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.

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.

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.

scholarly journals Monte Carlo Simulations of Coupled Transient Seepage Flow and Soil Deformation in Levees

2020 ◽  
Vol 21 (1) ◽  
pp. 147-156
Author(s):  
Fred Thomas Tracy ◽  
Jodi L. Ryder ◽  
Martin T. Schultz ◽  
Ghada S. Ellithy ◽  
Benjamin R. Breland ◽  
...  
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Boundary Conditions ◽  
High Performance ◽  
Hurricane Ike ◽  
Finite Element Program ◽  
Conservation Of Mass ◽  
Total Head ◽  
Element Program ◽  
Finite Element Node

The purpose of this research is to compare the results from two different computer programs of flow analysesof two levees at Port Arthur, Texas where rising water of a flood from Hurricane Ike occurred on the levees. The first program (Program 1) is a two-dimensional (2-D) transient finite element program that couples the conservation of mass flow equation with accompanying hydraulic boundary conditions with the conservation of force equations with accompanying x and y displacement and force boundary conditions, thus yielding total head, x displacement, and y displacement as unknowns at each finite element node. The second program (Program 2) is a 2-D transient finite element program that considers only the conservation of mass flowequation with its accompanying hydraulic boundary conditions, yielding only total head as the unknown at each finite element node. Compressive stresses can be computed at the centroid of each finite element when using the coupled program. Programs 1 and 2 were parallelized for high performance computing to consider thousands of realisations of the material properties. Since a single realisation requires as much as one hour of computer time for certain levees, the large realisation computation is made possible by utilising HPC. This Monte Carlo type analysis was used to compute the probability of unsatisfactory performance for under seepage, through seepage, and uplift for the two levees. Respective hydrographs from the flood resulting from Hurricane Ike were applied to each levee. When comparing the computations from the two programs, the most significant result was the two programs yielded significantly different values in the computed results in the two clay levees considered in this research.  

The Finite Element Analysis of Dynamic Interaction of High-Speed Shinkansen, the Rail, and Bridge

1993 ◽  
Author(s):  
Makoto Tanabe ◽  
Hajime Wakui ◽  
Nobuyuki Matsumoto
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
High Speed ◽  
Response Analysis ◽  
Element Formulation ◽  
Element Analysis ◽  
Finite Element Program ◽  
The Finite Element Analysis ◽  
Element Program ◽  
The Impact

Abstract A finite element formulation to solve the dynamic behavior of high-speed Shinkansen cars, rail, and bridge is given. A mechanical model to express the interaction between wheel and rail is described, in which the impact of the rail on the flange of wheel is also considered. The bridge is modeled by using various finite elements such as shell, beam, solid, spring, and mass. The equations of motions of bridge and Shinkansen cars are solved under the constitutive and constraint equations to express the interaction between rail and wheel. Numerical method based on a modal transformation to get the dynamic response effectively is discussed. A finite element program for the dynamic response analysis of Shinkansen cars, rail, and bridge at the high-speed running has been developed. Numerical examples are also demonstrated.

Static and Dynamic Analyses of the LSES Hull Structure

1978 ◽  
Vol 22 (02) ◽  
pp. 110-122
Author(s):  
A. S. Hananel ◽  
E. J. Dent ◽  
E. J. Philips ◽  
S. H. Chang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Surface Effect ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Program ◽  
Hull Structure ◽  
Surface Effect Ship ◽  
Hull Design ◽  
Element Program

To avoid the conservativeness in the large surface-effect ship hull design which results from simplifying assumptions in the stress analysis, the hull structure was analyzed as a three-dimensional elastic body. The NASTRAN finite-element program, level 15.0, was selected for use in this analysis as the most suitable program available. A finite-element model representing the true hull stiffness was used in obtaining the internal load and displacement distributions. The inertia effect of the ship masses was included with each set of static loads. This was done by using the Static Analysis with Inertia Relief solution included in NASTRAN. The stress redistribution around cutouts in the hull was treated in a separate study. The interaction between hull and deckhouse was investigated by attaching a model of the deckhouse onto the hull model, and then solving for the appropriate load conditions. The natural frequencies were obtained using a reduced finite-element model of both the hull and hull/deckhouse combination. A new technique was developed for determining the dynamic stresses and their proper superposition on the static stresses.

Predicting the Impact of Quenching on Mechanical Properties of Complex-Shaped Aluminum Alloy Parts

1995 ◽  
Vol 117 (2) ◽  
pp. 479-488 ◽  
Author(s):  
D. D. Hall ◽  
I. Mudawar
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Aluminum Alloy ◽  
Boundary Conditions ◽  
Finite Element Program ◽  
Part Geometry ◽  
Heat Treated ◽  
Element Program ◽  
Nozzle Configuration ◽  
The Impact

The mechanical properties of age-hardenable aluminum alloy extrusions are critically dependent on the rate at which the part is cooled (quenched) after the forming operation. The present study continues the development of an intelligent spray quenching system, which selects the optimal nozzle configuration based on part geometry and composition such that the magnitude and uniformity of hardness (or yield strength) is maximized while residual stresses are minimized. The quenching of a complex-shaped part with multiple, overlapping sprays was successfully modeled using spray heat transfer correlations as boundary conditions within a finite element program. The hardness distribution of the heat-treated part was accurately predicted using the quench factor technique; that is, the metallurgical transformations that occur within the part were linked to the cooling history predicted by the finite element program. This study represents the first successful attempt at systematically predicting the mechanical properties of a quenched metallic part from knowledge of only the spray boundary conditions.

Quasi-Eulerian Finite Element Formulation for Fluid-Structure Interaction

1980 ◽  
Vol 102 (1) ◽  
pp. 62-69 ◽  
Author(s):  
T. Belytschko ◽  
J. M. Kennedy ◽  
D. F. Schoeberle
Keyword(s):  
Finite Element ◽  
Interaction Analysis ◽  
Fluid Structure Interaction ◽  
General Purpose ◽  
Element Formulation ◽  
Finite Element Program ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Eulerian Formulation ◽  
Element Program

A quasi-Eulerian formulation is developed for fluid-structure interaction analysis in which the fluid nodes are allowed to move independent of the material thus facilitating the treatment of problems with large structural motions. The governing equations are presented in general form and then specialized to two-dimensional plane and axisymmetric geometries. These elements have been incorporated in a general purpose transient finite element program and results are presented for two problems and compared to experimental results.

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