A Finite Element Formulation for the Determination of Unknown Boundary Conditions for Three-Dimensional Steady Thermoelastic Problems

2004 ◽  
Vol 126 (1) ◽  
pp. 110-118 ◽  
Author(s):  
Brian H. Dennis ◽  
George S. Dulikravich ◽  
Shinobu Yoshimura
Keyword(s):  
Finite Element ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Element Formulation ◽  
Unknown Boundary ◽  
Fem Method ◽  
Three Dimensional Finite Element ◽  
Unknown Boundary Conditions

A three-dimensional finite element method (FEM) formulation for the prediction of unknown boundary conditions in linear steady thermoelastic continuum problems is presented. The present FEM 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 over-specified on other boundaries. The method can also handle multiple material domains and multiply connected domains with ease. A regularized form of the method is also presented. The regularization is necessary for solving problems where the over-specified boundary data contain errors. Several regularization approaches are shown. The inverse FEM method described is an extension of a method previously developed by the leading authors for two-dimensional steady thermoelastic inverse problems and three-dimensional thermal inverse problems. The method is demonstrated for several three-dimensional test cases involving simple geometries although it is applicable to arbitrary three-dimensional configurations. Several different solution techniques for sparse rectangular systems are briefly discussed.

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multi-Domain Three-Dimensional Electronic Components

2003 ◽  
Author(s):  
Brian H. Dennis ◽  
Zhen-Xue Han ◽  
George S. Dulikravich
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Measurement Errors ◽  
Sparse Matrix ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Junction Temperature ◽  
Element Formulation ◽  
Finite Element Program ◽  
Element Program

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multi-domain three-dimensional solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently over-specified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3-D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic three-dimensional problems on personal computer. The finite element formulation also allows for very straight-forward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die junction temperature distribution in a simple ball grid array (BGA) electronic package. Examples are presented with simulated measurement that include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the over-specified boundary conditions.

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multidomain Three-Dimensional Electronic Components

2004 ◽  
Vol 126 (4) ◽  
pp. 457-464 ◽  
Author(s):  
Brian H. Dennis ◽  
Zhen-xue Han ◽  
George S. Dulikravich
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Measurement Errors ◽  
Sparse Matrix ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Junction Temperature ◽  
Element Formulation ◽  
Finite Element Program ◽  
Element Program

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multidomain three-dimensional (3D) solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently overspecified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic 3D problems on personal computer. The finite element formulation also allows for very straightforward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die-junction temperature distribution in a simple ball grid array electronic package. Examples are presented with simulated measurements, which include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the overspecified boundary conditions.

An Evaluation of Three-Dimensional Diarthrodial Joint Contact Using Penetration Data and the Finite Element Method

2001 ◽  
Vol 123 (4) ◽  
pp. 333-340 ◽  
Author(s):  
W. L. Dunbar, ◽  
K. U¨n ◽  
P. S. Donzelli ◽  
R. L. Spilker
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Contact Boundary ◽  
Element Analysis ◽  
Joint Contact ◽  
Three Dimensional Finite Element

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to the method includes: (i) kinematic information describing an in vitro joint articulation, measured while the cartilage is deformed under physiological loads, (ii) geometric properties for the relaxed (undeformed) cartilage layers, obtained for the analyses in this study via stereophotogrammetry, and (iii) material parameters for the biphasic constitutive relations used to represent cartilage. Solid models of the relaxed tissue layers are assembled in physiological positions, resulting in a mathematical overlap of the cartilage layers. The overlap distribution is quantified and converted via the biphasic governing equations into applied traction boundary conditions for both the solid and fluid phases for each of the contacting layers. Linear, biphasic, three-dimensional, finite element analysis is performed using the contact boundary conditions derived for each of the contacting layers. The method is found to produce results consistent with the continuity requirements of biphasic contact. Comparison with results from independent, biphasic contact analyses of axisymmetric problems shows that the method slightly underestimates the contact area, leading to an overestimation of the total traction, but yields a good approximation to elastic stress and solid phase displacement.

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