Nonlinear Thermal Analysis Research Articles

Nonlinear thermal and flow-induced vibration analysis of fluid-conveying carbon nanotube resting on Winkler and Pasternak foundations

Thermal-mechanical modeling of carbon nanotubes comes with nonlinear equations which are difficult to solve exactly and analytically with any existing general analytical method. However, in many cases of developing symbolic solutions for the nonlinear equations, recourse is made to approximate analytical methods in which their accuracies largely depend on the number of terms included in the solutions. In this work, analytical solutions are presented using differential transformation method with after-treatment technique for nonlinear analysis of thermal and flow-induced vibration of fluid-conveying carbon nanotube resting on Winkler and Pasternak foundations. The developed analytical solutions are used to investigate the effects of nonlocal parameter, Knudsen number, temperature, foundation parameters and boundary conditions on the dynamic behaviour of the single-walled nanotube. Also, the developed analytical solutions are verified with the numerical solutions and validated with experimental results. Good agreements are established between the results of the analytical solutions and the numerical solutions, and also between the results of the analytical solutions and the experimental results. The analytical solutions as presented in this work can serve as benchmarks for other methods of solutions of the problem. They can also provide a starting point for a better understanding of the relationship between the physical quantities of the problems.

Invariant-based formulation of a triangular finite element for geometrically nonlinear thermal analysis of composite shells

The paper describes an invariant-based formulation of a triangular finite element for geometrically nonlinear analysis of shear flexible composite shells subjected to thermal loads. Transverse shear deformation is taken into account using the first order shear deformation theory. The focus is on the representation of the strain energy of the shell in terms of invariant quantities which depend on the components of the strain tensor and elastic constants of the material. Based on the invariant expression for the strain energy density, algorithmic relations are derived for computing the stiffness matrix of the shell finite element. The finite element formulation is used to study stability of equilibrium configurations in the region of large thermal displacements. A positive definite second variation of the total energy is used as a sufficient criterion for stability of equilibrium configurations. A series of numerical examples are given to estimate performance of the finite element in solving nonlinear problems of composite plates and shells under uniform temperature rise. Solution of some classical problems of laminated plates and shells shows that there exist equilibrium configurations not previously reported in the literature.

Evaluation of the delamination between resin and metallic components in a power module using nonlinear thermal stress analyses

Evaluation of the delamination between resin and metallic components in a power module using nonlinear thermal stress analyses

Nonlinear stability analysis of a perforated FGM plate under thermal load

ABSTRACTThe nonlinear thermal stability analysis of a perforated Ni/Al2O3 FGM plate with temperature-dependent thermoelastic material properties is carried out through a finite element approach based on the first-order shear deformation theory and the von-Karman's nonlinear kinematics. The thermoelastic material properties of the FGM plate are varied in the thickness direction, and the Mori-Tanaka homogenization scheme is applied to evaluate these properties. After validating the results of the current formulation, parametric studies are conducted to examine the effects of temperature-dependent material properties, material in-homogeneity, cutout shape and size, edge boundary conditions, aspect and slenderness ratios on the thermal buckling and postbuckling response of perforated FGM plate.

Probabilistic performance-based evaluation of a tall steel moment resisting frame under post-earthquake fires

Purpose This paper aims to develop a framework to assess the reliability of structures subject to a fire following an earthquake (FFE) event. The proposed framework is implemented in one seamless programming environment and is used to analyze an example nine-story steel moment-resisting frame (MRF) under an FFE. The framework includes uncertainties in load and material properties at elevated temperatures and evaluates the MRF performance based on various limit states. Design/methodology/approach Specifically, this work models the uncertainties in fire load density, yield strength and modulus of elasticity of steel. The location of fire compartment is also varied to investigate the effect of story level (lower vs higher) and bay location (interior vs exterior) of the fire on the post-earthquake performance of the frame. The frame is modeled in OpenSees to perform non-linear dynamic, thermal and reliability analyses of the structure. Findings Results show that interior bays are more susceptible than exterior bays to connection failure because of the development of larger tension forces during the cooling phase of the fire. Also, upper floors in general are more probable to reach specified damage states than lower floors because of the smaller beam sizes. Overall, results suggest that modern MRFs with a design that is governed by inter-story drifts have enough residual strength after an earthquake so that a subsequent fire typically does not lead to results significantly different compared to those of an event where the fire occurs without previous seismic damage. However, the seismic damage could lead to larger fire spread, increased danger to the building as a whole and larger associated economic losses. Originality/value Although the paper focuses on FFE, the proposed framework is general and can be extended to other multi-hazard scenarios.

Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness

The present work deals with geometrically non-linear post-buckling load–deflection behavior of functionally graded material (FGM) Timoshenko beam under in-plane thermal loading. Thermal loading is applied by providing non-uniform temperature rise across the beam thickness at steady-state condition. FGM is modeled by considering continuous distribution of metal and ceramic constituents across the thickness using power law variation of volume fraction. The effect of geometric non-linearity at large post-buckled configuration is incorporated using von Kármán type non-linear strain–displacement relationship. The governing equations are obtained using the minimum potential energy principle. The system of non-linear algebraic equations is solved using Broyden’s algorithm. Four different FGMs are considered. A comparative study for post-buckling load–deflection behavior in non-dimensional form is presented for different volume fraction exponents and also for different FGMs, each for different length–thickness ratios.

Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory

This paper presents an analytical investigation on nonlinear thermal dynamic behavior of imperfect functionally graded circular cylindrical shells eccentrically reinforced by outside stiffeners and surrounded on elastic foundations using the Reddy's third order shear deformation shell theory in thermal environment. Material properties are graded in the thickness direction according to Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents with metal–ceramic–metal layers. The shells are affected by mechanical, damping loads and temperature. The stress function and the Bubnov–Galerkin method are applied. Unlike previous publications, we propose a general formulation for forces and moments which allow the non-linear dynamic of shear deformable eccentrically stiffened shell to be studied taking into account the thermal stress in both the shells and the stiffeners. Numerical results are given for evaluating effects of temperature, material and geometrical properties, elastic foundation and eccentrically outside stiffeners on nonlinear dynamic of the shear deformable S-FGM shells. A good agreement is obtained by comparing the present analysis with other available in the literature.

Simulation of thermal ablation by high-intensity focused ultrasound with temperature-dependent properties

An integrated computational framework was developed in this study for modeling high-intensity focused ultrasound (HIFU) thermal ablation. The temperature field was obtained by solving the bioheat transfer equation (BHTE) through the finite element method; while, the thermal lesion was considered as a denatured material experiencing phase transformation and modeled with the latent heat. An equivalent attenuation coefficient, which considers the temperature-dependent properties of the target material and the ultrasound diffraction due to bubbles, was proposed in the nonlinear thermal transient analysis. Finally, a modified thermal dose formulation was proposed to predict the lesion size, shape and location. In-vitro thermal ablation experiments on transparent tissue phantoms at different energy levels were carried out to validate this computational framework. The temperature histories and lesion areas from the proposed model show good correlation with those from the in-vitro experiments.

Nonlinear thermal analysis of a hollow functionally graded cylinder with temperature-variable material properties

A nonlinear thermal analysis of a hollow functionally graded cylinder is performed in the present paper. A power function distribution is used for simulation of non-homogeneity of the material used. A temperature dependence is employed for the thermal conductivity. These simulations reduce the problem to a nonlinear differential equation with a variable coefficient. A semi-analytical method of successive approximations is employed for solving this equation. The convergence of the method is studied for different parameters of the problem by checking two criteria: convergence of the sum of the infinite series and condition of smallness of the residual of the responses. An exponentially function is used for simulation of the nonlinear dependence of cylinder material properties on temperature.

Non-Linear Thermal Stability Analysis of SMA Wire-Embedded Hybrid Laminated Composite Timoshenko Beams on Non-Linear Hardening Elastic Foundation

In the present study, non-linear thermal post-buckling analysis of hybrid laminated composite Timoshenko beams embedded with the shape memory alloy (SMA) wires resting on a non-linear hardening elastic foundation were studied. Mechanical properties of composite media are considered temperature-dependent. The theory of Timoshenko beams and von Kármán's strain-displacement relations are applied simultaneously in virtual work principles to derive the system of non-linear equilibrium equations. Various types of boundary conditions such as clamped, simply supported, and rolled edges were studied for edge supports. Generalized Differential Quadrature Method (GDQM) was utilized to discrete the equilibrium equations in space domain. Different types of lay-ups, such as symmetric and asymmetric, were considered. Post-buckling paths are depicted for different values of non-linear elastic foundation parameters, volume fractions, pre-strains of the SMA fibers, and boundary conditions. The one-dimensional thermo-mechanical constitutive law suggested by Brinson [1] is applied to model the SMA wires. Numerical results make it possible to recognize that increases in the volume fraction and pre-strain of SMA lead to a dramatic enhancement in thermal buckling and post-buckling capacity of the beam. Pre-buckling, buckling, and post-buckling behavior of the beam are totally different and this is due to variations among critical buckling, austenite start and finish temperatures. Due to the recovery stress of SMA wires, particular consequences are shown.

Задача о распределении температуры в полом цилиндре из функционально-градиентного материала, свойства которого зависят от температуры

Задача о распределении температуры в полом цилиндре из функционально-градиентного материала, свойства которого зависят от температуры

Nonlinear thermal analysis of functionally graded material plates using a NURBS based isogeometric approach

In the present investigation, static, thermo-mechanical buckling and free vibration analysis of functionally graded materials based on isogeometric approach and higher-order shear deformation plate theory is presented. Since the higher-order NURBS is well-suited for describing the exact geometry and providing C1-continuity, so they are used as basis functions in HSDT model and the shear locking problem does not exist in the stiffness formulation. The effective material properties of FGM plates are assumed to be temperature-dependent or temperature-independent and vary continuously through the thickness according to a simple power law distribution in terms of the volume fractions of the constituents. Behavior of FGM plates according to linear or nonlinear temperature distribution through the thickness subjected to mechanical loads is studied. The effects of aspect ratio, volume fraction index on the critical loads and temperatures are also considered. Free vibration analysis is presented and the influence of temperature rise on dynamic response are investigated. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones.

A 3D solid-like frame finite element applied to steel structures under high temperatures

This study presents the development of a finite element formulation based on positions to deal with steel structures under high temperatures. The nonlinear thermal analysis is done regarding cross sections using two-dimensional flat elements while the three dimensional structural members are modeled by physical and geometrical nonlinear solid-like frame elements of any order. The thermal analysis consists in achieving, along time, the temperature profile at frame elements cross sections that affects the constitutive relations and, consequently, residual stresses at the structural mechanical equilibrium. The proposed element presents a geometrically exact description for large displacements and rotations by means of translations and generalized vectors nodal parameters. The adopted three dimensional Thermo-elastoplastic constitutive relation is based on the von Mises yielding surface for which the temperature dependence is established and an alternative flow rule is developed. Several examples are presented in order to validate the formulation and to show its good results.

Finite Element Simulation of A-TIG Welding of Duplex Stainless Steel 2205 Using SYSWELD

Bead on plate activated tungsten inert gas (A-TIG) welding of duplex stainless steel (DSS) 2205 was performed to determine the thermal history, temperature distribution and the weld bead geometry. Finite element (FE) simulations were carried out using the software, SYSWELD considering the temperature dependent thermal and mechanical properties of the base material. A 3D double ellipsoidal heat source was employed for the non-linear thermal analysis. The transient temperature distribution, weld bead profile, weld bead dimensions, depth of penetration and bead width were calculated by FE simulation. The simulated weld bead profile was compared with the experimentally measured profile and found to be in agreement.

Nonlinear thermal bending of FGM cylindrical panels resting on elastic foundations under heat conduction

Nonlinear thermal bending analysis is presented for a simply supported functionally graded cylindrical panel resting on an elastic foundation. Material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction based on Mori–Tanaka micromechanics model. The formulations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity and include shell panel-foundation interaction and the thermal effects. A two-step perturbation technique is employed to determine the thermal load–deflection and thermal load-bending moment curves induced by heat conduction. The numerical illustrations concern nonlinear thermal bending response of FGM cylindrical panels with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects of the volume fraction index, foundation stiffness, the panel geometric parameters as well as the character of in-plane boundary conditions are also examined.

Thermal performance optimization of hollow clay bricks made up of paper waste

Abstract In this paper, the thermal behavior of hollow clay bricks made up of paper waste has been studied and their thermal performance has been optimized. On the one hand, both strength and thermal properties of different paper waste concentrations have been obtained by means of laboratory tests. Thermal conductivity of the microporous brick materials with additives produced in this study reduced from 0.68 W/m K to 0.39 W/m K compared with that of the sample without additives. On the other hand, the finite element method (FEM) has been applied to the nonlinear numerical thermal analysis of three different hollow bricks, including radiation and convection phenomena inside holes. Next, using the design of experiments (DOE) over the FEM models, several parameters such as the material conductivity, the convection and radiation properties and the mean brick temperature have been studied. In general, the thermal resistance is a nonlinear function that depends on the geometry of the recesses, the material properties and the temperature distribution. In all analyzed cases, minimizing the material thermal conductivity of bricks and decreasing the recesses surface radiation emissivity caused a lower thermal transmittance in the brick. Finally, the most important conclusions and the main findings of this research are exposed.

Numerical analysis of temperature field during hardfacing process and comparison with experimental results

The three-dimensional transient nonlinear thermal analysis of the hard facing process is performed by using the finite element method. The simulations were executed on the open source Salome platform 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 results.

Ultimate Strength of Uniaxially Compressed Mild Steel Plate at Elevated Temperatures

Mild steel plates used in buildings and offshore platforms are prone to fire accidents. These plates being ductile are designed effectively for buckling and ultimate strength characteristics under static loads. These characteristics get drastically affected due to reduction in stiffness of the stress strain characteristics of mild steel with increase in temperatures. This paper presents a numerical study conducted on clamped plates at elevated constant temperature for the assessment of reduced buckling and ultimate strengths. Coupled Nonlinear static thermal analysis on clamped plates was performed using standard FE software ANSYS®. Both geometric and material nonlinearities are considered in the analysis. The study comprises of plates with varying aspect ratio (1 to 4) and breadth to thickness (28 to 128) at constant elevated temperatures of 0 °C, 200 °C, 400 °C, 600 °C and 800 °C. Nondimensional plate slenderness ratios based on AISC and Eurocode at elevated temperature was evaluated. Several charts showing normalised buckling stress vs temperature and normalised ultimate strength vs temperature for varied nondimensional plate slenderness ratio and plate aspect ratios are drawn. The buckling and ultimate strengths from this study are found to be underestimated in comparison to Eurocode and AISC calculations. The reduction in buckling and ultimate strength was found to be significant beyond 400 °C. It is observed that for all plate aspect ratios, the effect of plate breadth to thickness ratio is important for temperatures below 500°C and at 800°C ultimate strength of plate is only about 10% of that of at normal temperature.

The virtual node polygonal element method for nonlinear thermal analysis with application to hybrid laser welding

The nonlinear heat transfer process occurring during hybrid laser welding was simulated using the Virtual-node Polygonal Element (VPE) method within the framework of the Finite Element Method (FEM). To achieve robustness in large-scale welding simulations, a dynamic mesh refinement with quadtree and octree data structures was used in the welding region. Accuracy, convergence and efficiency were verified by solving two and three dimensional problems. It is found that the present VPE can successfully simulate the hybrid laser welding process with good accuracy and convergence. The adaptive refined mesh box can synchronously move with the welding heat source, which dramatically reduces the number of field nodes. Compared with the standard FEM,the VPEM requires only approximately 42% of the total degrees of freedom used in standard FEM for the same accuracy. Furthermore, we compare the computational cost and accuracy of the method to that of the finite element method, the edge based virtual node polygonal element/virtual node method, the edge-based Smoothed Point Interpolation Meshless Method (ES-PIM), the edge-based Element (ES-PIM) the Element Free Galerkin (EFG) method and the Meshless Local Petrove-Galerkin Petrov–Galerkin (MLPG) method. Compared to all those methods, the proposed scheme is found competitive in terms of computational cost versus accuracy, and benefit from a simple implementation.

Nonlinear thermal buckling and postbuckling analyses of imperfect variable thickness temperature-dependent bidirectional functionally graded cylindrical shells

Influences of the thickness variability and bidirectional material heterogeneity on the thermal buckling of the cylindrical shells have not been investigated so far. In the present paper, nonlinear thermal buckling and postbuckling analyses of imperfect, variable thickness cylindrical shells made of bidirectional functionally graded materials undergoing uniform temperature rises are accomplished for the first time, employing a third-order shear-deformation theory, von Karman-type kinematic nonlinearity, and a nonlinear finite element method. Material properties may vary in both radial and axial directions and can be temperature-dependent. Buckling temperature is detected by a modified Budiansky's criterion. The results reveal that temperature-dependency of the material properties reduces the buckling temperature. Moreover, effects of the volume fraction index on decreasing the buckling temperature are more remarkable for higher radius to thickness ratios. Furthermore, effects of reduction of the thickness in the axial direction may be compensated by an appropriate distribution of the material properties.