Thermally nonlinear generalized thermoelasticity of a layer

This article addresses a clarification study on the thermally nonlinear Fourier/ non-Fourier dynamic coupled (generalized) thermoelasticity. Based on the Maxwell-Cattaneo’s heat conduction law and the infinitesimal theory of thermoelasticity, governing equations for the thermally nonlinear small deformation type of generalized thermoelasticity are derived. The Bubnov–Galerkin scheme is implemented for spatial discretization. The spatially discretized equations are directly discretized in time domain using the fully damped Newmark method. The Newton–Raphson procedure is used to linearize the finite element equations. The layers are exposed to a thermal shock, so that the displacement, temperature, and stress waves propagate in layers. The effects of the time evolution, thermoelastic coupling, and thermal relaxation time on the response of the layers are investigated. Results reveal the significance of the thermally nonlinear analysis of generalized thermoelasticity for the conditions where large temperature elevations exist.     

Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity

In this work, we consider the problem for an infinite medium with a spherical cavity on temperature-dependent properties subjected to a stress shock and thermal shock under the fractional-order theory of generalized thermoelasticity. The modulus of elasticity and the coe?cient of thermal conductivity are taken as linear function of temperature. The governing equations for the problem are formulated and then solved by Laplace transform together with its numerical inversion. The nondimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of temperature-dependent properties on the variations of the considered variables. The graphical results indicate that the temperature-dependent modulus of elasticity plays a significant role on all the physical quantities.     

Unified finite element approach for generalized coupled thermoelastic analysis of 3D beam-type structures,part 2: Numerical evaluations

This article aims to evaluate the high-fidelity one-dimensional finite elements that have been proposed in the companion article (Part 1). Simple structural configurations that are subjected to different loading and boundary conditions have been considered to demonstrate the generality of the proposed approach. Static, quasi-static, and dynamic analyses of the coupled and uncoupled thermoelasticity have been performed. The kinematics of the beam elements have been obtained using bidimensional Lagrangian expansions with different polynomial orders. In particular, bilinear, biquadratic, and bicubic expansions have been adopted to approximate both displacements and temperature change field. Convergence studies have been performed by considering finite beam elements with two, three, and four nodes. Analytical and numerical solutions have been reported to validate the current results. Besides time histories of displacements and temperature changes, the results have been presented using contour plots to highlight the three-dimensional capabilities of the refined beam elements.     

Unified finite element approach for generalized coupled thermoelastic analysis of 3D beam-type structures,part 1: Equations and formulation

An innovative 1D finite element (FE) approach is developed to analyze the 3D static, transient, and dynamic problems in the coupled and uncoupled thermoelasticity for the nonhomogeneous anisotropic materials. The Galerkin method is directly applied to the governing equations to obtain a weak formulation of the thermoelasticity problems with arbitrary loads and boundary conditions. To surmount the restrictions of the classical beam theories, a 1D FE procedure is proposed in the context of the Carrera Unified Formulation (CUF). Since coupled thermoelastic analyses are computationally demanding, the proposed 1D FE approach can be used as a powerful means to simulate the generalized coupled thermoelastic behavior of structures. This methodology, indeed, reduces the 3D problems to 1D models with 3D-like accuracies and very low computational costs. The Lord-Shulman and the Green-Lindsay models are considered as the generalized theories of thermoelasticity. Furthermore, as simplified cases, the classical coupled, dynamic uncoupled, quasi-static uncoupled and steady-state uncoupled theories of thermoelasticity may be derived from the formulation. Moreover, effects of the structural damping can be taken into account in the present formulation. The accuracy of the formulation has been evaluated through numerical simulations and comparisons, which have been presented in a companion article (Part 2).     

Fourier finite element model for prediction of thermal buckling in disc clutches and brakes

Numerical analyses are performed on thermal buckling of annular rings using a reduced Fourier method. The stress stiffness matrix is derived from the geometric nonlinearity in the Green strains with a predefined circumferential wave number. The method is first validated through the commercial software Abaqus using an axisymmetric model. It is then implemented to solve more general nonaxisymmetric problems with multiple waves along thecircumference. It is shown that there exists a particular wave number with which the buckling temperature reaches a minimum. This research has potential applications in automotive clutch and brake designs against thermal buckling.     

具有温度场的冷却叶片振动特性计算方法研究

根据稳态热传导的相关理论,建立了透平冷却叶片温度场和热应力场的四面体三维有限元分析模型和方法,并在此基础上建立了透平冷却叶片振动特性三维有限元分析方法,开发了相关计算软件。对某航空发动机透平高压第1级冷却叶片在不同工作条件下的振动特性进行了计算分析,同时研究了热应力、温度场、转速等对叶片振动特性的影响,表明本文中所建立模型和方法是科学、合理和精确的,为开展透平冷却叶片的设计和振动安全性评价奠定了基础。     

A finite element analysis for inverse heat conduction problems

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997     

Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock

A finite element formulation for stress analysis of functionally graded material (FGM) sandwich plates and shell panels under thermal shock is presented in this work. A higher-order layerwise theory in conjunction with Sanders’ approximation for shells is used to develop the finite element formulation for transient stress analysis of FGM sandwich panels. The top and the bottom surfaces of FGM sandwich panels are made of pure ceramic and metal, respectively, and core of the sandwich is assumed to be made of FGM. The temperature profile in the thickness direction of the panels is considered to be varying as per the Fourier’s law of heat conduction equation for unsteady state. The heat conduction equations are solved using the central difference method in conjunction with the Crank–Nicolson approach. Transient thermal displacements of the sandwich panels are obtained using Newmark average acceleration method and the transient thermal stresses are obtained using stress–strain relations, subsequently. Results obtained from the present layerwise finite element formulations are first validated with available solutions in literature. Parametric studies are taken up to study the effects of volume fraction index, temperature dependency of material properties, core thickness, panel configuration, geometric and thermal boundary conditions on transient thermal stresses of FGM sandwich plates and shells.     

A state-space finite element method for laminated composite plates under thermal loading

On the basis of the mixed variational principle, a state equation for the thermal elasticity in a laminated composite plate is yielded. A state-space finite element method is proposed to solve the established state equation, which is a nonhomogenous one. The horizontal plane of the laminated plate is modeled by traditional finite elements, while the variables along the thickness direction are obtained by the precise integration method. Because the discretization is implemented only on the horizontal plane, fewer elements are needed comparing with the traditional finite element method, in which the mesh is discretized in the whole structure. The different constraint conditions on the plate boundary are discussed. The calculated transverse thermal stresses by the present method satisfy the surface/interface conditions exactly. However, the numerical results by the traditional finite element method only approximately satisfy the surface/interface conditions. The transverse thermal stress distribution along the thickness direction evaluated by the present method is continuous across the interfaces of different layers in the laminated plate, whereas the traditional finite element method fails to provide the continuous transverse thermal stresses at the interfaces.     

A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochemistry, thermal and flow analysis in MARC

A 3D simulation tool for modeling solid oxide fuel cells is described. The tool combines the versatility and efficiency of a commercial finite element analysis code, MARC^®, with an in-house developed robust and flexible electrochemical (EC) module. Based upon characteristic parameters obtained experimentally and assigned by the user, the EC module calculates the current density distribution, heat generation, and fuel and oxidant species concentration, taking the temperature profile provided by MARC^® and operating conditions such as the fuel and oxidant flow rate and the total stack output voltage or current as the input. MARC^® performs flow and thermal analyses based on the initial and boundary thermal and flow conditions and the heat generation calculated by the EC module. The main coupling between MARC^® and EC is for MARC^® to supply the temperature field to EC and for EC to give the heat generation profile to MARC^®. The loosely coupled, iterative scheme is advantageous in terms of memory requirement, numerical stability and computational efficiency. The coupling is iterated to self-consistency for a steady-state solution. Sample results for steady states as well as the startup process for stacks with different flow designs are presented to illustrate the modeling capability and numerical performance characteristic of the simulation tool.