Transactions of Nanjing University of Aeronautics & Astronautics
Volume 31,Issue 2,2014 Table of Contents
2014, 31(2):119-127.
Abstract:
Exact solutions of three-dimensional (3D) crack problems are much less in number than those of two-dimensional ones, especially for multi-field coupling media exhibiting a certain kind of material anisotropy. An exact 3D thermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space, with impermeable electromagnetic conditions assumed on the crack faces. Exact 3D solutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable. The solutions, obtained by the potential theory method, are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions. Along with the previously reported solution, the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.
Exact solutions of three-dimensional (3D) crack problems are much less in number than those of two-dimensional ones, especially for multi-field coupling media exhibiting a certain kind of material anisotropy. An exact 3D thermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space, with impermeable electromagnetic conditions assumed on the crack faces. Exact 3D solutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable. The solutions, obtained by the potential theory method, are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions. Along with the previously reported solution, the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.
2014, 31(2):128-132.
Abstract:
Panel flutter phenomena can be strongly affected by thermal loads, and so a refined aeroelastic model is presented. Higher-order shell theories are used as structural models. The aerodynamic forces are described using the Piston theory. The temperature is considered uniform over the thickness of the panel. The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF), therefore the matrices are expressed in a compact form using the ″fundamental nuclei″. Composite and sandwich structures are considered and different boundary conditions are taken into account. The effects of the thermal load on the aeroelastic behavior are investigated.
Panel flutter phenomena can be strongly affected by thermal loads, and so a refined aeroelastic model is presented. Higher-order shell theories are used as structural models. The aerodynamic forces are described using the Piston theory. The temperature is considered uniform over the thickness of the panel. The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF), therefore the matrices are expressed in a compact form using the ″fundamental nuclei″. Composite and sandwich structures are considered and different boundary conditions are taken into account. The effects of the thermal load on the aeroelastic behavior are investigated.
2014, 31(2):133-136.
Abstract:
The paper deals with the thermoelastic damping in a rectangular auxetic plate during its free and forced vibrations. Contrary to existing descriptions the relaxation properties of the thermal field as well as the negative material (auxetic-material of negative Poisson′s ratio) properties are taken into considerations.
The paper deals with the thermoelastic damping in a rectangular auxetic plate during its free and forced vibrations. Contrary to existing descriptions the relaxation properties of the thermal field as well as the negative material (auxetic-material of negative Poisson′s ratio) properties are taken into considerations.
2014, 31(2):137-141.
Abstract:
There are two types of singularities in the linear thermoelasticity. The first one arises in the field of stresses if a force is applied to one point of the body. This singularity is physical and should be accepted. The second type of singularities is nonphysical and they arise in the fields of displacements and temperatures. There exist the nonlocal theories and gradient theories which have the goal to introduce the finite stresses instead of the infinite ones. The MAC model of the thermoelasticity is created to avoid the nonphysical singularities and it accepts the infinite stresses. MAC is the method of additional conditions, which allows introducing the new model to use the classical model, plus additional condition of the physical nonsingularity and/or condition of the good behavior of the solutions at infinity. The MAC Green′s functions for the heat conduction and for the elasticity could be introduced using the differential MAC models. The infinite and finite bodies are considered. The principle of superposition is applied to obtain the integral equations to solve the boundary value problems. The strength criteria based on finite stresses could be changed in this model because the infinite stresses are allowed. The strength criteria based on deformations are applicable. Classification of MAC models is given.
There are two types of singularities in the linear thermoelasticity. The first one arises in the field of stresses if a force is applied to one point of the body. This singularity is physical and should be accepted. The second type of singularities is nonphysical and they arise in the fields of displacements and temperatures. There exist the nonlocal theories and gradient theories which have the goal to introduce the finite stresses instead of the infinite ones. The MAC model of the thermoelasticity is created to avoid the nonphysical singularities and it accepts the infinite stresses. MAC is the method of additional conditions, which allows introducing the new model to use the classical model, plus additional condition of the physical nonsingularity and/or condition of the good behavior of the solutions at infinity. The MAC Green′s functions for the heat conduction and for the elasticity could be introduced using the differential MAC models. The infinite and finite bodies are considered. The principle of superposition is applied to obtain the integral equations to solve the boundary value problems. The strength criteria based on finite stresses could be changed in this model because the infinite stresses are allowed. The strength criteria based on deformations are applicable. Classification of MAC models is given.
2014, 31(2):142-146.
Abstract:
The thermoelastic plane problems of two-dimensional decagonal quasicrystals (QCs) are systematically investigated. By introducing a displacement function, the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation, and then general solutions are presented through an operator method. By virtue of the Almansi′s theorem, the general solutions are further established, and all expressions for the phonon, phason and thermal fields are described in terms of the potential functions. As an application of the general solution, for a steady point heat source in a semi-infinite quasicrystal plane, the closed form solutions are presented by four newly induced harmonic functions.
The thermoelastic plane problems of two-dimensional decagonal quasicrystals (QCs) are systematically investigated. By introducing a displacement function, the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation, and then general solutions are presented through an operator method. By virtue of the Almansi′s theorem, the general solutions are further established, and all expressions for the phonon, phason and thermal fields are described in terms of the potential functions. As an application of the general solution, for a steady point heat source in a semi-infinite quasicrystal plane, the closed form solutions are presented by four newly induced harmonic functions.
2014, 31(2):147-151.
Abstract:
The transient and thermo-electric finite element analysis (FEA) of a 2D lithium-on (Li-ion) battery is presented.The process of recharging and discharging of thin film lithium-ion (LiFePO4) battery in the presence of a transversal crack is numerically investigated. During this process significant temperature load influences the behavior of the battery and thermal fields can affect the way crack propagates into the thin film media. The simulations infer about relationship between temperature and electric field and their effect on crack propagation. A Li-ion battery model suitable for this investigation is implemented in the multi-physics software package by COMSOL Inc., and it is extended to include the thermal and electrical effects. Results and discussion are accompanied with pertinent conclusions.
The transient and thermo-electric finite element analysis (FEA) of a 2D lithium-on (Li-ion) battery is presented.The process of recharging and discharging of thin film lithium-ion (LiFePO4) battery in the presence of a transversal crack is numerically investigated. During this process significant temperature load influences the behavior of the battery and thermal fields can affect the way crack propagates into the thin film media. The simulations infer about relationship between temperature and electric field and their effect on crack propagation. A Li-ion battery model suitable for this investigation is implemented in the multi-physics software package by COMSOL Inc., and it is extended to include the thermal and electrical effects. Results and discussion are accompanied with pertinent conclusions.
2014, 31(2):152-156.
Abstract:
The main objective of this article is to investigate the behavior of gaseous systems with two and more independent gradients or thermodynamic forces exhibiting complicated behavior, when the convective flows occur. The existence of structural formations in these systems is shown by the schlieren method and the fast-response transducers. The linear analysis of stability can explain reasons of the appearance of convective instability in multicomponent gas mixtures.
The main objective of this article is to investigate the behavior of gaseous systems with two and more independent gradients or thermodynamic forces exhibiting complicated behavior, when the convective flows occur. The existence of structural formations in these systems is shown by the schlieren method and the fast-response transducers. The linear analysis of stability can explain reasons of the appearance of convective instability in multicomponent gas mixtures.
2014, 31(2):157-161.
Abstract:
Heat-ray absorbing sheet glass can decrease electric energy used for air-conditioning by controling the incoming heat-ray through windows into the rooms. On the other hand, the glasses increase the temperature and sometimes yield heat cracks by thermal stresses. It is important to know the state of thermal stress accurately in order to develop heat-ray absorbing sheet glasses with higher performance and without heat cracks. A conventional design manual at field site treats the steady state and the thermal boundary condition that all heat-rays are absorbed at glass surface. In this paper, it is assumed that the heat-ray is absorbed over all the plate thickness. The idea of the local absorptibity per unit length is introduced. The modeling of internal heat absorbing process is proposed. It can explain well that the total absorptivity depends on the plate thickness. The temperature and the thermal stresses are calculated and discussed. Sudden weather changes such as rain and/or wind after the glass is heated to be steady state are also discussed. Those weather changes are treated with the change of amount of absorbed heat-ray and/or the change of heat transfer coefficient between the glass surface and the outside atmosphere.
Heat-ray absorbing sheet glass can decrease electric energy used for air-conditioning by controling the incoming heat-ray through windows into the rooms. On the other hand, the glasses increase the temperature and sometimes yield heat cracks by thermal stresses. It is important to know the state of thermal stress accurately in order to develop heat-ray absorbing sheet glasses with higher performance and without heat cracks. A conventional design manual at field site treats the steady state and the thermal boundary condition that all heat-rays are absorbed at glass surface. In this paper, it is assumed that the heat-ray is absorbed over all the plate thickness. The idea of the local absorptibity per unit length is introduced. The modeling of internal heat absorbing process is proposed. It can explain well that the total absorptivity depends on the plate thickness. The temperature and the thermal stresses are calculated and discussed. Sudden weather changes such as rain and/or wind after the glass is heated to be steady state are also discussed. Those weather changes are treated with the change of amount of absorbed heat-ray and/or the change of heat transfer coefficient between the glass surface and the outside atmosphere.
9 Problem of Circular Hole in Thermopiezoelectric Media with Semi-permeable Thermal Boundary Condition
2014, 31(2):162-168.
Abstract:
The semi-permeable boundary condition is proposed to discuss the influence of the thermal conductivity acting on the stress and heat flow around the hole. Based on the Stroh formalism, the closed form solutions are derived, the stress and heat flow around the hole are discussed. The results show that the thermal boundary condition has significant influence on the hoop stress and heat flow around the hole. The hoop stress decreases dramatically with the increasement of the thermal conduction coefficient.
The semi-permeable boundary condition is proposed to discuss the influence of the thermal conductivity acting on the stress and heat flow around the hole. Based on the Stroh formalism, the closed form solutions are derived, the stress and heat flow around the hole are discussed. The results show that the thermal boundary condition has significant influence on the hoop stress and heat flow around the hole. The hoop stress decreases dramatically with the increasement of the thermal conduction coefficient.
10 Potential Method in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids
2014, 31(2):169-173.
Abstract:
The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered. The basic internal and external boundary value problems (BVPs) are formulated and uniqueness theorems are given. The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established. The integral representation of general solutions is obtained. The existence of regular solutions of the BVPs is proved by means of the potential method (boundary integral method) and the theory of singular integral equations.
The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered. The basic internal and external boundary value problems (BVPs) are formulated and uniqueness theorems are given. The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established. The integral representation of general solutions is obtained. The existence of regular solutions of the BVPs is proved by means of the potential method (boundary integral method) and the theory of singular integral equations.
2014, 31(2):174-178.
Abstract:
Heat-ray absorbing film is used to be bonded on the existing sheet glasses of the windows. It is effective for air-conditioning energy saving against the global warming, because it absorbs heat-ray in the thin film and decreases the incoming heat-ray into the room. On the other hand, the sheet glasses increase the temperature at the surface which the sheet is bonded and sometimes yield heat cracks by thermal stresses. It is important to know the state of thermal stresses accurately in order to develop the heat-ray absorbing film with higher performance and without heat cracks. In this paper, the analysis model is treated as the two-layer plate of the conventional soda sheet glass and the heat-ray absorbing film with different absorptivities. The unsteady temperature and thermal stresses are analyzed and calculated numerically. The influence of the patch side, which the heat-ray absorbing film is bonded at the exterior side or the interior side, on the heat-ray absorbing performance and the thermal stresses is discussed. It is found that the alternative patch side has no effect on the heat-ray absorbing performance and that the patch side is recommended to be interior side from a view point of decreasing thermal stresses against the heat crack of glasses.
Heat-ray absorbing film is used to be bonded on the existing sheet glasses of the windows. It is effective for air-conditioning energy saving against the global warming, because it absorbs heat-ray in the thin film and decreases the incoming heat-ray into the room. On the other hand, the sheet glasses increase the temperature at the surface which the sheet is bonded and sometimes yield heat cracks by thermal stresses. It is important to know the state of thermal stresses accurately in order to develop the heat-ray absorbing film with higher performance and without heat cracks. In this paper, the analysis model is treated as the two-layer plate of the conventional soda sheet glass and the heat-ray absorbing film with different absorptivities. The unsteady temperature and thermal stresses are analyzed and calculated numerically. The influence of the patch side, which the heat-ray absorbing film is bonded at the exterior side or the interior side, on the heat-ray absorbing performance and the thermal stresses is discussed. It is found that the alternative patch side has no effect on the heat-ray absorbing performance and that the patch side is recommended to be interior side from a view point of decreasing thermal stresses against the heat crack of glasses.
2014, 31(2):179-184.
Abstract:
Experimental investigations and associated methods are provided to characterize the mechanical properties of a lithium-ion battery accounting for operating temperature variation and thermal effects. Material properties for LiFePO4 cathode and anode samples taken from an off-the-shelf battery are evaluated in new and fatigued (subjected to charging and discharging cycles) conditions.
Experimental investigations and associated methods are provided to characterize the mechanical properties of a lithium-ion battery accounting for operating temperature variation and thermal effects. Material properties for LiFePO4 cathode and anode samples taken from an off-the-shelf battery are evaluated in new and fatigued (subjected to charging and discharging cycles) conditions.
2014, 31(2):185-189.
Abstract:
The thermal expansion strain is considered as a special case of eigenstrain. The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents: Impotent eigenst rain (not causing stress in any point of a body) and nilpotent eigenstrain (not causing strain in any point of a body). According to this theorem, the thermal stress can be easily found through the nilpotent eigenstrain. If the eigenstrain is an impotent one, the thermal stress vanishes. In this case, the eigenstrain must be compatible. The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.
The thermal expansion strain is considered as a special case of eigenstrain. The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents: Impotent eigenst rain (not causing stress in any point of a body) and nilpotent eigenstrain (not causing strain in any point of a body). According to this theorem, the thermal stress can be easily found through the nilpotent eigenstrain. If the eigenstrain is an impotent one, the thermal stress vanishes. In this case, the eigenstrain must be compatible. The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.
2014, 31(2):190-195.
Abstract:
The quality of injection plastic molded parts relates to precise geometry, smooth surface, strength, durability, and other indicators that are associated with the mold, materials, injection process, and service environment. The warpage is one of main defects of injection products, which cost much time and materials. In order to minimize warpage to ensure the precise shape of molded parts, it needs to combine design, service conditions, process parameters, material properties, and other factors in the design and manufacturing. Finite element tools and material database are used to analyze the occurrence of warpage, and analysis results contribute to the improvement and optimization of injection molding process of typical parts. To find the optimal process parameters in the solution space, experimental data are used to establish backpropagation (BP) network for predicting warpage of a bearing stand based on analysis with Moldflow. With a proper transfer function and the BP network architecture, results from the BP network method satisfiy the criteria of accuracy. The optimal solutions are searched in the BP network by the genetic algorithm with the finding that the optimization method based on the BP network is efficient.
The quality of injection plastic molded parts relates to precise geometry, smooth surface, strength, durability, and other indicators that are associated with the mold, materials, injection process, and service environment. The warpage is one of main defects of injection products, which cost much time and materials. In order to minimize warpage to ensure the precise shape of molded parts, it needs to combine design, service conditions, process parameters, material properties, and other factors in the design and manufacturing. Finite element tools and material database are used to analyze the occurrence of warpage, and analysis results contribute to the improvement and optimization of injection molding process of typical parts. To find the optimal process parameters in the solution space, experimental data are used to establish backpropagation (BP) network for predicting warpage of a bearing stand based on analysis with Moldflow. With a proper transfer function and the BP network architecture, results from the BP network method satisfiy the criteria of accuracy. The optimal solutions are searched in the BP network by the genetic algorithm with the finding that the optimization method based on the BP network is efficient.
2014, 31(2):196-200.
Abstract:
Catastrophic degradation of high power laser diodes is due to the generation of extended defects inside the active parts of the laser structure during the laser operation. The mechanism driving the degradation is strongly related to the existence of localized thermal stresses generated during the laser operation. These thermal stresses can overcome the yield strength of the materials forming the active part of the laser diode. Different factors contribute to reduce the laser power threshold for degradation. Among them the thermal transport across the laser structure constitutes a critical issue for the reliability of the device.
Catastrophic degradation of high power laser diodes is due to the generation of extended defects inside the active parts of the laser structure during the laser operation. The mechanism driving the degradation is strongly related to the existence of localized thermal stresses generated during the laser operation. These thermal stresses can overcome the yield strength of the materials forming the active part of the laser diode. Different factors contribute to reduce the laser power threshold for degradation. Among them the thermal transport across the laser structure constitutes a critical issue for the reliability of the device.
2014, 31(2):201-204.
Abstract:
Manufacturing of composite materials is usually accompanied with residual stresses. These stresses should be evaluated and assessed. To this end, a micromechanical model for periodic material whose temperature dependent constituents behave as thermorheologically complex materials (TCM) has been developed. This model, referred as the high fidelity generalized method of cells (HFGMC), takes into account the detailed interaction between the fiber and resin, their volume ratios, the fibers distribution and their waviness. This model is linked, in conjunction with a special UMAT subroutine, to the ABAQUS finite element code for prediction of the response of thermoviscoelastic composite structures during cool down process.The present investigation shows the effect of the cool down rate on the residual stress developed in the composite cylindrical structures.
Manufacturing of composite materials is usually accompanied with residual stresses. These stresses should be evaluated and assessed. To this end, a micromechanical model for periodic material whose temperature dependent constituents behave as thermorheologically complex materials (TCM) has been developed. This model, referred as the high fidelity generalized method of cells (HFGMC), takes into account the detailed interaction between the fiber and resin, their volume ratios, the fibers distribution and their waviness. This model is linked, in conjunction with a special UMAT subroutine, to the ABAQUS finite element code for prediction of the response of thermoviscoelastic composite structures during cool down process.The present investigation shows the effect of the cool down rate on the residual stress developed in the composite cylindrical structures.
2014, 31(2):205-209.
Abstract:
In a linear framework, the problem of stability of closed cylindrical shell is briefly discussed. The cylindrical shell is immersed in a supersonic gas flow and under the influence of temperature field varying along the thickness. An unperturbed uniform velocity flow field, directed along the short edges of the shell, is applied. Due to the inhomogeneity of the temperature field distribution across the thickness shell buckling instability occurs. This instability accounts for the deformed shape of the shell, to be referred as the unperturbed state. Stability conditions and boundary for the unperturbed state of the system under consideration are presented following the basic theory of aero-thermo-elasticity. The stability boundary depends on the variables characterizing the flow speed, the temperature at the middle plane of the shell and the temperature gradient in the direction normal to that plane. It is shown that the combined effect of the temperature field and flowing stream regulates the process of stability, and the temperature field can significantly change the flutter critical speed.
In a linear framework, the problem of stability of closed cylindrical shell is briefly discussed. The cylindrical shell is immersed in a supersonic gas flow and under the influence of temperature field varying along the thickness. An unperturbed uniform velocity flow field, directed along the short edges of the shell, is applied. Due to the inhomogeneity of the temperature field distribution across the thickness shell buckling instability occurs. This instability accounts for the deformed shape of the shell, to be referred as the unperturbed state. Stability conditions and boundary for the unperturbed state of the system under consideration are presented following the basic theory of aero-thermo-elasticity. The stability boundary depends on the variables characterizing the flow speed, the temperature at the middle plane of the shell and the temperature gradient in the direction normal to that plane. It is shown that the combined effect of the temperature field and flowing stream regulates the process of stability, and the temperature field can significantly change the flutter critical speed.
2014, 31(2):210-218.
Abstract:
The different temperature-induced nonlinear behavior near a conducting crack tip in a ferroelectric single crystal is studied based on a phase field approach containing the time-dependent Ginzburg-Landau equation. Since domain switching in a crack tip plays an important role in the fracture behavior, by using three-dimensional nonlinear finite element method, the temperature-induced domain switching behavior of a ferroelectric single crystal is simulated under applied electrical and mechanical loads. The simulations show that increasing the temperature will enhance the crack propagation under a strong electric field, which results in switching-weakening. In particular, increasing the temperature from 300°C to 600°C will impede the crack propagation under combined mechanical and electric field loading, which results in switching-toughening. Salient features of the results are consistent with many experimental observations.
The different temperature-induced nonlinear behavior near a conducting crack tip in a ferroelectric single crystal is studied based on a phase field approach containing the time-dependent Ginzburg-Landau equation. Since domain switching in a crack tip plays an important role in the fracture behavior, by using three-dimensional nonlinear finite element method, the temperature-induced domain switching behavior of a ferroelectric single crystal is simulated under applied electrical and mechanical loads. The simulations show that increasing the temperature will enhance the crack propagation under a strong electric field, which results in switching-weakening. In particular, increasing the temperature from 300°C to 600°C will impede the crack propagation under combined mechanical and electric field loading, which results in switching-toughening. Salient features of the results are consistent with many experimental observations.
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