Numerical analysis of the damage mechanics variable and vibration of a viscothermoelastic microbeam with variable thermal conductivity

In the present paper, the analysis for thermoelastic homogeneous isotropic microbeams has been constructed. A generalized viscothermoelasticity theory of one relaxation time with variable thermal conductivity in the context of damage mechanics definition has been applied based on simply supported conditions for aspect ratios. Laplace transform has been applied for the governing differential equations, and its inverse has been carried out by using the Tzou method. Microbeam of silicon nitride has been considered when it is subjected to ramp-type heating and simply supported. The results have been illustrated in figures to stand on the impacts of the viscothermoelastic parameter, the thermal conductivity parameter, the value of the beam thickness, and the ramp-type heating parameter. The influences of the mentioned parameters are significant on all the studied functions, and the ramp-type heating parameter plays a vital role in thermodynamically damping of the energy which has been generated on the beam

Exact thermoelastic analysis of a thick cylindrical functionally graded material shell under unsteady heating using first order shear deformation theory

In this article, a new analytical formulation is presented for axisymmetric thick-walled FGM cylinder with power-law variation in mechanical and thermal properties under transient heating using first order shear deformation theory. Equilibrium equations are derived by virtual work principles and energy method. The unsteady heat conduction equation is solved using the method of separation of variables, generalized Bessel functions and an Eigen-function method. Validation of the analytical solutions is conducted with a finite element method (FEM). The effects of time on stress and displacement distribution are studied in detail. The numerical values used in this study are selected based on earlier studies. The influence of effect of transient heat transfer on heterogeneous thick-walled cylinder elasticity is clearly demonstrated. In particular the significant influence of time and heterogenous constant on radial displacement, hoop stress and temperature distributions is computed. The study is relevant to rocket chamber thermo-mechanics, propulsion duct thermophysical design, industrial thermal storage systems etc

Photothermal excitation in non-local semiconductor materials with variable moisture thermal conductivity according to moisture diffusivity

In this work, a new model is described for the case of interference between thermal, plasma and elastic waves in a non-local excited semiconductor medium. The governing equations have been put under the influence of moisture diffusion in one dimension (1D) when the moisture thermal conductivity of the non-local medium is taken in variable form. Linear transformations were used to describe the dimensionless model. The photo-thermoelasticity theory according to moisture diffusivity was applied to describe the governing equations using Laplace transforms to obtain analytical solutions. In the time domain, complete solutions are obtained linearly when the conditions are applied (thermal ramp type and non-Gaussian plasma shock) to the surface through numerical methods of inverse Laplace transforms. Numerical simulation is used to display the basic physical quantities under study graphically. The current research has yielded several specific examples of great significance. Many comparisons are made under the influence of fundamental physical variables such as relaxation times, variable thermal conductivity, non-local parameters, and reference moisture parameters through graphing and describing them theoretically

Solution of Coupled Thermoelasticity Problem in Rotating Disks

The main purpose of this dissertation is to study coupled thermoelastic behaviors in disks subjected to thermal shock loads based on the generalized and classic theories of coupled thermoelasticity. To this end, this research has been carried out in two stages. In the first stage, thermoelasticity problems in an axisymmetric rotating disk with constant thickness made of a homogeneous isotropic material are analytically solved and closed-form formulations are presented for temperature and displacement fields. Since, the analytical solution is not always feasible, the finite element (FE) method can be employed for more sophisticated coupled thermoelasticity problems. Accordingly, in the second stage of the research, a novel refined 1D finite element approach with 3D-like accuracies are developed for theories of coupled thermoelasticity. Then, the developed FE models are applied for a 3D solution of the dynamic generalized coupled thermoelasticity problem in disks. Use of the reduced models with low computational costs may be of interest in a laborious time history analysis of the dynamic problems. The obtained analytical and numerical solutions are in good agreement with the results available in the literature. It is further shown that the proposed analytical and FE methods are quite efficient with very high rate of convergence

Advances in Multiscale and Multifield Solid Material Interfaces

Interfaces play an essential role in determining the mechanical properties and the structural integrity of a wide variety of technological materials. As new manufacturing methods become available, interface engineering and architecture at multiscale length levels in multi-physics materials open up to applications with high innovation potential. This Special Issue is dedicated to recent advances in fundamental and applications of solid material interfaces

Free vibration solution of thick plate by using three-dimensional coupled thermoelastic theory

This paper reports on the free vibration solution of a thick plate by using three dimensional coupled thermoelastic theory. Many previously works reveal that the mechanical and thermal are coupled together, which mean that the deformation of the solid will produce temperature variation inside the solid. First, based on the three dimensional coupled thermoelastic theory, the governing equations of the thick rectangular plate for free vibration analysis are derived. Unlike the traditional first order or third order shear deformation theory with which the deformations along the thick direction are described by the deformations of the middle surface, a new form which use functions to describe the deformations along plate thick direction (the z direction) is presented in this paper. Galerkin method and Laplace transform are applied to convert the governing equations into a series of first order ordinary differential equations as well as the boundary conditions to obtain the closed solution of the coupled thermoelastic rectangular plate. The Newton iterative method is applied to solve the eigenfunction. Finally, a thick plate with four edges simply supported has been investigated by using the proposed method. Eigensolutions and the damping effects of the plate with thermoelastic coupling are investigated by numerical example