Nonlinear Thermal Analysis Research Articles

Non-Linear structural and thermal analysis of automotive brake disc

The disc brake is considered as one of the most significant part of the vehicle. It is used to decelerate the motion of the vehicle and stop it when necessary. When brakes are applied to stop the vehicle the brake pads come in contact with the brake disc which increases the temperature of the disc plate and is subjected to thermal stress. The main objective is to replace the currently used brake-pad material with a material that has enhanced properties and increases the life of the component. When sudden braking is applied forced stresses act on the disc brake and eventually there is a probability of the disc getting damaged. Thus, the static analysis is also taken into consideration which validates the ductility of the material. This work involves design and modelling of brake disc and studying its structural and thermal validated results. The modelling is done in Solidworks with specific dimensions and analysis is done using ANSYS Workbench. Grey cast iron and carbon ceramic are the materials taken into consideration. After validation it was found out that carbon ceramic disc brake yields better results than the other in structural and thermal aspects for same boundary and loading conditions.

Significance of fin tip temperature on the heat transfer rate and thermal efficiency of a convective-radiative rectangular fin with variable thermal conductivity

In this work, effect of fin tip temperature on the rate of heat transfer and thermal efficiency of a rectangular convective-radiative fin with temperature-dependent thermal conductivity is analyzed using differential transformation method. The results of the power series solutions are verified numerically, and very good agreements are established. Also, the symbolic solutions are used to examine the effects of the conductive-convective and nonlinear thermal conductivity parameters on the thermal performance of the passive device. It is found that when the nonlinear thermal conductivity parameter increases, the fin tip temperature increases. However, the temperature at the tip of the fin decreases as the conductive-convective parameter increases. The thermal efficiency of the fin increases as the fin tip temperature and nonlinear thermal conductivity parameters are augmented but an increase conductive-convective parameter causes the fin tip temperature and the thermal efficiency of the extended surface to reduce. An increase in the conductive-convective parameter causes decrease the temperature distribution and thermal efficiency in the passive device. However, the efficiency of the fin increases as the nonlinear thermal conductivity parameter increases. When nonlinear thermal conductivity and conductive-convective parameters increase, the rate of heat transfer at the fin base increases. The developed analytical solutions provide a good platform for the nonlinear thermal analysis of the fin and proper design of the extended surfaces in thermal systems.

Nonlinear thermal instability and vibration analysis of pre/post-buckled FG porous nanotubes using nonlocal strain gradient theory

Current research presents the nonlinear static/dynamic response of functionally graded (FG) porous nanotubes in the thermal pre- and post-buckling regimes. The case of temperature-dependent FG nanotubes with even distributed porosities subjected to uniform temperature rise is considered. The stability and vibration characteristics are analyzed for the uniformly heated nanotube surrounded by a nonlinear elastic foundation. The nonlinear equations of motion are derived using the Hamilton principle for the thermally pre/post-buckled nanotube in the framework of nonlocal strain gradient theory. The size-dependent governing equations are established based on the uncoupled thermoelasticity, the von Kármán assumption and the high-order shear deformation theory. The nonlinear governing equations are reduced for the nonlocal strain gradient-based model of nanotubes with immovable simply supported boundary conditions. The system of equations is solved for the nonlinear problems of free vibration and post-buckling of the heated tube using two-step perturbation technique and Galerkin procedure. The novel parametric examples are carried out to investigate the effect of nonlocal and length scale parameters, porosity distribution, functionally graded pattern, elastic foundations and geometrical parameters on the thermoelastic response of tubes. The obtained results highlight the importance of static/dynamic analysis of FG porous nanotubes in the thermal pre-buckling and post-buckling regimes.

Nonlinear thermal flutter analysis of variable angle tow composite curved panels in supersonic airflow

The advanced Automated Fibre Placement (AFP) technologies make the synthesis of Variable Angle Tow (VAT) composites possible, which provides an extended space for the design of lightweight structures. At the same time, the variable stiffness feature inherent in tow-steered composite panels also poses a huge challenge to solve the mechanical problems including the panel flutter problem. In this article, the nonlinear thermal flutter characteristics of an infinitely long VAT composite curved panel in supersonic airflow is investigated for the first time. The proposed panel model is based on the Donnell’s shallow shell theory and accounts for the von Kármán’s geometrical nonlinearity. The aerodynamic load induced by the supersonic airflow passing over the panel surface is constructed from the first-order piston theory, whilst the thermal load imposed on the curved panel follows the quasi-steady thermal stress theory. The aerothermoelastic equations of motion that govern the nonlinear thermal flutter problem are determined via Hamilton’s variational principle. The Galerkin’s method is applied to convert the partial differential governing equation with variable coefficients into a set of ordinary differential equations, and the resulting nonlinear equations dependent upon time are solved through the fourth order Runge–Kutta method. Several qualitative tools, including the time history, phase portrait, Poincaré map and bifurcation diagram, are employed to study the dynamic behaviours, and a variety of attractors, both regular and chaotic, are observed. The accuracy and effectiveness of the proposed Galerkin procedure are validated by comparing with those available in literature. Effects of height-rise parameter, temperature parameter and fibre orientation angle on the nonlinear flutter responses of VAT composite curved panels in thermal environments are discussed in details.

Nonlinear Thermal Analysis of AlGaN/GaN HEMTs With Temperature-Dependent Parameters

In this article, an efficient numerical algorithm is proposed to capture the thermal profile of AlGaN/GaN high electron mobility transistors (HEMTs) with nonlinear electrothermal coupling effects. The finite element method is employed to solve the steady heat conduction equation with different kinds of boundary conditions. To accurately evaluate the temperature distribution of AlGaN/GaN HEMTs, the temperature-dependent properties of both thermal conductivity and heat source are taken into consideration. In order to accelerate the convergence in simulation, the Anderson acceleration (AA) scheme is utilized to solve the nonlinear coupling problems. Numerical examples demonstrate the high accuracy and excellent convergence of the proposed method for nonlinear thermal analysis of AlGaN/GaN HEMTs.

Nonlinear thermal analysis of multilayered composite and FGM plates with temperature-dependent properties based on an asymptotic numerical method

Nonlinear thermal analysis of multilayered composite and FGM plates with temperature-dependent properties based on an asymptotic numerical method

Effects of the structural strength of fire protection insulation systems in offshore installations

Mineral wool is an insulation material commonly used in passive fire protection (PFP) systems on offshore installations. Insulation materials have only been considered functional materials for thermal analysis in the conventional offshore PFP system design method. Hence, the structural performance of insulation has yet to be considered in the design of PFP systems. However, the structural elements of offshore PFP systems are often designed with excessive dimensions to satisfy structural requirements under external loads such as wind, fire and explosive pressure. To verify the structural contribution of insulation material, it was considered a structural material in this study. A series of material tensile tests was undertaken with two types of mineral wool at room temperature and at elevated temperatures for fire conditions. The mechanical properties were then verified with modified methods, and a database was constructed for application in a series of nonlinear structural and thermal finite-element analyses of an offshore bulkhead-type PFP system. Numerical analyses were performed with a conventional model without insulation and with a new suggested model with insulation. These analyses showed the structural contribution of the insulation in the structural behaviour of the PFP panel. The results suggest the need to consider the structural strength of the insulation material in PFP systems during the structural design step for offshore installations.

Investigation of thermal preloading and porosity effects on the nonlocal nonlinear instability of FG nanobeams with geometrical imperfection

The aim of the present research is twofold. The first is to present a study on nonlinear thermo-mechanical bending and thermal postbuckling analysis of functionally graded (FG) porous perfect/imperfect nanobeam according to the nonlocal elasticity theory. The second, concurrent aim is to address the snap-through phenomenon in the thermally preloaded graded porous nanobeams due to lateral mechanical load. Two types of thermal loading including, uniform temperature rise and heat conduction through the thickness as well as two cases of porosity distribution, including uniform and uneven, are considered. Geometrically imperfect FG porous nanobeam with four different types of immovable boundary conditions is also taken into account. Thermo-mechanical material properties of the porous nanobeam are assumed to be position-dependent according to the modified rule of mixture. The nonlinear equilibrium equations are constructed using the Euler–Bernoulli beam model and von-Kármán type of geometrical nonlinearity. Chebyshev polynomial based Ritz method is utilized into the principle of virtual displacement to obtain the matrix representation of the nonlocal governing equations. Two different strategies, including the Newton–Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling curves of the graded nanobeam. Afterwards, to capture the snapping behavior and trace the path beyond the limit loads of the thermally preloaded nanobeam, the cylindrical arch-length technique is adopted. Numerical results are provided to explore the effect of different parameters such as the power-law index, nonlocal parameter, boundary conditions, porosity distribution, thermal loading, and imperfection amplitude on the nonlinear thermo-mechanical bending and instability of the FG nanobeam.

Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory

In the present study, the nonlinear thermal buckling, postbuckling, and snap-through phenomenon of higher-order shear deformable tapered bidirectional functionally graded (BDFG) microbeams are comprehensively investigated under different types of thermal loading, for the first time. The thermomechanical properties of the BDFG microbeam are assumed to be functions of temperature, axial, and thickness directions. Reddy’s parabolic shear deformation beam theory with the von Karman nonlinearity is employed to derive the variable coefficient governing nonlinear differential equations on the basis the physical neutral surface concept. Size-dependent effect is captured in the formulation employing the modified couple stress theory. The generalized differential quadrature method (GDQM) is used to discretize the motion equations considering different boundary conditions. The resulting system of nonlinear algebraic equations is solved iteratively using Newton’s method. Theoretical analysis and numerical results indicate that, depending on the shear deformation beam theory, boundary conditions, and the type of thermal load, the response of the BDFG microbeam may be of the bifurcation or snap-through buckling type of instability. Numerical parametric studies are conducted to explore the influences of thermal load type, material property gradient indexes, boundary conditions, material temperature dependency, taperness ratio, and microstructural length scale on critical thermal buckling load, thermal postbuckling, and equilibrium paths of the BDFG microbeam.

Nonlinear static and dynamic thermal buckling analysis of imperfect multilayer FG cylindrical shells with an FG porous core resting on nonlinear elastic foundation

In this article, a semi-analytical and analytical method for the nonlinear static and dynamic thermal buckling behavior of imperfect multilayer FG cylindrical shells with an FG porous core in the thermal environment is investigated. The structure is embedded within a generalized nonlinear elastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a nonlinear cubic stiffness. Two types of multilayer FG cylindrical shells with an FG porosity core distribution consist of a uniform porosity distribution and a non-uniform porosity distribution core are considered. Using the Galerkin method with regard to the von Kármán equations, the discretized motion equation is obtained. The fourth-order Runge-Kutta method is utilized to obtain the nonlinear dynamic thermal buckling responses. The effects of various geometrical characteristics, material parameters, and elastic foundation coefficients are investigated on the nonlinear static thermal buckling and dynamic thermal buckling behavior of the multilayer FG system with an FG porous core. The results show that the various types of porosity core, imperfection and the elastic foundation parameters have strongly effect on the thermal buckling behaviors of the multilayer FG cylindrical shells with an FG porous core.

Application of transient nonlinear thermal analysis on quenching of hot die steel

Hot die steels contact with high temperature metals, and possess well thermal conductivity, wear resistance and red hardness. The carbon content should be controlled in the range of 0.3wt.% to 0.6wt.%, and added alloy elements to improve hardenability. The complex composition of the alloy affects its thermal and physical properties. For billets with large volume, it is difficult to measure the temperature of all parts. Through numerical simulation, the temperature field distribution in quenching process of hollow steel pipe with a length of 7 m is obtained by adopting the transient nonlinear thermal analysis algorithm of general finite element software. The results show that the steel temperature decreases to the target temperature of 19°C, it takes about 10 to 12 minutes for the thin wall and 18 to 20 minutes for the thick wall. It is about 4 minutes to descend martensite transition temperature of 265°C at the thick end. Steel temperature decreases to medium temperature, with the wall thickness increases, time slightly longer. The characteristics and phase changing latent heat of hot die steel quenching process are taken into account, and the corresponding treatment is carried out when setting thermophysical parameters. The accurate simulation results are obtained and have certain significance for the research of related materials heat treatment.

Experimental and numerical study of temperature field during hard facing of different carbon steels

In this research the 3-D transient non-linear thermal analysis of the hard-facing process was performed by using the experimental testing and finite element method. Testing was done at three different carbon steels and the obtained results were compared to one obtained by empirical formulas and welding recommendations. Experimental testing was done on hard faced specimens (plates) with different thickness. Temperatures and temperature cycles was measured by using thermocouples in order to determine maximal temperature and cooling time between 800?C and 500?C. After experimental testing the finite element method analysis was done. The simulations were executed on the open source platform Salome using the open source finite element solver Code Aster. The Gaussian double ellipsoid was selected in order to enable greater possibilities for the calculation of the moving heat source. The numerical results were compared with available experimental and mathematical results.

A new $${\varvec{n}}$$th-order shear deformation theory for isogeometric thermal buckling analysis of FGM plates with temperature-dependent material properties

This study presents an isogeometric analysis (IGA) for investigating the buckling behavior of functionally graded material (FGM) plates in thermal environments. The material properties of the FGM plate are considered to be graded across the thickness, and temperature dependency of the material properties is taken into account. A new nth-order shear deformation theory with the von Karman type of geometric nonlinearity, in which the optimum order number to best approximate the thermal buckling problem can be chosen, is developed. The principle of virtual work is used to derive the governing equations for the nonlinear thermal buckling analysis. The nth-order shear deformation theory is incorporated into the non-uniform rational B-spline-based IGA which fulfills the $$C^{1}$$ -continuity requirement of the proposed higher-order plate theory. The discrete nonlinear system equations are solved by utilizing the modified Newton–Raphson iterative technique. Parametric studies on the buckling behavior of FGM plates subjected to diverse through-thickness temperature variations are performed, and the influence of temperature dependency of the material properties is examined. Results validate the performance accuracy and effectiveness of the proposed IGA based on the nth-order shear deformation theory, and they demonstrate that temperature-dependent material properties should be included in the thermal buckling analysis.

Nonlinear thermal analysis of a convective-radiative longitudinal porous fin of functionally graded material for efficient cooling of consumer electronics

In this paper, nonlinear thermal analysis and optimisation of a convective-radiative longitudinal porous fin of functionally graded material is presented. The present work aims at characterisation of optimum parameters for heat transfer enhancement. The developed thermal models are solved using differential transform method. The effects of non-homogeneous index of functionally graded material, convective and radiative parameters on the thermal performance of the porous heatsink are investigated. Parametric study shows that increase in the non-homogeneous index of functionally graded material, convective and radiative parameter improve the thermal efficiency of the porous fin heat sink. The result of the present solution is validated using established approximate analytical and numerical solutions. It is hoped that the results of the present study would assist in the design of thermally-efficient cooling approaches for various consumer electronics.

Nonlinear Static and Dynamic Thermal Buckling Analysis of Spiral Stiffened Functionally Graded Cylindrical Shells with Elastic Foundation

In this paper, an analytical method is used to study the nonlinear static and dynamic thermal buckling analysis of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells. The SSFG cylindrical shell is surrounded by a linear and nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties are temperature dependent and assumed to be continuously graded in the thickness direction. Also, for thermal buckling analysis, the uniform and linear temperature distribution in thickness direction is considered. The SSFG cylindrical shells are considered with various angles for spiral stiffeners. The strain–displacement relations are obtained based on the von Kármán nonlinear equations and the classical plate theory of shells. The smeared stiffener technique and the Galerkin method are applied to solve the nonlinear problem. In order to find the nonlinear dynamic thermal buckling responses, the fourth-order Runge–Kutta method is used. To validate the results, comparisons are made with those available in literature and good agreements are shown. The effects of various geometrical and material parameters are investigated on the nonlinear static and dynamic thermal buckling response of SSFG cylindrical shells.

Nonlinear thermal buckling analyses of functionally graded circular plates using higher-order shear deformation theory with a new transverse shear function and an enhanced mesh-free method

This study presents nonlinear buckling analyses of functionally graded (FG) circular plates in thermal environments using a mesh-free method. The thermal buckling response is formulated based on higher-order shear deformation plate theory in which a new transverse shear function is incorporated to better represent the displacement fields. An enhanced mesh-free radial point interpolation method (RPIM) in which the shape functions are constructed without any fitting parameters by virtue of the radial basis function in a compactly supported form is developed and utilized to explore the thermal buckling behavior. A radial basis function in a compactly supported form is proposed and included in the RPIM. Two types of FG circular plates with different FGM orientation, i.e., metal–ceramic FG circular plates and ceramic–metal FG circular plates, are considered in the analyses. The effectiveness and accuracy of the enhanced RPIM based on the higher-order shear deformation theory is first confirmed by simulating a numerical example found in the literature and comparing the results with the analytical solutions. Detailed parametric studies are then performed to investigate the effects of the volume fraction, plate thickness-to-radius ratio and metallic surface temperature on the critical buckling temperatures of FG circular plates subjected to various through-thickness temperature distributions. Results demonstrate that the enhanced mesh-free RPIM based on the higher-order shear deformation plate theory with the proposed transverse shear function can effectively predict the thermal buckling responses of FG circular plates, and that the volume fraction, plate thickness-to-radius ratio, bottom surface temperature and FGM orientation have considerable effects on the critical buckling temperatures.

Non-linear thermogravimetric mass spectrometry of carbon materials providing direct speciation separation of oxygen functional groups

Thermogravimetric mass spectrometry (TG-MS) is an established way to analyze oxygen containing surface functional groups of carbon materials. Thermal stabilities and structures of functional groups influence their decomposition temperatures and products (CO, CO2). In this work, a non-linear procedure with isothermal steps is presented enabling a separation of functional groups by different decomposition temperatures. Nitrosulfuric acid functionalized carbon materials like multi-walled carbon nanotubes (MWCNT) and graphite were used to design the temperature program. Comparative studies of linear and non-linear heating experiments in argon and hydrogen containing atmosphere were performed to state the benefits and limits of both methods. The distinct advantage of non-linear thermal analysis is demonstrated by an application-oriented experiment where only selected functional groups are consumed.

Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

This paper deals with the semi-analytical nonlinear thermal vibration analysis of functionally graded (FG) nanoplates modeled by four-variable refined plate theory. The nanoplate is resting on a nonlinear hardening elastic medium and subjected to uniform and nonlinear temperature rises. Temperature-dependent gradient material properties of the nanoplate are described via simple power-law model. A closed-form expression for nonlinear frequency is presented using a novel Hamiltonian approach as well as He’s variational method. To the best of the author’s knowledge, the nonlinear governing equations and their solution for a refined four-variable nanoplate are very rare in the literature. It is seen that the nonlinear vibration frequency is affected by the uniform temperature rise, nonlinear temperature rise, scale parameter, maximum amplitude, material gradation, foundation parameters and temperature-dependency. The presented formulation and solution approaches can be used in future investigations on macro to nanoscale plates.

Generalized differential quadrature nonlinear buckling analysis of smart SMA/FG laminated beam resting on nonlinear elastic medium under thermal loading

ABSTRACTThe nonlinear thermal buckling analysis of functionally graded (FG) beam integrated with shape memory alloy (SMA) layer(s), with different lay-up configurations and supported on a nonlinear elastic foundation, has been investigated. The FG layer is graded through the beam thickness direction and thermomechanical properties are assumed to be temperature dependent. The Brinson one-dimensional constitutive law are used to model the characteristics of SMA. The von Kármán strain–displacement fields with the Timoshenko beam theory are applied to the Hamilton’s principle to derive the set of nonlinear equilibrium equations. Generalized differential quadrature method along with direct iterative scheme is utilized to discretize and solve the nonlinear equilibrium equations. The accuracy of proposed model is compared and validated with previous research in literature. The detailed parametric study has been performed to investigate the influence of geometrical, material, and some other key parameters on the nonlinear thermal buckling solutions. The results show that selecting the proper lay-up is of great importance because the type of SMA/FG lay-up can considerably affect the nonlinear buckling solutions. Moreover, adequate application of SMA layers in a proper lay-up configuration significantly postpones the thermal buckling temperature of the beam.

Nonlinear thermal buckling analyses of functionally graded plates by a mesh-free radial point interpolation method

This study intends to analyze nonlinear buckling behavior of functionally graded (FG) plates under thermal loading by a mesh-free method. The buckling formulation is derived based on the higher-order shear deformation plate theory in which the von Kármán large deflection assumption is employed. An improved mesh-free radial point interpolation method (RPIM) which incorporates the normalized radial basis function capable of building the shape functions without any fitting parameters is presented and utilized to scrutinize the buckling responses. The nonlinear equations are solved by the modified Newton–Raphson iterative technique. Verification of the improved RPIM is implemented by simulating several numerical examples available in the literature and comparing the outcomes with the analytical results. Detailed parametric studies demonstrate that the improved mesh-free RPIM can effectively predict the thermal buckling responses of FG plates, and the volume fraction, plate length-to-thickness ratio, aspect ratio, boundary condition have considerable effects on the critical buckling temperatures of FG plates subjected to various types of temperature variations through the thickness.