Three-Dimensional Versus Two-Dimensional Finite Element Modeling of Flip-Chip Packages

1999 ◽  
Vol 121 (3) ◽  
pp. 196-201 ◽  
Author(s):  
Q. Yao ◽  
J. Qu
Keyword(s):  
Finite Element ◽  
Flip Chip ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mechanical Interaction ◽  
Printed Wiring Board ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Flip Chip Assembly ◽  
Wiring Board

In this study, both two-dimensional and three-dimensional finite element analyses were used to study the stress distribution in and deflection of the flip chip assembly under thermal loading. It is found that the three-dimensional results compared favorably with experimental measurements, while the two-dimensional results consistently overestimate both stresses and deflection. Among the two-dimensional models, the plane stress assumption seems to yield results closer to the full three-dimensional predictions. Furthermore, three-dimensional models were used to investigate the effect of printed wiring board size on the overall deflection of the flip-chip assembly. This size effect of the printed wiring board has significant implications on the design of multi-chip modules. The results indicate that a square array placement pattern is preferable to a staggered array for multiple chip modules in order to reduce mechanical interaction between chips. For square arrays, such mechanical interaction between chips can be neglected when the minimum distance between adjacent chips is more than 2 times the chip size.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

Thermomechanical Durability Analysis of Flip Chip Solder Interconnects: Part 2—With Underfill

1999 ◽  
Vol 121 (4) ◽  
pp. 237-241 ◽  
Author(s):  
K. Darbha ◽  
J. H. Okura ◽  
S. Shetty ◽  
A. Dasgupta ◽  
T. Reinikainen ◽  
...  
Keyword(s):  
Finite Element ◽  
Flip Chip ◽  
Three Dimensional ◽  
Element Model ◽  
Empirical Models ◽  
Two Dimensional ◽  
Solder Interconnects ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Underfill Material

The effect of underfill material on reliability of flip chip on board (FCOB) assemblies is investigated in this study by using two-dimensional and three-dimensional finite element simulations under thermal cycling stresses from −55°C to 80°C. Accelerated testing of FCOB conducted by the authors reveals that the presence of underfill can increase the fatigue durability of solder interconnects by two orders of magnitude. Similar data has been extensively reported in the literature. It is the intent of this paper to develop a generic and fundamental predictive model that explains this trend. While empirical models have been reported by other investigators based on experimental data, the main drawback is that many of these empirical models are not truly predictive, and can not be applied to different flip chip architectures using different underfills. In the proposed model, the energy-partitioning (EP) damage model is enhanced in order to capture the underlying mechanisms so that a predictive capability can be developed. A two-dimensional finite element model is developed for stress analysis. This model accounts for underfill over regions of solder in an approximate manner by using overlay elements, and is calibrated using a three-dimensional finite element model. The model constant for the enhanced EP model is derived by fitting model predictions (combination of two-dimensional and three-dimensional model results) to experimental results for a given temperature history. The accuracy of the enhanced EP model is then verified for a different loading profile. The modeling not only reveals the influence of underfill material on solder joint durability, but also provides the acceleration factor to assess durability under life cycle environment, from accelerated test results. Experimental results are used to validate the trends predicted by the analytical model. The final goal is to define the optimum design and process parameters of the underfill material in FCOB assemblies in order to extend the fatigue endurance of the solder joints under cyclic thermal loading environments.

Inclusion of Local Shell Behavior of Tubes Into a Two-Dimensional Beam Approximation of Deformation in Nuclear Fuel Channels

2002 ◽  
Author(s):  
S. Khajehpour ◽  
R. G. Sauve´ ◽  
N. Badie
Keyword(s):  
Finite Element ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Local Deformation ◽  
Beam Model ◽  
Two Dimensional ◽  
Dimensional Modeling ◽  
Dimensional Finite Element ◽  
Nonlinear Force ◽  
Three Dimensional Finite Element

A method has been developed to incorporate the local three-dimensional shell behavior of two concentric tubes in the two-dimensional beam modeling of the problem. The two dimensional modeling of fuel channels in CANDU pressurized heavy water nuclear reactors is used in lieu of a more accurate three dimensional finite element approach in order to reduce the on-line simulation time which greatly affects the SLAR (Spacer Location And Repositioning) maintenance operation cost during outage. However, effort must be made to include the three-dimensional shell behavior of these channels into the two-dimensional modeling. In recent studies a nonlinear force-dependent model for contact stiffness between the calandria tube and pressure tube has been developed. However, local deformation of calandria the tube at spacer locations due to in-reactor creep leads to settling of the spacer into the calandria tube that consequently reduces the gap between the two tubes. In this work, the effect of local deformation (elastic and creep) of calandria tubes on modeling of contact at spacer locations is assessed using a three dimensional finite element code. The result is incorporated into a two-dimensional beam model of the problem as a reduction in size of the spacers that separate the two tubes. It is shown that the proposed method increases the accuracy of prediction of contact time and the spacer. In general, the method described in this paper suggests a way to incorporate local shell deformation into beam models of slender shell structure.

scholarly journals Three-Dimensional Response of the Supported-Deep Excavation System: Case Study of a Large Scale Underground Metro Station

Geosciences ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 76
Author(s):  
Ashraf Hefny ◽  
Mohamed Ezzat Al-Atroush ◽  
Mai Abualkhair ◽  
Mariam Juma Alnuaimi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
Deep Excavation ◽  
Metro Station ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The complexities and the economic computational infeasibility associated in some cases, with three-dimensional finite element models, has imposed a motive for many investigators to accept numerical modeling simplification solutions such as assuming two-dimensional (2D) plane strain conditions in simulation of several supported-deep excavation problems, especially for cases with a relatively high aspect ratio in plan dimensions. In this research, a two-dimensional finite element model was established to simulate the behavior of the supporting system of a large-scale deep excavation utilized in the construction of an underground metro station Rod El Farrag project (Egypt). The essential geotechnical engineering properties of soil layers were calculated using results of in-situ and laboratory tests and empirical correlations with SPT-N values. On the other hand, a three-dimensional finite element model was established with the same parameters adopted in the two-dimensional model. Sufficient sensitivity numerical analyses were performed to make the three-dimensional finite element model economically feasible. Results of the two-dimensional model were compared with those obtained from the field measurements and the three-dimensional numerical model. The comparison results showed that 3D high stiffening at the primary walls’ corners and also at the locations of cross walls has a significant effect on both the lateral wall deformations and the neighboring soil vertical settlement.

Study on Stability of High Embankments on Rock Slope under Complicated Stress Conditions

2011 ◽  
Vol 368-373 ◽  
pp. 1642-1648
Author(s):  
Gui Ling Ding
Keyword(s):  
Finite Element ◽  
Slip Surface ◽  
Three Dimensional ◽  
Slope Instability ◽  
Instability Criterion ◽  
Two Dimensional ◽  
Study Results ◽  
Geological Conditions ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Three-dimensional finite element analysis should be used in stability analysis of slope because it can overcome the short advantages of two-dimensional finite element and can simulate the complex topographic and geological conditions. Based on the large-scale triaxial shear test, the modified Duncan-Chang model is established. Based on strength reduction elasto-plastic finite element, stability of high fill embankment was studied with three-dimensional finite element method considering the complex terrain conditions. Study results suggest that plastic strain and displacement mutant of slip surface node can be a sign of slope instability as a whole. At the same time calculation of three-dimensional finite element also does not converge. Therefore, it can be slope instability criterion calculate whether the finite element static analysis converges or not. On the other hand, stability safety factor of high fill embankment under three-dimensional conditions is larger than that of two-dimensional conditions, which shows that boundary conditions of high fill embankment enhance its stability.

Mechanics of Die-less Asymmetric Rolling for Fabrication of Compound Curved Plates

2003 ◽  
Vol 125 (4) ◽  
pp. 787-793 ◽  
Author(s):  
Jong-Gye Shin ◽  
Yang-Ryul Choi ◽  
Hyunjune Yim
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
Asymmetric Rolling ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
First Time ◽  
Curvature Control

The mechanics of die-less asymmetric rolling has been investigated in depth, for the first time, using a two-dimensional analytical model and a three-dimensional finite element model. In doing so, the physical understanding of mechanics underlying die-less asymmetric rolling has greatly been enhanced. Moreover, the asymmetry in roller radii was found to be the most effective parameter for curvature control, in the considered ranges of various parameters.

THREE DIMENSIONAL FINITE ELEMENT SIMULATION OF THE FRETTING WEAR PROBLEMS

2006 ◽  
Vol 20 (25n27) ◽  
pp. 3890-3895 ◽  
Author(s):  
CHOON YEOL LEE ◽  
JOON WOO BAE ◽  
BYUNG SUN CHOI ◽  
YOUNG SUCK CHAI
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Fretting Wear ◽  
Symmetric Model ◽  
Two Dimensional ◽  
Element Analysis ◽  
Inconel 690 ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The structural integrity of steam generators in nuclear power plants is very much dependent upon the fretting wear characteristics of Inconel 690 U-tubes. In this study, a finite element analysis was used to investigate fretting wear on the secondary side of the steam generator, which arises from flow-induced vibrations (FIV) between the U-tubes and supports or foreign objects. Two-dimensional and three-dimensional finite element analyses were adopted to investigate the fretting wear problems. The purpose of the two-dimensional analysis, which simulated the contact between a punch and a plate, was to demonstrate the validity of using finite element analysis to analyze fretting wear problems. This was achieved by controlling the value of the wear constant and the number of cycles. The two-dimensional solutions obtained from this study were in good agreement with previous results reported by Strömberg. In the three-dimensional finite element analysis, a quarterly symmetric model was used to simulate tubes contacting at right angles. The results of the analyses showed donut-shaped wear along the contacting boundary, which is a typical feature of fretting wear.

scholarly journals A study for the prediction of corona power on electrostatic precipitator based on simple and easy two-dimensional electrostatic simulation

2020 ◽  
Vol 9 (2) ◽  
pp. 586
Author(s):  
Chang-Hee Cho ◽  
Dong-Hoon Kim ◽  
Sang-Eon Park
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Response Surface ◽  
Electrostatic Precipitator ◽  
Three Dimensional ◽  
Element Model ◽  
Design Parameters ◽  
Two Dimensional ◽  
Stored Energy ◽  
Dimensional Finite Element

This study examines how the designing of an electrostatic precipitator can be carried out in a simple way. While it is of value to find out the theoretical values of design parameters using three-dimensional finite element model and numerical method, this study shows that employ-ing a two-dimensional finite element model and easily usable public-domain program is equally simple and fast. Variations of some physical properties occurring between an electrode and a duct are expressed using two design parameters. In this process, the design of the experi-ment and the response surface method are used based on the two-dimensional finite element model, as well as electrostatic simulation. A test using an electrostatic precipitator is performed and it is confirmed that a variation of corona power by the test is most similar with the varia-tion of stored energy by the simulation. A conversion factor that can predict corona power with the response surface function for the stored energy is proposed.  

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