The theoretical formulations are based on the classical shell theory with Sanders' nonlinear kinematic relations. Then, using Hamilton's principle, equations of motion are derived for the piezoelectric FGM cylindrical shell. A finite difference based method combined with the Runge–Kutta method is employed to predict the postbuckling equilibrium paths, and the dynamic buckling temperature difference is detected according to Budiansky's stability criterion. Numerical results are presented to demonstrate the effects of the applied actuator voltage, shell geometry, volume fraction exponent of FGM, and the temperature dependency of the material properties on the postbuckling behavior of the shell. The results for simpler states are validated with the known data in the literature.     

Thermal Buckling of Simply Supported Piezoelectric FGM Cylindrical Shells

A thermal buckling analysis is presented for functionally graded cylindrical shells that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of thermal load and constant applied actuator voltage. The material properties are assumed to vary as a power form of the thickness coordinate. Derivation of the equations is based on the higher-order shear deformation shell theory using the Sanders nonlinear kinematic relations. Results for the buckling temperatures are obtained in the closed form solution. The effects of the applied actuator voltage, shell geometry, and volume fraction exponent of functionally graded material on the buckling temperature are investigated. The results for simpler states are validated with known data in the literature.     

Thermoelastic Buckling Analysis of Functionally Graded Circular Plates Integrated with Piezoelectric Layers

Thermal buckling of circular plates made of functionally graded materials with surface-bounded piezoelectric layers are studied. The material properties of the FG plates are assumed to vary continuously through the plate thickness by distribution of power law of the volume fraction of the constituent materials. The general thermoelastic nonlinear equilibrium and linear stability equations for the piezoelectric FG plate are derived using the variational formulations. Buckling temperatures are derived for solid circular plates under uniform temperature rise, nonlinear and linear temperature variation through the thickness for immovable clamped edge of boundary conditions. The effects of piezo-to-host thickness ratio, applied actuator voltage, boundary condition, and power law index of functionally graded plates on the buckling temperature of plate are investigated. The results are verified with the data in literature.     

THERMOELASTIC BEHAVIOR OF A COMPOSITE SLAB UNDER A RAPID DUAL-PHASE-LAG HEATING

This work is concerned with the investigation of the thermoelastic response of a composite slab (a two-, thin-, metallic-layered plate) under the effect of an intense rapid heating applied to one side. The dual-phase-lag heat conduction model is used to derive the heat equation in each layer. The heat equations are solved using the Laplace transform technique and the Riemann-sum method. As a result, the thermal behavior, in the form of the temperature distribution along the thickness direction of the slab, is determined. The governing equation of plate deflection is formulated and solved for simply supported edge conditions. As a result, the plate deflections and the thermal stresses are calculated numerically using the finite difference method. Thermal stress distribution is found to depend on the temperature distribution in addition to the difference in the thermal and mechanical properties of the materials that compose the two layers.     

Dynamic Thermal Postbuckling Analysis of Shear Deformable Piezoelectric-FGM Cylindrical Shells

Dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage is studied. The shell material is graded across the thickness according to a power law. The material properties of the functionally graded cylindrical shells are considered to be temperature dependent. The theoretical formulations are based on the Sanders nonlinear kinematic relations, which account for the transverse shear strains, and the third-order shear deformation shell theory is employed. Hamilton's principle is used to derive the equations of motion governing piezoelectric FGM cylindrical shells. A finite difference approximation combined with the Runge-Kutta method is employed to predict the postbuckling equilibrium paths, and the dynamic buckling temperature difference is detected according to Budiansky's stability criterion. Numerical results are presented to demonstrate the effects of the applied actuator voltage, shell geometry, volume fraction exponent in the power-law variation of the FGM, and the temperature dependency of the material properties on the postbuckling behavior of the shell. The results for simpler states are validated with the known results in the literature.     

Numerical analysis of high-temperature proton exchange membrane fuel cells during start-up by inlet gas heating and applied voltage

This paper investigates the start-up or warm-up process of a high-temperature proton exchange membrane fuel cell (HT-PEMFC) from room temperature to a desired temperature of ～180 °C. The heating strategy considered in this study involves an initial heating of the HT-PEMFC by a process referred to as inlet gas heating to a temperature above 100 °C. After the fuel cell reaches above 100 °C, a voltage is applied, where electrochemical reaction heating is expected to contribute to the heating process. Thus, a numerical transient non-isothermal three-dimensional model is derived to mimic the start-up process. Operational parameters such as anode inlet temperature, cathode inlet temperature, applied voltage and voltage application temperature are varied and their effects on the maximum temperature in the membrane electrode assembly (MEA) and temperature difference in the MEA are studied. Firstly, the distribution of temperature along the channel length indicates an increase of temperature during gas heating and as the voltage is applied at the voltage application temperature, the temperature increases at the centre of the MEA due to exothermic reactions. The two-dimensional temperature distribution indicates a temperature difference between the centre of the MEA and the regions below the bipolar plate where the temperature is relatively lower. Considering the whole start-up process with respect to time, the temperature difference exists throughout the process. This will be the key focus in the parametric study. The parametric study indicates that the inlet gas temperatures, applied voltage and the voltage application temperature affect the maximum temperature in the MEA and most importantly, the temperature difference in the MEA. This can cause thermal stresses to build-up if the increase rate of temperature difference is excessive. Setting the applied voltage high (thus, lower current density) is necessary to reduce the increase rate of temperature difference.     

Preliminary experiments on the control of natural convection in differentially-heated cavities

Aiming at the control of natural convection flows and heat transfer in air-filled differentially-heated cavities, experimental attempts were carried out in order to achieve the stability of such flows to various excitations. The mechanism of control chosen in these experiments introduces thermal disturbances via a thin pipe located inside the boundary layer at the bottom of the hot wall. Its temperature varies periodically due to alternating electrical heating and continuous water cooling. The effects of this disturbance in temperature are investigated for a Rayleigh number value chosen just greater than the first bifurcation value from a steady state flow to a monoperiodic state. The results show the distribution of the overall and local Nusselt numbers. The introduction of this obstacle induces a 10% decrease in heat transfer. Temperature oscillations of the actuator provoke modifications of the flow field. In particular, an amplification of unsteadiness in the outer borders of boundary layers is observed and a displacement of secondary vortices is encountered. Explanations are given by a detailed examination of flow structures, such as the spatial distribution of velocities and their fluctuations.     

Numerical simulation and analysis of thermal stress distributions for a planar solid oxide fuel cell stack with external manifold structure

A three-dimensional numerical model based on the finite element method (FEM) is constructed to calculate the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack with external manifold structure. The stack is composed of 5 units which include cell, metallic interconnect, seal and anode/cathode current collectors. The temperature profile is described according to measured temperature points in the stack. It can be clearly seen that the maximum stress concentration area appears at the corner of the components when the stack is heated from room temperature (RT) to 780 °C. The effects of stack components on maximum stress concentration have been investigated under the operation temperature, as well as the thermal stress simulation results. It is obvious that the coefficient of thermal expansion (CTE) mismatch between the interconnect and the seal plays an important role in determining the thermal stress distribution in the stack. However, different compressive loads have almost no effect on stress distribution, and the influence of glass-based seal depends on the elastic modulus. The simulation results can be applied for optimizing the structural design of the stack and minimizing the high stress concentration in components.