Transient Thermoelastic Problem Research Articles

Variational temporal convolutional networks for I-FENN thermoelasticity

Machine learning (ML) has been used to solve multiphysics problems like thermoelasticity through multi-layer perceptron (MLP) networks. However, MLPs have high computational costs and need to be trained for each prediction instance. To overcome these limitations, we introduced an integrated finite element neural network (I-FENN) framework to solve transient thermoelasticity problems in Abueidda and Mobasher (2024). This approach used a physics-informed temporal convolutional network (PI-TCN) within a finite element scheme for solving transient thermoelasticity problems. In this paper, we introduce an I-FENN framework using a new variational TCN model trained to minimize the thermoelastic variational form rather than the strong form of the energy balance. We mathematically prove that the I-FENN setup based on minimizing the variational form of transient thermoelasticity still leads to the same solution as the strong form. Introducing the variational form to the ML model brings the advantages of lower requirement for the differentiability of the basis function and, thus, lower memory requirement and higher computational efficiency. Also, it automatically satisfies zero Neumann boundary conditions, thus reducing the complexity of the loss function. The formulation based on the variational form complies with thermodynamic requirements. The proposed loss function reduces the difference between predicted and target data while minimizing the variational form of thermoelasticity equations, combining the benefits of both data-driven and variational methods. In addition, this study uses finite element shape functions for spatial gradient calculations and compares their performance against automatic differentiation. Our results reveal that models leveraging shape functions exhibit higher accuracy in capturing the behavior of the thermoelasticity problem and faster convergence. Adding the variational term and using shape functions for gradient calculations ensure better adherence to the underlying physics. We demonstrate the capabilities of this I-FENN framework through multiple numerical examples. Additionally, we discuss the convergence of the proposed variational TCN model and the impact of hyperparameters on its performance. The proposed approach offers a well-founded and flexible platform for solving fully coupled thermoelasticity problems while retaining computational efficiency, where the efficiency scales proportional to the model size.

Complex-geometry simulations of transient thermoelasticity with the Shifted Boundary Method

We propose a formulation of the Shifted Boundary Method, an immersed/embedded/unfitted boundary method, for transient thermo-elasticity problems characterized by very complex geometries. With an extensive set of numerical experiments, we demonstrate that the SBM performs accurately and robustly, even when the geometry is represented in stereolithography format (STL, or Standard Tessellation Language) with gaps and overlaps. We conclude with a thermoelastic analysis of an advanced fluid tank design, obtained with topology optimization methodologies and a candidate for additive manufacturing processes. This final example represents what is foreseen as the typical application of the SBM in the context of the simulation of additively manufactured components.

Transient Thermoelastic Analysis of Rectangular Plates with Time-Dependent Convection and Radiation Boundaries

Approximate analytical solutions are presented for the transient thermoelastic problem of rectangular plates with time-dependent convection and radiation boundaries. To include the nonlinear radiation boundary, the whole heating process is divided into several time steps, and a linearized approximation is used to simplify the radiation term for each step. The one-dimensional transient temperature along the thickness direction is solved using the technique of the separation of variables. The displacement and stress solutions are obtained by applying the state-space method to the three-dimensional thermoelasticity equations. The accuracy of the present solutions is demonstrated by comparison with the reported results in the open literature and the finite element solutions. In the numerical examples, two kinds of thermal boundaries, namely, time-independent convection boundaries and time-dependent convection and radiation boundaries, are considered to show the availability of the present solutions.

Thermal and fracture analysis of collinear interface cracks in graded coating systems under ramp-type heating

Ceramic based thermal barrier coatings are extensively employed to shield critical engineering components from harsh temperature environments, where the typical Fourier's law may not be able to provide an accurate assessment of the physical process. This work adopts a more generalized heat conduction approach to reveal the thermal and fracture interaction mechanism of two collinear interface cracks in orthotropic functionally graded thermal coating systems by dual-phase-lag theory. The heating rate of the imposed thermal loading on the exterior bounding surface is modeled by ramp-type function, where the ramping period is comparable to the certain time spent for building the local thermal equilibrium within composites. The methods of Fourier transform and Laplace transform in conjunction with the singular integral equations are applied to solve the complex transient thermoelastic problem. Parametric investigations are conducted to investigate the impacts of ramping time, thermal lags, nonhomogeneous parameters, and crack spacing on the thermal and fracture characteristics. According to the maximum hoop stress criterion, higher fracture risk is discovered with the approaching of collinear interface cracks.

Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework

This paper considers a transient thermoelastic problem in an isotropic homogeneous elastic thin circular plate with clamped edges subjected to thermal load within the fractional-order theory framework. The prescribed ramp-type surface temperature is on the plate's top face, while the bottom face is kept at zero. The three-dimensional heat conduction equation is solved using a Laplace transformation and the classical solution method. The Gaver–Stehfest approach was used to invert Laplace domain outcomes. The thermal moment is derived based on temperature change, and its bending stresses are obtained using the resultant moment and resultant forces per unit length. The results are illustrated by numerical calculations considering the material to be an Aluminum-like medium, and corresponding graphs are plotted.

Geometric nonlinear transient analysis of mechanically and thermally shocked functionally graded shell panels

The present paper investigates the von-Karman geometrically nonlinear structural responses of ceramic-metal functionally graded shell panels under the effect of the cases of mechanical and thermal shocks on their ceramic-rich surface. The constituents in the FGM are temperature-dependent and are graded as per the recently proposed four-parameter power laws while their effective properties in the shells are obtained using the Mori-Tanaka homogenization scheme. The transient thermoelastic problem is solved by importing the temporally varying temperature distribution from the nonlinear 1D heat equation as thermal loads into the FE code developed for thin and moderately thick shells based on higher-order shear deformation theory. The nonlinearity in the heat equation is linearized using Picard method in each Crank-Nicholson time-step while the linearization step in the geometric nonlinear problem uses Newton-Raphson method in each Newmark time-step. The new results presented in the manuscript study the effect of geometric nonlinearity on the responses of FG shell panels and the effect of different parameters of four-parameter FG laws. It was observed that including geometric nonlinearity significantly affects the responses of the shell panel structures when the loading direction, either mechanical or thermal, along with the gradation direction is reversed.

Inverse transient thermoelastic problem with heat source in an annular disc

This article deals with formulating an inverse problem of heat conduction to analyse thermoelastic stress in a thick annular disc due to internal heat generation within the solid. The integral transformation techniques, Marchi-Zgrablich transform and finite MarchiFasulo integral transform, are employed in order to solve governing transient heat conduction equation, under stated thermal boundary conditions. The outcomes obtained from analytical solution are represented in the form of infinite series consisting Bessel’s functions. Numerical verification is done for a particular case of a thick annular disc made of aluminummetal and results are depicted graphically.

Investigation on the generalized thermoelastic-diffusive problem with variable properties in three different memory-dependent effect theories

The applicability of the generalized thermoelastic theories with integer-order derivative in solving anomalous or transient thermoelastic diffusion problems is questionable. Due to the feature of memory-dependence and heredity, the fractional-order derivative and the memory-dependent derivative are introduced to modify the generalized thermoelastic theories for extending their applicability. To demonstrate the features of such theories, the thermoelastic-diffusive dynamic response of an infinite elastic medium containing a spherical cavity with variable material properties is investigated in three different generalized theories with memory-dependent effect, which are incorporated in a unified form. Of them, two are based on fractional-order derivative and the other one is based on the memory-dependent derivative. The corresponding governing equations are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress, concentration and chemical potential under the three theories are obtained and illustrated graphically for comparing with those obtained from one of the integer-order theories. The effects of the fractional-order parameter, the time-delay factor, the variable thermal conductivity and diffusivity on the variations of the considered variables are considered and discussed in detail.

Analysis of transient uncoupled thermoelastic problems involving moving point heat sources using the method of fundamental solutions

The method of fundamental solutions (MFS) is very effective for analysis of problems with moving domain loads. In this work, the MFS is formulated for solution of two dimensional transient uncoupled thermoelastic problems involving moving point heat sources. At first, the time-dependent temperature field is obtained by solving the transient heat conduction equation involving a moving heat source term. Then, at each time point, the temperature field is used in the constitutive and equilibrium equations to determine the displacement field. The intensity and location of the point heat source can be arbitrary functions of time. The particular solutions for temperature and stress are described by simple and closed-form expressions and they are used without considering any internal points. Two numerical example problems are provided to demonstrate the efficiency of the presented formulation. The obtained numerical results show that the presented MFS is very efficient and useful. Unlike the finite element method, only a small number of collocation and source points are sufficient to achieve very accurate results in the proposed MFS.

Thermoelastic Behavior Inthin Hollow Cylinder using Internal Moving Heat Source

A hollow cylinder having cylindrical hole at the center has been examined under the temperature variation condition. This composition deals with study of temperature distribution in thin hollow cylinder and corresponding stresses. The author has worked to carry out the transient thermo elastic problem for evaluation of temperature distribution, displacement and thermal stresses of a thin hollow cylinder. The known non homogeneous boundary conditions are applied to obtain the solution of this problem. The integral transform technique yields the solution to the problem. The analysis contains an infinite series. The variation of said parameters observed and analyzed by using necessary graphs.

A meshfree method with dynamic node reconfiguration for analysis of thermo-elastic problems with moving concentrated heat sources

In this work, a novel approach for efficient analysis of transient thermo-elastic problems including a moving point heat source is presented. This approach is based on a meshfree method with dynamic reconfiguration of the nodal points. In order to accurately capture the large temperature gradients at the location of the concentrated heat source, a fine configuration of nodal points at this location is selected. In contrast, a coarser nodal arrangement is used in other parts of the problem domain. During the problem analysis, the fine nodal arrangement moves with the point heat source. Consequently, the meshfree methods are ideally suited to this approach. In the present work, the meshfree radial point interpolation method (RPIM) is adopted for the numerical analyses. Since the density of the nodal points varies in different parts of the domain, the background decomposition method (BDM) is used for efficient computation of the domain integrals. In the BDM, the density of the integration points conform to that of the nodal points and thus the computational effort is minimized. Some numerical examples are provided to assess the accuracy and usefulness of the proposed approach in computation of the temperature, displacement, and stress fields.

Transient Thermoelastic Problem of Annular Disc Due to Axisymmetric Heat Supply and Removal of Heat Supply

Transient Thermoelastic Problem of Annular Disc Due to Axisymmetric Heat Supply and Removal of Heat Supply

On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source

The present article attempts to investigate transient thermoelastic problem of a functionally graded thin rectangular plate with thermosensitive and spatial variable dependent material properties. All the material properties are assumed to be isotropic. Kirchhoff’s variable transformation is used to deal with the nonlinearity of the three dimensional heat conduction equation and that equation is solved by the integral transform method considering an instantaneous point heat source. The thermoelastic behavior of the rectangular plate is studied together with the thermal deflection and thermally induced resultant moments. Numerical computations are carried out for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.

Simulation of residual thermal stresses in high-porous fibrous silicon nitride ceramics

The residual thermal stresses induced in high-porous fibrous silicon nitride ceramics with fine reinforcement inclusions have been computed within numerical experiment. The computations have been performed employing a coupled transient linear thermoelastic problem. The initial state characterized by zero internal stresses is observed when the material is synthesized at high temperatures. Three-dimensional representative fragments of fibrous structures generated with stochastic algorithms accounting for the set microstructural parameters have been used for the simulation. The effect of the volume content and size of reinforcement as silicon carbide spherical inclusions on residual thermal stresses has been demonstrated. The simulations show that the residual stresses are commonly higher than the ultimate strength of the porous materials under study.

Fast solution methods of parameterized high-fidelity models

High-fidelity simulation based on solving partial differential equations has become an indispensable approach in innovative research of nuclear energy. However, due to the prohibitively high computation cost, it is yet unfeasible to run simulations on the whole reactor core level with all the physics resolved on fine meshes, especially in the analysis which need carry out many times of calculations. Model order reduction strategies are promising ways to achieve significant speedups by replacing the original large-scale model by a reduced order model of substantially smaller scale. Two effective model order reduction techniques, i.e., the reduced basis finite element method and the POD-Galerkin method, are studied and applied in the present study to solve the transient thermo-elastic problem and the fluid dynamics problem, respectively. For the former, the boundary conditions, the physical parameters and the body heat source are treated as parameters. The greedy-POD algorithm is applied to construct reduced basis space and the for the latter, the Reynolds number is treated as a parameter. The pure POD method is applied to construct the basis space. During on the online stage, three to five orders of computation speed up has been achieved by using the built reduced order models compared with that by the full order models while the accuracy of the results is well ensured. It is demonstrated that model order reduction techniques will be a practical way to deploy numerical reactors.

Analysis of transient plane thermal stresses in functionally graded orthotropic strip

This research is concerned with the transient plane thermoelastic problems in functionally graded orthotropic materials. The material properties such as the specific heat c, the density ρ, the thermal conductivities λx and λy, the coefficients of linear thermal expansion αx and αy, Young’s moduli Ex and Ey in x and y directions, respectively, are assumed to be functions of position (x). Laplace transform and separation of variables are used to analyze the temperature field in functionally graded orthotropic strips. The stress function is used for the plane thermoelastic problem in the functionally graded orthotropic materials. As a specific example, functionally graded orthotropic strip was analyzed. Numerical results are shown for the effects of orthotropy of material properties on temperature and thermal stresses. They show that the effects of orthotropy on temperature and thermal stresses are very large. The proposed analytical method is useful in the design of structures exposed to severe temperature environment. As a specific example, functionally graded orthotropic strip was analyzed.

Investigation of thermoelastic problem of multiple-disc friction clutches applying different thermal loads

The designers of friction clutch systems in vehicular applications should always take into account a number of essential criteria. The friction clutch should be able to transfer the torque from the driving shaft to the driven one within a short time and minimum amount of shocks and vibrations to make the engagement (disengagement) as gentle as possible. Furthermore, it is well known that high surface temperatures were noticed during the beginning of engagement period due to slipping between the contacting elements of the friction clutch system with ensuing heat generation. The transient thermoelastic problem of multi-disc systems has been deeply investigated by many scientists and researchers using numerical techniques such as finite element method. In this analysis, the influence of the sliding speed on the thermoelastic behavior when the initial heat generated is constant was studied. For this purpose an axisymmetric finite element models were developed and used in the simulation shown in the paper.

Thermoelastic Response Of A Thin Rectangular Plate Due To Heat Generation And Its Thermal Stresses

This paper is concerned with steady-state as well as transient thermoelastic problem in which we need to determine the temperature distribution, displacement function and thermal stresses of a thin rectangular plate when the boundary conditions are known. Integral transform techniques are used to obtain the solution of the problem.

Transient thermoelastic problem of a nonhomogeneous rectangular plate

ABSTRACTThis article deals with the determination of temperature distribution, displacement, and thermal stresses in a rectangular plate with inhomogeneous material properties. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law in y coordinate. The system of fundamental equations formulated has been solved by integral transform method. The effects of thermal and mechanical inhomogeneity on temperature and thermal stress distributions are examined. Numerical calculations are performed by taking into account the variation in inhomogeneous property of shear modulus of elasticity and depicted graphically.

Evaluation of the T-stress for cracks in functionally graded materials by the FEM

Using the quarter-point crack tip element, a simple formula is derived which provides a quick and expedient means to evaluate the elastic T-stress in the finite element method (FEM) fracture mechanics analysis of functionally graded materials (FGMs). The formula is derived by comparing the variation of displacements in the quarter-point element with the corresponding asymptotic expression for the displacement field in the vicinity of a crack-tip. The asymptotic fields in the crack-tip vicinity in a FGM with continuously varying material properties are the same as in a homogeneous one. The simplicity of the use of this formula for T-stress evaluation in FEM fracture mechanics analysis is demonstrated by its application to some transient elastodynamic and thermoelastic problems.