Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

Effect of 6H-SiC crystal growth shapes on thermo-elastic stress in the growing crystal

The effect of 6H-SiC crystal growth shapes on the thermo-elastic stress distribution in the growing crystal was systematically in- vestigated by using a finite element method. The thermo-elastic stress distribution in the crystal with a flat growth shape was more homoge- neous than that in the crystals with concave and convex growth shapes, and the value of thermo-elasticity in the crystal with a fiat growth shape was also smaller than that in the two other types of crystals. The maximum values of thermo-elastic stress appeared at interfaces be- tween the crystal and the graphite lid. If the lid was of the same properties as 6H-SiC, the thermo-elastic stress would decrease in two orders of magnitude. Thus, to grow 6H-SiC single crystals of high quality, a transition layer of SiC formed by deposition or reaction is suggested; meanwhile the thermal field in the growth chamber should be adjusted to maintain the crystals with fiat growth shapes.

Uniqueness for the Linear Theory of Generalized Thermo-Elasticity

In this paper, the uniqueness for the linear theory of a new generalized thermo-elastic model of the continuum with the centre symmetry is shown under less assumptions, whose constitutive equations contain deformation, temperature and its rate as well as its gradient, electric field and its gradient. So the phase variation is pemitted when the deformation proceeds as long as the constitutive equations preserve their Original forms.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

A NEW UNIQUENESS THEOREM OF THE LINEAR THERMO-ELASTIC DYNAMICS ON UNBOUNDED DOMAINS

In the present paper, the uniqueness of the solution to the initial boundary value problem of the linear thermo-elastic dynamics on unbounded domains is obtained under less restrictive conditions, including abandoning the positive semi-definiteness of the elasticity tensor and boundness of the material tensor and restrictions on the acoustic tensor and the coupled tensor, and the results in [1] are refined. The conclusion here is valid for the case on bounded domains and the linear elastic dynamics on unbounded domains, hence the results in [2 similar to 4] are refined too. Abandoning the positive semi-definiteness of elasticity tensor permits that the uniqueness of the kinetic process is still valid for deformation of the wider materials, especially for the case that there are phase-transition during deformation process provided that the constitutive equations are unchanged in forms.

The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media

The equilibrium equations of anisotropic media, coupled to the heat conduction equations, are studied here based on the standard spaces of the physical presentation, in which an new thermo-elastic model based on the second law of thermodynamics is induced. The uncoupled heat wave equation for anisotropic media is deduced. The results show that the equation of heat wave is of the properties of dissipative waves. In final part of this paper, we discuss the propagation behaviour of heat waves for transversely isotropic media.

Numerical Analysis of Thermo-Elastic Contact Problem of Disc Brakes for Vehicle on Gradient Surfaces

In this study, the thermo-elastic effects of frictional heat generation in a disc brake system due to braking actions were simulated. The mathematical model that defined the problem was developed from the kinetic and potential energies of moving vehicles on the gradient surfaces. This problem was solved for the selected geometry of disc brake and pad with their material properties selected from existing literatures using the finite element method and the computational results were obtained. The thermal deformation obtained was in good agreement with similar literature results. Also, for the same braking period and conditions, the results showed that a vehicle ascending a hill gave a higher temperature rise, Von Mises stress and thermal deformation on brake contact surfaces than when descending hill. Therefore, the braking period required to bring a moving vehicle in ascendent motion to a lower speed is expected to be shorter because of the gravity effect than horizontal motion, while descendent motion requires longer braking period.

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

The therrno-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-stretch bounded to the macro-deformation： in this case the microstructure disappears apparently （it becomes latent） and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies.

Topology Optimization of Transient Thermo-elastic Structure Considering Regional Temperature Control

In this paper,a topology optimization model for transient thermo-elastic coupling problems is proposed.Based on the method of solid isotropic material with penalization,the coupled equations of transient thermomechanical field are established.In this model,the objective is to minimize the global structural compliance with volume and maximum temperature constraints during the working time.To efficiently restrict the maximum temperature of the transient thermo-elastic structure in time and spatial dimensions,the regional temperature control scheme is constructed using the aggregation function.The adjoint variable method is adopted to derive the sensitivity of objective function and constraints,and the design variables are updated through the method of moving asymptotes to obtain clear optimal topologies.The effects of the duration and magnitude of the thermal and structural loads on the optimization results are discussed through several numerical examples.

An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing

Combination of topology optimization and additive manufacturing technologies provides an effective approach for the development of light-weight and high-performance structures.A heavy-loaded aerospace bracket is designed by topology optimization and manufactured by additive manufacturing technology in this work.Considering both mechanical forces and temperature loads,a formulation of thermo-elastic topology optimization is firstly proposed and the sensitivity analysis is derived in detail.Then the procedure of numerical optimization design is presented and the final design is additively manufactured using Selective Laser Melting(SLM).The mass of the aerospace bracket is reduced by over 18%,benefiting from topology and size optimization,and the three constraints are satisfied as well in the final design.This work indicates that the integration of thermo-elastic topology optimization and additive manufacturing technologies can be a rather powerful tool kit for the design of structures under thermal-mechanical loading.

A magneto -thermo-elastic problem for a half-space without energy dissipation subjected to rotation and gravity field

The prime objective of the present paper is to analyze the effects of the rotation,magnetic field and gravity in a thermo-elastic half-space containing heat source on the boundary of the half-space.The medium assumed under consideration is traction free,homogeneous,isotropic,as well as without energy dissipation.The normal mode analysis and eigenvalue approach technique are used to solve the resulting non-dimensional coupled equations.The comparisons for the physical quantities are established numerically and represented graphically in different cases with respect to the used effects.A comparative and remarkable study has been carried out through various graphs to deliberate the consequences of different parameter on the displacement components,stress components and temperature.

Propagation of Thermo-Elastic Waves at Several Typical Interfaces Based on the Theory of Dipolar Gradient Elasticity

The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model.This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic,composite and sandwich structures.Cylindrical and spherical panels,cylinders and plates are analyzed in orthogonal mixed curved reference coordinates.The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels.The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate.The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature.The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses.As a consequence,the sovra-temperature description is assumed to be an unknown variable of themodel and it is calculated in the sameway as the three displacements.The final systemis based on a set of coupled homogeneous differential relations of second order in the thickness coordinate.This system is reduced in a first order differential relation system by redoubling the number of unknowns.Therefore,the exponential matrix methodology is applied to calculate the solution.The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components.After an appropriate preliminary validation,new benchmarks are discussed for several thickness ratios,geometrical data,lamination sequences,materials and sovra-temperature values imposed at the outer faces.Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation.Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

The Hyperbolic Two Temperature Semiconducting Thermoelastic Waves by Laser Pulses

A novel model of a hyperbolic two-temperature theory is investigated to study the propagation the thermoelastic waves on semiconductor materials.The governing equations are studied during the photo-excitation processes in the context of the photothermal theory.The outer surface of o semiconductor medium is illuminated by a laser pulse.The generalized photo-thermoelasticity theory in two dimensions(2D)deformation is used in many models(Lord–Shulman(LS),Green–Lindsay(GL)and the classical dynamical coupled theory(CD)).The combinations processes between the hyperbolic two-temperature theory and photo-thermoelasticity theory under the effect of laser pulses are obtained analytically.The harmonic wave technique is used to obtain the exact solutions of the main physical fields under investigation.The mechanical,thermal and recombination plasma loads are applied at the free surface of the medium to obtain the complete solutions of the basic physical fields.Some comparisons are made between the three thermoelastcity theories under the electrical effect of thermoelectric coupling parameter.The influence of hyperbolic two-temperature,two-temperature and one temperature parameters on the distributions of wave propagation of physical fields for semiconductor silicon(Si)medium is shown graphically and discussed.

Design optimization of cast Cu-Al-Be-B alloys for high damping capacity

This paper investigated high-damping Cu-Al-Be-B cast alloys using metallographic analysis, X-ray diffraction (XRD) and electrical resistance measurements for transformation temperatures. The results showed that beryllium can stabilize β phase, resulting in a thermo-elastic martensite microstructure leading to high-damping capacity in cast Cu-Al-Be-B alloys. Trace additions of boron to Cu-Al-Be alloys can significantly refine the grains, providing high strength and ductility to the alloys. A factorial design of experiment method was used to optimize the composition and properties of cast Cu-Al-Be-B alloys. The optimal microstructure for thermo-elastic martensite can be obtained by adjusting the amounts of aluminum and beryllium to eutectoid or pseudo-eutectoid compositions. An optimized cast Cu-Al-Be-B alloy was developed to provide excellent mechanical properties, tensile strength σ_b=767MPa, elongation δ=7.62%, and damping capacity S. D. C=18.70%.

Stress analysis of thermally affected rotating nanoshafts with varying material properties

Based on the surface elasticity theory of GurtinMurdoch, thermo-elastic fields within rotating nanoshafts with varying material properties subjected to a thermal field are explicitly examined. Accounting for the surface energy effect, the nonclassical boundary conditions are enforced in the cases of fixed-free and free-free conditions. The effects of variation of material properties, temperature of the environment, angular velocity, and radius of the outer radius on the radial displacement, hoop and radial stresses are investigated. In all performed studies, the role of the surface effect on the thermo-elastic field of the nanostructure is methodically discussed.

3D thermally induced analysis of annular plates of functionally graded materials

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.

Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads

An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated,based on the two-dimensional(2-D)thermo-elasticity theory.Firstly,the beam was divided into a series of layers with uniform material properties along the interfaces of the beam.The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load.Secondly,the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer.Thirdly,based on the interfacial continuity conditions between adjacent layers,the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method.The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces.The convergence of the present solutions was checked.The comparative study of the present solutions with the Timoshenko’s solutions and the finite element(FE)solutions was carried out.The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.

Asymptotic and numerical study of a surface breaking crack subject to a transient thermal loading

An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.

Elasticity solution of laminated beams subjected to thermo-loads

According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.