GENERALIZED COUPLED THERMOELASTICITY OF DISKS BASED ON THE LORD–SHULMAN MODEL

A one-dimensional generalized thermoelasticity model of a disk based on the Lord–Shulman theory is presented. The dynamic thermoelastic response of the disk under axisymmetric thermal shock loading is studied. The effects of the relaxation time and coupling coefficient are studied. The Laplace transform method is used to transform the coupled governing equations into the space domain, where the Galerkin finite element method is employed to solve the resulting equations in the transformed domain. The dimensionless temperature, displacement, and stresses in the transformed domain are inverted to obtain the actual physical quantities using the numerical inversion of the Laplace transform method.     

THERMAL ELASTIC-PLASTIC STRESS ANALYSIS OF STEEL WOVEN REINFORCED ALUMINUM METAL–MATRIX COMPOSITE LAMINATED PLATES

In this study, an elastic-plastic stress analysis is carried out on symmetric cross-ply [0°/90°]₂ and angle-ply [30°/?30°]₂, [45°/?45°]₂, [60°/?60°]₂ steel woven reinforced aluminum metal–matrix laminated plates under thermal loads varying linearly along the thickness. Laminated composite plates are simply supported and subjected to linear temperature change through the thickness as T ₀ at the upper and lower surfaces and T at the middle plane, respectively. An analytical solution is performed for satisfying thermal elastic-plastic stress–strain relations and boundary conditions for small plastic deformations. The composite materials are assumed to be linearly hardening. The Tsai–Hill criterion is used as a yield criterion. Plastic and residual stress distributions along the thickness of the plates are obtained. Plastic and residual stress components, σ _x ) _p , (σ _y ) _p and (σ _x ) _r , (σ_y) _r , have some magnitude but (τ _xy ) _p and (τ _xy ) _r are zero for all stacking sequences. All the residual stress components are in static balance with respect to the middle plane of the laminates since they are symmetric in opposite signs. The magnitude of the residual stress components is the highest at the upper and lower surfaces.     

IMPORTANCE OF INERTIA TERM IN DYNAMIC CRACK PROBLEMS CONSIDERING LORD–SHULMAN THEORY OF THERMOELASTICITY

A numerical technique is presented for the accurate calculation of stress intensity factors as a function of time for generalized coupled thermoelastic problems. In this task, the effect of the inertia term is investigated, considering different theories of thermoelasticity, and its importance is shown.

A boundary element method using the Laplace transform in time domain is developed for the analysis of fracture mechanics; dynamic coupled thermoelasticity problems with relaxation time are considered in the two-dimensional finite domain. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. Actual physical quantities in the time domain are obtained using the numerical inversion of the Laplace transform method.

The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. The thermal dynamic stress intensity factor for mode I is evaluated using the J-integral method. The accuracy of the method is investigated through comparison of the results with the data available in literature.

The J integral, which represents the dynamic energy release rate for propagating cracks, contains a boundary integral and a domain integral. The boundary integral contains strain energy, tractions, and strains whereas the domain integral contains inertia and strains. The J-integral method allows these two terms to be calculated separately. In this way, the importance of each term may be investigated by considering different theories of dynamic thermoelasticity.     

HEAT TRANSFER OF SOLID–LIQUID PHASE-CHANGE MATERIAL SUSPENSIONS IN CIRCULAR PIPES: EFFECTS OF WALL CONDUCTION

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.     

COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE k–ϵ– –f MODEL

A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.