Temperature-dependent Material Properties Research Articles

Free vibration behaviour of bio-inspired helicoidal laminated composite panels of revolution under thermal conditions: Multi-output machine learning approach

The present work aims to study the free vibration behaviour of bio-inspired helicoidal laminated composite spherical, toroid, and conical shell panels using a single-output Support Vector Machine (SVM) algorithm trained in the chassis of parabolic shear deformation theory under thermal conditions. Different helicoidal lamination schemes are adopted, such as Fibonacci, semi-circular, exponential, recursive, and linear helicoidal schemes. Temperature-dependent material properties are adopted. The effect of the geometry of the shell, temperature, and lamination scheme on the free vibration behaviour of spherical, toroid, and conical shell panels is studied. Also, the mode shapes are obtained using different multi-output SVM surrogate in which the displacements are obtained at different locations and are predicted to obtain the fundamental mode shape. The trained surrogate model can predict the values of fundamental frequency and mode shapes much faster than the parabolic shear deformation theory.

Computational analysis of wildland fire resistance for transmission line tower

Finite element (FE) analysis of the transmission towers under a fire event and the accompanying wind is presented. Several key aspects (including temperature-dependent non-linear material properties, geometric non-linearity, member eccentricity due to the single-leg bolted connection, and the temperature-dependent connection behaviour in both the axial and the rotational directions) are considered. A quasi-static analysis is also employed in the FE model using the explicit solver available in Abaqus. The member temperature variation during a realistic fire event is derived analytically based on the fire intensity and the resultant vertical gas temperature distribution so that the effect of the realistic wildland fire can be input as a member temperature profile. First, fire design guidance in terms of the most critical heating and wind pattern, as well as the effect of fire-affected heights are provided based on the case study results. Then, further fire analysis is carried out to investigate the most critical fire scenario and to evaluate the vulnerability of the tower during a realistic fire event. Lastly, an evaluation of a commonly used spray-on thermal insulation and its effectiveness in reducing the member temperature and preserving ultimate strength during a catastrophic wildland fire event are presented. The FE simulations revealed that a 45-degree wind associated with partial side heating leads to a more critical degradation of the overall strength, whereas the effect of fire height is less obvious. In terms of the fire scenario, a longer fire duration associated with a slower wind is more critical for the fire resistance/rating.

Energy-based damage assessment method for masonry walls under seismic and fire loads

The evaluation of the out-of-plane (OOP) behavior for infilled walls is a critical aspect of regional seismic and fire resilience assessment. This study presents a detailed finite element (FE) model that comprehensively captures the seismic and fire behaviors of masonry walls. The FE model incorporates key factors governing the thermo-mechanical behavior of masonry walls, including temperature-dependent material properties, nonlinearities in geometry and material, block cracking and crushing, and mortar damage. Then, an energy-based damage criterion is proposed based on the principle of energy conservation, leveraging the combined mixed fracture energy and internal energy of elements. In addition, this study defines the damage levels of masonry walls under OOP loading and fire and determines corresponding damage indices using the proposed energy-based damage criterion. This criterion is further compared with a stiffness-based damage criterion. Finally, the proposed damage assessment method is employed to evaluate the damage evolution of infilled walls under seismic, fire and post-earthquake fire scenarios, and to conduct a fragility analysis. The results demonstrate a high degree of agreement between the predicted and measured damage states of masonry walls under seismic and fire loads. More severe seismic damage does not always result in diminished fire resilience. Evaluating post-earthquake fire damage requires considering the impact of displacement directions caused by earthquakes and fires.

A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields

The flexible rotors within aero-engines operate in complex thermal environments, where temperature influences both the vibration frequency and amplitude. This study establishes a simple thermal flexible rotor dynamics model to rapidly and precisely predict thermo-elastic coupling vibration characteristics within a non-uniform temperature field. The thermal potential energy of the thermal rotor element is derived for any temperature field, and the motion equation is obtained using the Euler-Lagrange equation. Specifically, the generalized vector of an arbitrary point and cross-sectional non-uniform thermal stress of the thermal rotor element are considered in the thermal potential energy. The model's frequency error is <1 % under identical boundary conditions. Numerical findings indicate that thermal stress, temperature-dependent material properties, and the coupling effect collectively reduce the natural frequency (NF), with thermal stress having a more pronounced impact under axial constraint. Additionally, thermal stress and material decrease the amplitude across a broad range of rotation speeds, contrasting with thermal bending. This model will play a key role in the iterative calculation of thermo-elastic coupling vibration control due to its accuracy and simplicity.

A study on solid-shell finite element formulations applied to nonlinear thermoelastic analysis of thin-walled structures

The solid-shell elements have shown great advantages in three-dimensional (3D) finite element (FE) simulation of thin-walled structures. To overcome the numerical lockings for 3D element with a large span-thickness ratio, the assumed natural strain (ANS) method combined by either the hybrid stress (HS) or enhanced assumed strain (EAS) formulations are commonly used. In this work, two types of finite element formulations of the solid-shell elements are developed for nonlinear thermoelastic analysis of thin-walled structures, which are termed as the “ANS+HS” and “ANS+EAS” formulations. Accordingly, two eight-node solid-shell elements (CSSH8 and CSSE8) are developed based on the “ANS+HS” and “ANS+EAS” formulations, respectively. The Green–Lagrange displacement–strain relation is applied to involve the geometrical nonlinearities, and both the thermal expansion and temperature-dependent material properties are considered. Nonlinear thermoelastic equilibrium equations are constructed in the framework of the two types of finite element formulations using the Hellinger–Reissner and conventional variational principles, respectively. The proposed method can easily realize three different coupling analyses for thermal–mechanical loads by modifying the parameters of nonlinear thermoelastic equilibrium equations. Numerical examples demonstrate that the proposed method using CSSH8 and CSSE8 elements traces the nonlinear thermoelastic response of the isogrid stiffened panel as accurately as the shell, solid-shell, and solid elements of ABAQUS. Furthermore, the path-following capability of the proposed method using the CSSH8 with “ANS+HS” formulation is slightly superior to that using the CSSE8 with “ANS+EAS” formulation, but both better than ABAQUS.

Asymptotic solutions for heat transfer and stresses in functionally graded porous sandwich pipes subjected to nonuniform pressures and thermal loads

In this work, thermomechanical behaviors of temperature-dependent (TD) functionally graded porous (FGP) sandwich pipes subjected to nonuniform pressures and thermal loads are studied. Because the material properties are variable across the wall of the pipe, seeking exact solutions for the pipe is almost impossible. We use a slice model where the pipe is partitioned into plenty of annular slices and each slice is assumed to have uniform material properties. First, the nonlinear heat transfer along the pipe wall thickness is obtained by introducing an iterative procedure. Then, by using the Fourier series, the mechanical problem is decomposed into axisymmetric and nonaxisymmetric parts. Both the parts can be treated by the state space method and transfer matrix method, and then the superposition principle is used to obtain the displacement and stress distributions. The model results are in good consistency with those obtained from the numerical simulation and those reported in the literature. Finally, an FGP sandwich pipe is considered to discuss the effects of the temperature dependence of material properties (TDMP), power-law index, porosity, and pressure distribution on its thermomechanical behaviors.

Lateral-Torsional Failure and DSM Design of CFS Lipped Channel Beams at Room and Elevated Temperatures

About a decade ago, in-depth investigations on the behaviour of cold-formed steel (CFS) single-span simply supported lipped channel beams failing in lateral-torsional modes at both room and elevated temperatures were reported at QUT (Queensland Technical University). They revealed a significant underestimation of the lateral-torsional (LT) failure moments by the Direct Strength Method (DSM) global design curve at room temperature, then codified in the Australian/New Zealand and North American specifications. In order to remedy this situation, these authors proposed two novel DSM-based beam strength curve sets, which were found to substantially improve the LT failure moment prediction quality, both at room and elevated temperatures. This work aims at extending the scope of the above investigations, by analysing a visibly larger set of CFS lipped channel beams at elevated temperatures (up to 800 °C), exhibiting (i) various cross-section dimensions and yield stresses, selected to cover wider LT slenderness ranges, (ii) two end support conditions, differing only in the end cross-section wall displacement/rotation and warping restraints (either fully free or fully prevented), and (iii) temperature-dependent steel material properties according with the model prescribed in Part 1-2 of Eurocode 3. The results presented and discussed consist of beam LT post-buckling equilibrium paths and failure moments, obtained through Abaqus shell finite element GMNIA that include critical-mode (LT) initial geometrical imperfections. Lastly, the numerical failure moment data obtained in this work and reported in the literature are used to develop and propose a new unified set of DSM-based strength curves capable of adequately handling beam LT failures at room or elevated temperatures. Since it is shown that the proposed strength curve set provides a quite good LT failure moment prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS beams failing in LT modes at room and elevated temperatures.

Analytical prediction of temperature effects on Lamb wave response in smart plates and its experimental verification

Abstract This article examines the effectiveness of a recently developed theoretical model for the generation and sensing of Lamb waves in thin plates with surface-bonded piezoelectric transducers in predicting temperature effects on Lamb waves and their time reversibility. In particular, the analytical model provides a closed-form solution, which incorporates both the shear-lag effect of the bonding layer and the system inertia in transducer-plate interaction modeling. Temperature-dependent material properties and thermal expansion of the system constituents are considered to predict the Lamb wave signal under a thermal environment. The accuracy of the theoretical prediction is assessed in comparison with experimental results obtained using an aluminum plate with adhesively bonded lead zirconate titanate transducers to its surface at different system temperatures ranging from 20°C to 75°C. Comparison is also made with experimental data and analytical solutions presented earlier without considering the inertia effect. The study reveals that the current solution accurately predicts the change in Lamb wave signal due to temperature variation, including the frequency dependency of the peak amplitude change with temperature rise. However, the theoretical model fails to predict the experimental trends when the inertia terms are neglected. The current model is also used to study the contributions of individual system parameters to the overall temperature effect on the time reversibility of Lamb waves and its dependence on the excitation frequency.

Free vibration of spinning stepped functionally graded circular cylindrical shells in a thermal environment

This paper investigates the free vibration of spinning stepped functionally graded material (FGM) circular cylindrical shells with general boundary conditions in a thermal environment. The artificial spring is implemented to simulate the general boundary constraints. Temperature-dependent material properties change constantly along the thickness direction. The Donnell-Mushtari shell theory is applied to derive the energy functions of thin stepped circular cylindrical shells, where the effect of centrifugal force and Coriolis force is taken into account. The modified Fourier-Ritz method is utilized to derive the frequency equations of the spinning stepped FGM circular cylindrical shells. The influences of spring stiffness, power-law index, and temperature on the traveling wave frequencies are investigated. The influence of configuration on the forward wave frequency and critical speed of three stepped shells, including the one-end thickened, the two-end thickened, and the middle-thickened stepped shells, is discussed. For each configuration, design strategies for the stepped shells are proposed.

A novel meshless radial basis reproducing kernel particle approach for 3D thermo-mechanical analysis of mushy zone phase-change problems

This paper presents a three-dimensional thermo-elastoplastic computational model for the analysis of phase change problems involving the mushy zone. The model utilizes a novel meshless radial basis reproducing kernel particle approach, incorporating a high-order kernel that integrates Gaussian and cosine functions. An energy balance equation for the entire domain is formulated using the effective heat capacity method, based on the enthalpy formulation. The governing equations are discretized using the Galerkin weak form to compute thermal residual stresses, with essential boundary conditions enforced through the penalty method. Plastic deformation is characterized using the von Mises criterion with isotropic hardening, and the strain term resulting from temperature-dependent material properties is incorporated into the incremental solution process. Determination of the plastic strain increment is based on the Prandtl–Reuss flow rule. The accuracy and efficiency of the proposed meshless approach were rigorously evaluated through numerical examples encompassing two- and three-dimensional problems. The computational results were compared against available analytical and validated numerical solutions. This comprehensive assessment substantiated the robustness and precision of the developed technique. The case studies presented elucidate the capacity of the novel meshless model to effectively predict temperature distributions and residual stress fields within mushy zone phase change phenomena, accommodating both regular and irregular geometries under various boundary conditions. Notably, the model demonstrated consistent stability and high accuracy across the spectrum of simulated scenarios, thus underscoring its potential as a valuable tool for investigating complex phase change processes.

Elasticity solutions of clamped laminated arches with temperature-dependent material properties under thermo-mechanical loading

The mechanical behaviors of the clamped laminated arch with temperature-dependent material properties under the thermal and mechanical loadings are studied in this paper. An analytical method based on the theory of thermoelasticity is proposed for predicting the exact solutions of stresses and displacements in the arch with arbitrary thickness and layer numbers. The clamped support is equivalent to a simply support with a support reaction with the unit pulse function and the Dirac function. The space state method is utilized to establish the state equation by employing the displacements and stresses as the state variables. A slice model is introduced to simplify the coefficient matrix. Based on the continuities at the interfaces, the displacement and stress relationships between the internal and external surfaces of the laminated arch are derived with the transfer matrix method. Exact solutions for the displacements and stresses can be obtained according to the stress boundary conditions on the surfaces of the laminated arch. Finally, convergence and comparison studies demonstrate the excellent efficiency and accuracy of the present method. The influences of material dependency with temperature, thermal load, and thickness-to-radius ratio on the distributions of displacements and stresses are discussed in detail.

Integrating Numerical Simulation and Experimental Validation to Analyze Temperature Distribution in Friction Stir Welding of Dissimilar Aluminum Alloy

This study explores the temperature distribution in Aluminum alloys, specifically AA2024 T351 and AA6351 T6, during friction stir welding (FSW). Utilizing COMSOL Multiphysics software, the research investigates FSW at rotational speeds of 800, 1200, and 1600 rpm, while maintaining a constant welding speed (35 mm/min) and axial force (3 kN). The simulation incorporates temperature-dependent material properties. The findings reveal that the maximum temperature occurs at the upper part of the stir zone for both alloys. Experimental validation demonstrates excellent agreement with the simulated temperature distribution, reaffirming the accuracy of the COMSOL Multiphysics model.

A Meshless Method of Radial Basis Function-Finite Difference Approach to 3-Dimensional Numerical Simulation on Selective Laser Melting Process

Selective laser melting (SLM) is a rapidly evolving technology that requires extensive knowledge and management for broader industrial adoption due to the complexity of phenomena involved. The selection of parameters and numerical analysis for the SLM process are both costly and time-consuming. In this paper, a three-dimensional radial basis function-finite difference (RBF-FD) meshless model is introduced to accurately and efficiently simulate the molten pool size and temperature distribution during the SLM process for austenitic stainless steel (AISI 316L). Two different volumetric moving heat source models were presented, namely the ray-tracing method heat source model and the double-ellipsoidal shape heat source model. The temperature-dependent material properties and phase change process were also considered, based on experiments and effective models. Results of the model for the molten pool size were validated with those of the literature. The proposed approach can be used to predict the effect of different laser power and scan speed on the molten pool size and temperature gradient along the depth direction. The result reveals that the depth of the molten pool is more sensitive to laser power than scan speed. Under the same scan speed, a 22% change in laser power (45 ± 10 W) affects the maximum temperature proportionally by about 9%. The developed algorithm is computationally efficient and suitable for industrial applications.

Divertor heat load estimates on NSTX and DIII-D using new and open-source 2D inversion analysis code

A thermography inversion algorithm has been developed in the open-source Python-based computer code, HYPERION, to calculate the heat flux incident on plasma-facing components (PFCs) in axisymmetric tokamaks. The chosen mesh size at the surface significantly affects the calculated transient heat flux results. The calculated transient heat flux will exceed the real value when the mesh size tends to zero but will underestimate the real value when the mesh size is large. A criterion for determining the appropriate mesh size for the transient heat flux calculation will be discussed. The numerical scheme for HYPERION uses a 2D fully implicit finite-difference approach, allowing temperature-dependent thermal properties of PFC materials. The inversion algorithm is benchmarked against established heat flux calculation codes, TACO and THEODOR, based on thermography data from NSTX and DIII-D respectively. The primary benefits of HYPERION compared to TACO and THEODOR are that it is open-source and it allows for the optimization of mesh thickness along the substrate. The algorithm also accounts for the thermal properties of thin surface layers that characteristically form on PFCs due to plasma-material interactions. The agreement between HYPERION and THEODOR is excellent, as the percent difference between the codes is ∼5% on average in the case of the DIII-D data for moderate to high heat flux. Verification tests with TACO show slightly higher average percent differences of 8% and 12%. In using HYPERION to study filaments in heat flux, the initial results indicate that small ELMs filaments significantly broaden the divertor heat flux, and decrease divertor peak flux. Compared to the inter-ELM, the small ELM filaments decrease the divertor peak surface temperature. With intermittent divertor filaments, the divertor heat flux width is comparable with that found in L-mode.

Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

Thermal conductance of interfaces between titanium nitride and group IV semiconductors at high temperatures

Measuring the temperature dependence of material properties is a standard method for better understanding the microscopic origins for that property. Surprisingly, only a few experimental studies of thermal boundary conductance at high temperatures exist. This lack of high temperature data makes it difficult to evaluate competing theories for how inelastic processes contribute to thermal conductance. To address this, we report time domain thermoreflectance measurements of the thermal boundary conductance for TiN on diamond, silicon-carbide, silicon, and germanium between 120 and 1000 K. In all systems, the interface conductance increases monotonically without stagnating at higher temperatures. For TiN/SiC interfaces, G ranges from 330 to 1000 MW/m2-K, with a room temperature conductance of 750 MW/m2-K. The interface conductance for TiN/diamond ranges from 140 to 950 MW/m2-K. Notably, for all four interfacial systems, the conductance continues to increase with temperature even after all phonon modes in the vibrationally soft material are thermally excited. This observation suggests that inelastic processes are significant contributors to the thermal conductance in all four interfacial systems, regardless of whether the materials forming the interface are vibrationally similar or dissimilar. Our study fills a notable gap in the literature for how interfacial conductance evolves at high temperatures and tests burgeoning theories for the role of inelastic processes in interfacial thermal transport.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Study on similarity criterion for fluid-thermal coupling responses of metal plate simultaneously exposed to laser irradiation and airflow

Similarity criterion considering the multifield coupling effect is essential for the scaled thermal test under both laser irradiation and airflow. This paper establishes the similarity criterion for the fluid-thermal coupling responses of metal plate simultaneously exposed to the laser irradiation and high-speed airflow by nondimensionalizing the governing equations. The main dimensionless parameters are obtained, and the scaling law when the temperature scaling factor is equal to 1, which means the temperature remains unchanged in the real and scaled model, is firstly established. Moreover, to broaden the applicability, the scaling law when the temperature scaling factor is not equal to 1 is further deduced, and the correction method based on numerical simulation is proposed to eliminate the error caused by the difference of temperature-dependent material properties in the real and scaled model. Numerical cases are conducted and compared to verify the established scaling laws. Results show that errors of the predicted fluid-thermal responses between the real and scaled model are less than 1 %, affirming the reliability of the scaling laws.

A novel hybrid-stress method using an eight-node solid-shell element for nonlinear thermoelastic analysis of composite laminated thin-walled structures

Composite laminated thin-walled structures, widely used in high-speed aircrafts, undergo a complex thermal–mechanical coupling environment. Geometrical nonlinearities with a thermal effect bring significant challenge to finite element analysis of structures. In this paper, a novel hybrid-stress method based on the solid-shell element is proposed for nonlinear thermoelastic analysis. An eight-node solid-shell element (CSSH8) is developed based on the assumed natural strain method and hybrid-stress formulations to overcome various locking problems and achieve an effective 3D simulation for structures with a large span-thickness ratio. The Green–Lagrange displacement-strain relation is selected to take the geometrical nonlinearities into account. The modified generalized laminate constitutive model is extended to consider both the thermal expansion and temperature-dependent material properties. A temperature variation along the laminate thickness can also be assumed in the constitutive model. Nonlinear thermoelastic equilibrium equations are derived using the Hellinger–Reissner variational principle, in which five different coupling cases for thermal–mechanical loads can be fully involved. Numerical examples demonstrate that the proposed method with CSSH8 element is insensitive to various distorted meshes and numerically robust to pass the buckling point; meanwhile large step sizes can be achieved in the path-following nonlinear thermoelastic analysis.