A general finite element method: Extension of variational analysis for nonlinear heat conduction with temperature-dependent properties and boundary conditions, and its implementation as local refinement

2021 ◽  
Vol 100 ◽  
pp. 11-29
Author(s):  
Xin Yao ◽  
Yihe Wang ◽  
Jianxing Leng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Variational Analysis ◽  
Nonlinear Heat Conduction ◽  
Temperature Dependent ◽  
Local Refinement ◽  
Temperature Dependent Properties ◽  
Element Method

Finite-Element Method Applied to Heat Conduction in Solids with Nonlinear Boundary Conditions

1973 ◽  
Vol 95 (1) ◽  
pp. 126-129 ◽  
Author(s):  
R. E. Beckett ◽  
S.-C. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Transient Heat Conduction ◽  
Nonlinear Boundary Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Element Method

By use of an implicit iteration technique, the finite-element method applied to the heat-conduction problems of solids is no longer restricted to the linear heat-flux boundary conditions, but is extended to include nonlinear radiation–convection boundary conditions. The variation of surface temperatures within each time increment is taken into account; hence a rather large time-step size can be assigned to obtain transient heat-conduction solutions without introducing instability in the surface temperature of a body.

A Least-Squares Finite Element Formulation for Inverse Detection of Unknown Boundary Conditions in Steady Heat Conduction

2008 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Unknown Boundary ◽  
Unknown Boundary Conditions ◽  
Steady Heat Conduction ◽  
Steady Heat ◽  
Element Method

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in steady heat conduction is presented. The method is capable of determining temperatures and heat fluxes in locations where such quantities are unknown provided such quantities are sufficiently overspecified in other locations. In several finite element and boundary element inverse implementations, the resulting system of equations becomes become rectangular if the number of overspecified conditions exceeds the number of unknown conditions. In the case of the finite element method, these rectangular matrices are sparse and can be difficult to solve efficiently. Often we must resort to the use of direct factorizations that require large amounts of core memory for realistic geometries. This difficulty has prevented the solution of large-scale inverse problems that require fine meshes to resolve complex 3-D geometries and material interfaces. In addition, the Galerkin finite element method (GFEM) does not provide the same level of accuracy for both temperature and heat flux. In this paper, an alternative finite element approach based on LSFEM will be shown. The LSFEM formulation always results in a symmetric positivedefinite matrix that can be readily treated with standard sparse matrix solvers. In this approach, the differential equation is cast in first-order form so equal order basis functions can be used for both temperature and heat flux. Enforcement of the overspecified boundary conditions is straightforward in the proposed formulation. The methods allows for direct treatment of complex geometries composed of heterogeneous materials.

Finite Element Verification of Transmission Conditions for Thin Reactive Heat-Conducting Interphases

2008 ◽  
Vol 273-276 ◽  
pp. 400-405 ◽  
Author(s):  
Andreas Öchsner ◽  
Wiktoria Miszuris
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Intermediate Layer ◽  
Transmission Conditions ◽  
Heat Conducting ◽  
The Finite Element Method ◽  
Temperature Dependent ◽  
Bonded Materials ◽  
Element Method

Imperfect transmission conditions modelling a thin reactive 2D intermediate layer between two bonded materials in a dissimilar strip have been derived and analytically analysed in another paper of this issue. In this paper, the validity of these transmission conditions for heat conduction problems has been investigated due to the finite element method (FEM) for two formulations of a reactive layer: namely, based on a constant and a temperature-dependent source or sink formulation. It is shown that the accuracy of the transmission conditions is excellent for the investigated examples.

scholarly journals FINITE ELEMENT METHOD FOR HEAT TRANSFER PHENOMENON ON A CLOSED RECTANGULAR PLATE

2020 ◽  
Vol 5 ◽  
Author(s):  
Collins O. Akeremale ◽  
Olusegun A Olaiju ◽  
Yeak Su Hoe
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
The Finite Element Method ◽  
Element Method

In the diagnosis and control of various thermal systems, the philosophy of heat fluxes, and temperatures are very crucial. Temperature as an integral property of any thermal system is understood and also, has well-developed measurement approaches. Though finite difference (FD) had been used to ascertain the distribution of temperature, however, this current article investigates the impact of finite element method (FEM) on temperature distribution in a square plate geometry to compare with finite difference approach. Most times, in industries, cold and hot fluids run through rectangular channels, even in many technical types of equipment. Hence, the distribution of temperature of the plate with different boundary conditions is studied. In this work, let’s develop a finite element method (code) for the solution of a closed squared aluminum plate in a two-dimensional (2D) mixed boundary heat transfer problem at different boundary conditions. To analyze the heat conduction problems, let’s solve the two smooth mixed boundary heat conduction problems using the finite element method and compare the temperature distribution of the plate obtained using the finite difference to that of the plate obtained using the finite element method. The temperature distribution of heat conduction in the 2D heated plate using a finite element method was used to justify the effectiveness of the heat conduction compared with the analytical and finite difference methods

Steady State Heat Conduction Modeling by the Generalized Finite Element Method

2018 ◽  
Author(s):  
Humberto Alves da Silveira Monteiro ◽  
Guilherme Garcia Botelho ◽  
Roque Luiz da Silva Pitangueira ◽  
Rodrigo Peixoto ◽  
FELICIO BARROS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Generalized Finite Element Method ◽  
State Heat ◽  
Steady State Heat ◽  
Generalized Finite Element ◽  
Element Method

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

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