Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM

2001 ◽  
Author(s):  
Brian H. Dennis ◽  
George S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Multiply Connected ◽  
Three Dimensional Objects ◽  
Solid Objects ◽  
System Solution

Abstract A finite element method (FEM) formulation is presented for the prediction of unknown steady boundary conditions in heat conduction on multiply connected three-dimensional solid objects. The present FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, regularization, and sample results for 3-D problems are presented.

Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries

1999 ◽  
Vol 121 (3) ◽  
pp. 537-545 ◽  
Author(s):  
B. H. Dennis ◽  
G. S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Linear System ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
System Solution ◽  
Method Formulation ◽  
Element Method

A finite element method formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and combined thermoelasticity continuum problems is presented. The present finite element method formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently overspecified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for two-dimensional problems are presented.

Evaluation of Intensity of Singularity at 3D Piezoelectric Bonded Joints Using a Conservative Integral

2015 ◽  
Author(s):  
Chonlada Luangarpa ◽  
Hideo Koguchi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electric Potential ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Bonded Joints ◽  
Conservative Integral ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In the present study, a conservative integral based on the Betti reciprocal principle is formulated in order to obtain the intensity of singularity at a vertex of the interface in three-dimensional piezoelectric bi-material bonded joints. To our knowledge, there are few studies on the determination of the intensity of singularity in the three-dimensional piezoelectric bonded joints. In addition, no study on the determination of the intensity of singularity in the 3D piezoelectric bonded joints using the conservative integral has been conducted. Eigenanalysis formulated using a three-dimensional finite element method (FEM) is used to calculate the order of stress singularity, angular variables of mechanical displacements, stresses, electric displacements and electric potential. In order to investigate the influence of an integral area on the accuracy of the results, models with various integral areas are used. The results are compared with those obtained from FEM.

An Inverse Finite Element Method for the Determination of Unsteady Temperatures and Heat Fluxes on Surfaces of 3-D Objects

2013 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Inverse Heat Conduction Problem ◽  
Heat Fluxes ◽  
Inverse Finite Element Method ◽  
Element Method

The direct measurement of temperatures and heat fluxes may be difficult or impossible on boundaries that are obstructed, such as internal cavities, or exposed to harsh environmental conditions that would destroy the thermal sensors. In such circumstances, one may inversely determine the temperature and heat fluxes on these unknown boundaries by using over-specified conditions on boundaries where such information can be readily collected. This assumes the geometry and material properties of the domain are known. Algorithms for solving these problems, such those based on finite difference, finite element, and boundary element, are well known for the case where measured boundary conditions are not a function of time. In this work, I demonstrate an inverse finite element method that effectively solves this inverse heat conduction problem using over-specified temperatures and heat fluxes that are time varying. The material properties may highly heterogeneous and non-linear. A boundary regularization method in space and time is used to stabilize the method for cases involving errors in temperature and heat flux measurements. Several three dimensional examples are given using simulated measurements with and without measurement errors, to demonstrate the accuracy of the method.

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