Institute of Mechanics,
Chinese Academy of Sciences
2019 Vol.9(5)
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Theoretical and Applied Mechanics Letters 2019, 9(5): 277-278.
doi: 10.1016/j.taml.2019.05.011
Abstract:
Theoretical and Applied Mechanics Letters 2019, 9(5): 279-284.
doi: 10.1016/j.taml.2019.06.006
Abstract:
Thermo-elastic analysis of simply-supported orthotropic laminated beams subjected to high temperature and mechanical load is presented on the basis of the exact two-dimensional thermo-elasticity theory. The beam is composed of several orthotropic layers, each with temperature-dependent material properties. The governing equation for each layer is analytically solved using the state space method. The displacement and stress solutions of the beam are obtained using the transfer-matrix method. A numerical example is included to study the effects of temperature on the mechanical responses of a sandwich beam. The results reveal two main effects of temperature: (i) inducing deformations and stresses by itself; (ii) affecting the deformations and stresses induced by the mechanical load.
Thermo-elastic analysis of simply-supported orthotropic laminated beams subjected to high temperature and mechanical load is presented on the basis of the exact two-dimensional thermo-elasticity theory. The beam is composed of several orthotropic layers, each with temperature-dependent material properties. The governing equation for each layer is analytically solved using the state space method. The displacement and stress solutions of the beam are obtained using the transfer-matrix method. A numerical example is included to study the effects of temperature on the mechanical responses of a sandwich beam. The results reveal two main effects of temperature: (i) inducing deformations and stresses by itself; (ii) affecting the deformations and stresses induced by the mechanical load.
Theoretical and Applied Mechanics Letters 2019, 9(5): 285-288.
doi: 10.1016/j.taml.2019.05.001
Abstract:
In this paper the problem of linear stability of a closed cylindrical shell under the action of both non-uniform temperature field and supersonic gas flow is considered. The stability conditions for the unperturbed state of the aerothermoelastic system are obtained. It is shown that, by the combined action of the temperature field and the ambient supersonic flow, the process of linear stability can be controlled and the temperature field affects significantly the critical flutter speed.
In this paper the problem of linear stability of a closed cylindrical shell under the action of both non-uniform temperature field and supersonic gas flow is considered. The stability conditions for the unperturbed state of the aerothermoelastic system are obtained. It is shown that, by the combined action of the temperature field and the ambient supersonic flow, the process of linear stability can be controlled and the temperature field affects significantly the critical flutter speed.
Theoretical and Applied Mechanics Letters 2019, 9(5): 289-292.
doi: 10.1016/j.taml.2019.06.009
Abstract:
In this paper, the problem of a functionally graded piezoelectric material strip (FGPM strip) containing an infinite row of parallel cracks perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Fourier transforms, the electro-thermo-elastic problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.
In this paper, the problem of a functionally graded piezoelectric material strip (FGPM strip) containing an infinite row of parallel cracks perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Fourier transforms, the electro-thermo-elastic problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.
Theoretical and Applied Mechanics Letters 2019, 9(5): 293-296.
doi: 10.1016/j.taml.2019.05.007
Abstract:
Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.
Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.
Theoretical and Applied Mechanics Letters 2019, 9(5): 297-301.
doi: 10.1016/j.taml.2019.05.008
Abstract:
Within the framework of three-dimensional elasticity theory, this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field. The present analytical solutions are validated through comparisons against those available in open literature. A parametric study is conducted to examine the effects of gradient distribution, different temperature fields, different diameter ratio and boundary conditions on the deformation and stress fields of the plate. The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials (FGM) annular plates.
Within the framework of three-dimensional elasticity theory, this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field. The present analytical solutions are validated through comparisons against those available in open literature. A parametric study is conducted to examine the effects of gradient distribution, different temperature fields, different diameter ratio and boundary conditions on the deformation and stress fields of the plate. The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials (FGM) annular plates.
Theoretical and Applied Mechanics Letters 2019, 9(5): 302-307.
doi: 10.1016/j.taml.2019.05.003
Abstract:
Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction are investigated analytically and numerically. The corresponding dispersion relation is a sixth-order algebraic equation, governed by six non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter, the ratio between extensional and torsional moduli, the Fourier number, and the dimensionless thermal relaxation. The behavior of the solutions is discussed from two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxation on the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wave celerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered. However, with large wavenumbers, the solutions behave differently depending on the thermal relaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from the classical result of the speed of second sound.
Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction are investigated analytically and numerically. The corresponding dispersion relation is a sixth-order algebraic equation, governed by six non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter, the ratio between extensional and torsional moduli, the Fourier number, and the dimensionless thermal relaxation. The behavior of the solutions is discussed from two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxation on the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wave celerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered. However, with large wavenumbers, the solutions behave differently depending on the thermal relaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from the classical result of the speed of second sound.
Theoretical and Applied Mechanics Letters 2019, 9(5): 308-311.
doi: 10.1016/j.taml.2019.06.008
Abstract:
Increasing operating speed of modern passenger railway vehicles leads to higher thermal load on the braking system. Organic composite brake pads are poor thermal conductors, hence frictional heat is absorbed mainly by the disc. In this study three brake pad types were tested on the dynamometer. Metallic fibres, steel and copper, were introduced to the formulation of two materials. The third was a non-metallic material - a reference case. Dynamometer test comprised emergency brake applications to determine the frictional characteristics of the materials and constant-power drag braking to analyse the effect of metal fibres on temperature evolution, measured by six thermocouples embedded in the brake disc. Mean friction coefficient is analysed and discussed. It is concluded that conductive fibre in the friction material formulation may influence its tribological characteristics. Despite high thermal conductivity, metal fibres in the concentration tested in this study, did not reduce temperature of the brake disc.
Increasing operating speed of modern passenger railway vehicles leads to higher thermal load on the braking system. Organic composite brake pads are poor thermal conductors, hence frictional heat is absorbed mainly by the disc. In this study three brake pad types were tested on the dynamometer. Metallic fibres, steel and copper, were introduced to the formulation of two materials. The third was a non-metallic material - a reference case. Dynamometer test comprised emergency brake applications to determine the frictional characteristics of the materials and constant-power drag braking to analyse the effect of metal fibres on temperature evolution, measured by six thermocouples embedded in the brake disc. Mean friction coefficient is analysed and discussed. It is concluded that conductive fibre in the friction material formulation may influence its tribological characteristics. Despite high thermal conductivity, metal fibres in the concentration tested in this study, did not reduce temperature of the brake disc.
Theoretical and Applied Mechanics Letters 2019, 9(5): 312-319.
doi: 10.1016/j.taml.2019.04.007
Abstract:
In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thin plates on elastic foundations, the static problem of circular thin plates on Gibson elastic foundation is solved using an iterative method based on the modified Vlasov model. On the basis of the principle of minimum potential energy, the governing differential equations and boundary conditions for circular thin plates on modified Vlasov foundation considering the characteristics of Gibson soil are derived. The equations for the attenuation parameter in bending problem are also obtained, and the issue of unknown parameters being difficult to determine is solved using the iterative method. Numerical examples are analyzed and the results are in good agreement with those form other literatures. It proves that the method is practical and accurate. The inhomogeneity of modified Vlasov foundations has some influence on the deformation and internal force behavior of circular thin plates. The effects of various parameters on the bending of circular plates and characteristic parameters of the foundation are discussed. The modified model further enriches and develops the elastic foundations. Relevant conclusions that are meaningful to engineering practice are drawn.
In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thin plates on elastic foundations, the static problem of circular thin plates on Gibson elastic foundation is solved using an iterative method based on the modified Vlasov model. On the basis of the principle of minimum potential energy, the governing differential equations and boundary conditions for circular thin plates on modified Vlasov foundation considering the characteristics of Gibson soil are derived. The equations for the attenuation parameter in bending problem are also obtained, and the issue of unknown parameters being difficult to determine is solved using the iterative method. Numerical examples are analyzed and the results are in good agreement with those form other literatures. It proves that the method is practical and accurate. The inhomogeneity of modified Vlasov foundations has some influence on the deformation and internal force behavior of circular thin plates. The effects of various parameters on the bending of circular plates and characteristic parameters of the foundation are discussed. The modified model further enriches and develops the elastic foundations. Relevant conclusions that are meaningful to engineering practice are drawn.
Theoretical and Applied Mechanics Letters 2019, 9(5): 320-327.
doi: 10.1016/j.taml.2019.05.002
Abstract:
This study addresses the issue of ship accidental grounding as an impact phenomenon, with the assumption that an interaction of its structure with the oceanic seabed (obstruction), idealized as rock topology, is capable of initiating a so-called hard ground scenario. This occurrence variation was considered by performing two main instances, encompassing raking and stranding, often experienced by oil/chemical tankers as thin-walled structures. In addition, a failure criterion was implemented on the structural geometry, in order to define its ultimate limit and possible damage, during interaction with the obstructions. Subsequently, the analysis results were compiled to assess structural crashworthiness as well as progressive failure of the double bottom part of the tanker, where energy criterion indicated the raking to be more destructive. Meanwhile, detailed observation of the failure sequence indicated the stranding to have successfully breached the inner bottom shell.
This study addresses the issue of ship accidental grounding as an impact phenomenon, with the assumption that an interaction of its structure with the oceanic seabed (obstruction), idealized as rock topology, is capable of initiating a so-called hard ground scenario. This occurrence variation was considered by performing two main instances, encompassing raking and stranding, often experienced by oil/chemical tankers as thin-walled structures. In addition, a failure criterion was implemented on the structural geometry, in order to define its ultimate limit and possible damage, during interaction with the obstructions. Subsequently, the analysis results were compiled to assess structural crashworthiness as well as progressive failure of the double bottom part of the tanker, where energy criterion indicated the raking to be more destructive. Meanwhile, detailed observation of the failure sequence indicated the stranding to have successfully breached the inner bottom shell.
Theoretical and Applied Mechanics Letters 2019, 9(5): 328-337.
doi: 10.1016/j.taml.2019.05.009
Abstract:
This paper is concerned with propagation of water waves induced by moving bodies with uniform velocity on the bottom of a channel, a simple model for prescribed underwater landslides. The fluid is assumed to be inviscid and incompressible, and the flow, irrotational. We apply this model to a variety of test problems, and particular attention is paid to long-time dynamics of waves induced by two landslide bodies moving with the same speed. We focus on the transcritical regime where the linear theory fails to depict the wave phenomena even in the qualitative sense since it predicts an infinite growth in amplitude. In order to resolve this problem, weakly nonlinear theory or direct numerical simulations for the fully nonlinear equations is required. Comparing results of the linear full-dispersion theory, the linear shallow water equations, the forced Korteweg-de Vries model, and the full Euler equations, we show that water waves generated by prescribed underwater landslides are characterized by the Froude number, sizes of landslide bodies and distance between them. Particularly, in the transcritical regime, the second body plays a key role in controlling the criticality for equal landslide bodies, while for unequal body heights, the higher one controls the criticality. The results obtained in the current paper complement numerical studies based on the forced Korteweg-de Vries equation and the nonlinear shallow water equations by Grimshaw and Maleewong (J. Fluid Mech. 2015, 2016).
This paper is concerned with propagation of water waves induced by moving bodies with uniform velocity on the bottom of a channel, a simple model for prescribed underwater landslides. The fluid is assumed to be inviscid and incompressible, and the flow, irrotational. We apply this model to a variety of test problems, and particular attention is paid to long-time dynamics of waves induced by two landslide bodies moving with the same speed. We focus on the transcritical regime where the linear theory fails to depict the wave phenomena even in the qualitative sense since it predicts an infinite growth in amplitude. In order to resolve this problem, weakly nonlinear theory or direct numerical simulations for the fully nonlinear equations is required. Comparing results of the linear full-dispersion theory, the linear shallow water equations, the forced Korteweg-de Vries model, and the full Euler equations, we show that water waves generated by prescribed underwater landslides are characterized by the Froude number, sizes of landslide bodies and distance between them. Particularly, in the transcritical regime, the second body plays a key role in controlling the criticality for equal landslide bodies, while for unequal body heights, the higher one controls the criticality. The results obtained in the current paper complement numerical studies based on the forced Korteweg-de Vries equation and the nonlinear shallow water equations by Grimshaw and Maleewong (J. Fluid Mech. 2015, 2016).
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