This study presents a coupled thermo-mechanical model to investigate the three-dimensional response of multilayer skin tissue under flat-top laser irradiation. The Pennes bioheat transfer equation is reformulated to derive an analytical solution for the three-dimensional temperature field using the method of separation of variables combined with Newton-Cotes quadrature. Based on the temperature distribution, the Timoshenko-Mindlin plate theory is applied to construct nonlinear governing equations for transversely isotropic skin composed of the epidermis, dermis, and subcutaneous layers. The mechanical response is solved using the finite difference method and Newmark integration. Parametric studies reveal that shorter-wavelength lasers lead to greater thermal stress and deformation, while increased blood perfusion mitigates surface stress due to enhanced heat dissipation. A smaller laser spot radius results in higher stress concentrations because of increased energy density. The model's predictions agree well with numerical simulations, confirming its capability to capture the evolution of internal stress in skin tissue under laser exposure. The analytical solution of the 3D temperature field provides a theoretical foundation for optimising laser parameters in thermal therapies.
In this article, we investigate the interfacial mechanical behavior of an axially graded one-dimensional hexagonal piezoelectric quasicrystal (PQC) thin film perfectly bonded to an elastic substrate with an adhesive interlayer. A theoretical model is developed to describe the film-substrate system under combined thermal and electrical loading. Using the potential theory and the Hankel transform, we derive the surface displacements on substrate. Under the perfect bonding condition, a governing integral-differential equation is established for the phonon interfacial shear stress, which is solved numerically with Chebyshev polynomial expansions. Detailed discussions are conducted to examine how the adhesive layer, film geometry, and material gradation affect the interfacial behavior. These findings provide useful guidance for the reliable design of PQC film-substrate systems.
This research delves into the effects of rotation and a refined Ohm's law on thermoelastic semiconductor materials that contain voids. The investigation specifically considers the influence of humidity diffusivity and microtemperature effects on these materials. The methodology employed involves the application of harmonic wave propagation techniques to simplify and solve the complex governing equations that describe the behavior of the semiconductor material. The results obtained from this analysis are then meticulously analyzed with a particular focus on the impact of rotation and the interplay between temperature gradient and electric current density. The analysis reveals that both rotation and plasma waves exert a considerable influence on the variations observed in the field quantities within the semiconductor material. This finding is consistent with and corroborates the results of previous research conducted in this area. For numerical simulation and to provide concrete examples, germanium is selected as the material of choice. This selection is motivated by germanium's widespread relevance and practical applications in various manufacturing processes across diverse industries.
In the ongoing study, by presenting a numerical solution approach, the thermal-induced dynamic response of porous axisymmetric cylindrical shell composed of functionally graded material (FGM) resting on an elastic substrate exposed to a rapid cooling shock is analyzed, which hasn't been studied hitherto. The cylindrical shell is composed of stainless steel (SUS 304) and low carbon-steel (AISI 1020), whose properties are distributed through the thickness based upon the power-law scheme. By employing the transient heat conduction in the one-dimensional Fourier conformation, the solution of the temperature equation is derived. With the aid of the available laboratory data, the temperature-dependent properties attributed to the FGM cylindrical shell are evaluated. The obtained nonlinear differential equations of motion are achieved incorporating the geometrical nonlinearity in the von K & aacute;rm & aacute;n form, the first order shear deformation shell formulations and the Hamilton's principle. In order to linearize and extract the dynamic response of the equations of motion and the temperature equation, Newton-Raphson, generalized differential quadrature (GDQ) methods and Newmark-beta integration pattern have been used. Validation of the results is done with reliable references and then by presenting a parametric examination, the influences of diverse factors including thermal load rapidity time, power-law index, elastic foundation parameters, and temperature differences on the oscillation feedback and stress distribution of the shell exposed to the rapid cooling shock are examined. It is concluded that through moving from the neutral surface to the top and bottom surfaces of the FGM cylindrical shell, the stress increases, and in a particular surface, the longitudinal stress is more than the circumferential stress.
In this research work, we considered the solid right circular cone with assumption of deformation is purely radial, whose lateral surface is traction free and subjected to a prescribed temperature distribution. The problem is examined under fractional order thermoelasticity theory. General solutions are obtained for set of boundary conditions by using Laplace transform technique and spherical Bessel functions. Bromwich inversion formula applied for the inversion Laplace transform process. The numerical results for temperature, displacement, and stress are calculated. These results illustrated graphically.
This paper investigates thermoelastic friction contact of functionally graded piezoelectric material (FGPM) coated half-plane under plane strain state, considering the influence of thermal convection term in heat conduction. The thermo-electro-elastic parameters of FGPM coatings vary exponentially with thickness. To solve the heat conduction equation analytically, a multilayer model is employed to simulate the exponential variation of the thermal diffusion coefficient. Using the transfer matrix method, superposition theorem, and Fourier integral transformation, the thermal-electric-elastic coupled frictional contact problem is transformed into the first and second Cauchy singular integral equations. These integral equations are then numerically discretized into an overdetermined system, and the optimal solution is obtained via the least squares method. The treatment method of thermal diffusion coefficient, the graded index, sliding velocity and friction coefficient on surface contact stress, temperature field, and electric displacement are discussed in detail. Numerical results show that reducing the friction coefficient, adjusting the graded index, and decreasing the sliding velocity can mitigate thermoelastic damage at the friction contact surface of piezoelectric materials.
'This work is concerned with finite-time blow-up in a coupled system of nonlinear wave equations with distributed delay, damping, and source terms-a phenomenon crucial for the thermo-mechanical stability of viscoelastic structures. By using the concavity method, we establish sufficient conditions for the nonexistence of global solutions, emphasizing the way in which thermal memory and delay kernels control the switch between energy dissipation and explosive instability. Numerical analysis in Abaqus/CAE reinforces the theoretical results and gives details on the influence of damping coefficients, delay kernels, and source exponents on the onset and rate of blow-up. Energy dissipation is treated as a thermal analogue. The most important comparison provides evidence that, while the undamped model undergoes unrealistic, unsustainable oscillations, the solution of the damped model enjoys progressive energy decay and realistic thermal dissipative behavior, thus underlining the role of damping in maintaining structural integrity. The excellent agreement of analytical and numerical results bridges the gap between mathematical theory and engineering simulation and allows for a deeper understanding of nonlinear thermo-dynamic instability in delayed wave systems.
This study develops a semi-analytical transient thermoelastic formulation for thin circular disks subjected to a radially shifted Gaussian surface heat flux, a profile highly representative of helical undulator conditions in synchrotron radiation, semiconductor processing, and laser systems. The axisymmetric transient temperature field is obtained through a Bessel eigenfunction expansion, while the in-plane stresses are evaluated under a quasi-static plane-stress assumption. In addition to characterizing transient fields with high fidelity, this formulation elucidates a physical mechanism inaccessible through local-temperature heuristics: in-plane stresses are fundamentally governed by the geometrically weighted spatial accumulation of thermal contributions. Consequently, stress extrema are systematically non-coincident with the temperature maximum and migrate inward as transient diffusion progresses. These results establish a universal and precise framework for optimizing the mechanical integrity of high-heat components in extreme thermal environments.
This work presents one-dimensional (1D) beam kinematic models with variable fidelity for analyzing coupled thermo-elastic problems in components of electronic interest. By employing the Carrera Unified Formulation (CUF), the proposed methodology enables accurate predictions of displacements, stresses, and temperature distributions in homogeneous isotropic structures subjected to complex heat sources. Transforming the complex three-dimensional (3D) problem into a computationally efficient one-dimensional (1D) framework allows for an optimal balance between accuracy and low computational cost. Classical thermo-elasticity theories are adopted to describe the physical behavior, and the formulation is applied to various flexible electronic components to demonstrate its versatility. Several numerical simulations, including convergence studies and validation against full 3D solid models, confirm the reliability and accuracy of the proposed technique. The results highlight the method's strong potential for guiding and accelerating the design and fabrication of next-generation flexible electronic devices (FEDs) in advanced engineering applications.
In this paper, a linear coupled model of Moore-Gibson-Thompson thermoporoelasticity is proposed, and the basic three-dimensional boundary value problems (BVPs) of steady vibrations are thoroughly investigated using the potential method (the boundary integral equation method). The governing equations for motion and steady vibrations within this model are presented. The coupled system of equations is formulated in terms of the displacement vector field and the changes of the following three mechanical values: the volume fraction of pores, the fluid pressure in the pore network, and the temperature of a porous material. Green's identities are established, and the uniqueness theorems for classical solutions of both internal and external BVPs are proved. The fundamental solution to the system of steady vibration equations is explicitly constructed. Subsequently, surface and volume potentials are introduced, and their essential properties are derived. Singular integral operators relevant to the BVPs are defined, and their symbolic determinants and indices are calculated. Finally, the existence theorems for classical solutions to these BVPs are proven using the potential method and the theory of two-dimensional singular integral equations.
Thermal residual stresses generated during the cooling of metal-ceramic composites produced by powder metallurgy remain a critical challenge for ensuring their reliable performance. The objective of this paper is to present and assess a methodology for constructing a finite element model for determining thermal residual stresses in metal-ceramic composites using the microstructure of the composite obtained from X-ray microcomputed tomography (micro-XCT) images for the mesh creation. The effectiveness of the micro-XCT-based finite element model is validated through a case study of residual stress behavior observed in an alumina-chromium composite that was consolidated by hot pressing. The influence of the choice of material models for the matrix and reinforcement and of the type of finite elements on the accuracy of the numerical simulations is analyzed. A comparison between the computed residual stresses and neutron diffraction measurements demonstrates a correlation validating the modeling approach. Of all the factors considered in the micro-XCT-based finite element simulations such as mesh quality, constitutive models for phase materials and the temperature dependence of the coefficients of thermal expansion mesh quality had the greatest impact on the accuracy of the numerical results in comparison to the residual stress measurement data obtained from neutron diffraction.
The present paper investigates the geometrically nonlinear thermo-elastic response of composite plates undergoing large rotations/displacements, with a focus on post-buckling and 3D thermal stresses. The governing equations are derived from the Principle of Virtual Displacement (PVD), whereby the full Green-Lagrange strain tensor is adopted in a total Lagrangian framework. The thermal load is described using a decoupled approach, and constant thermal distribution is considered. The employed plate elements are developed through the Carrera Unified Formulation (CUF) and their formal expression is independent of the theory approximation order. Thus, low-order equivalent-single-layer (ESL) to high-order layer-wise (LW) models can be implemented with ease. The nonlinear problem is solved through the Newton-Raphson procedure combined with the arc-length constraint. Plates with different geometries and materials are analyzed, and linear and nonlinear analyses are compared. From the results, it is shown that LW models are needed to describe the 3D thermal stresses in nonlinear equilibrium states, whereas ESL finite elements are enough to describe the global deformation state.
This study explores how nanobeams vibrate when Klein-Gordon nonlocal effects and a two-parameter Pasternak viscoelastic foundation are considered, along with thermal relaxation. Using the Laplace transform, the governing equations were solved, and the temperature, moment, and displacement responses were plotted. The results show how the Pasternak parameters, KG nonlocality, and different thermoelastic models shape the beam's behavior. Compared with earlier nonlocal and Bernoulli-Euler models, the predictions align well, highlighting the usefulness of this approach in mechanical and materials engineering.
Thermoelastic damping is a major source of energy dissipation in micro- and nano-scale structures. The Lord-Shulman heat conduction model, due to its hyperbolic nature, provides a more realistic description of heat transfer compared to the classical Fourier theory. In this study, thermoelastic damping in microbeams is investigated by incorporating small-scale effects. The Timoshenko beam theory is adopted, and the governing equations are derived using Hamilton's principle in conjunction with the Lord-Shulman heat conduction model. To account for size dependency, the nonlocal strain gradient theory (NSGT) is employed, resulting in a set of coupled equations for mechanical motion and heat conduction. These equations are solved simultaneously using the Galerkin method combined with the complex frequency approach. The effects of nonlocal and strain gradient parameters on thermoelastic damping are examined in detail. Additionally, the influence of beam thickness, boundary conditions, length-to-thickness ratio, and different mechanical and thermal models is systematically analyzed. The results of this study provide useful insights for the design and optimization of micro- and nanoscale devices where energy dissipation plays a critical role.
In the study of thermoelastic wave propagation in a rotating semiconductor material exposed to a laser beam and the effect of initial stress, this research addresses a significant gap in the study. The novelty of this work lies in the development of a new coupled dynamic model that incorporates mechanical and photothermal stresses along with temperature interactions in an elastic semiconductor medium. The resulting nondimensional coupled equations are solved using the eigenvalue approach and normal mode analysis methods. The displacement components, temperature distribution, and plasma distribution (carrier density phase) are displayed against various parameters using MATLAB. Graphical representations of the variations in displacement and stress fields illustrate the interaction between mechanical and thermal responses. These findings provide essential insights for the study of temperature, displacement, and stress, as well as for the design of sophisticated engineered materials for thermoelastic applications. The accuracy of our physical quantities is compared graphically with previous studies, demonstrating the significant influence of external factors on photothermal processes. This paper contributes to the analysis of thermoelastic problems involving rotation, initial stress, and laser pulse duration.
