2007 ansys conf gromala mue

ANSYS Conference & 25th CADFEM Users’ Meeting 2007 November 21-23, 2007 Congress Center Dresden, Germany 1

ANSYS & LS-Dyna Simulation of Electronic Modules Subjected to Free Drop Test

Przemyslaw Gromala, Axel Müller, Sven Rzepka

Qimonda Dresden GmbH & Co. OHG

Koenigsbruecker Str. 180

D-01099 Dresden

[email protected]

Summary

Modal, harmonic and transient simulations have been performed on typical electronic modules con-sisting of a printed circuit board to which ball grid array (BGA) components are mounted. The BGA solder joints are modeled as continuous layers applying effective values for stiffness and density. This way, the simulation run time was minimized without reducing the accuracy of the targeted global re-sults: natural frequencies, spatial distribution and magnitudes of acceleration, deformation, and strain. These results allow the identification of the first failing component correctly as it was found in subse-quent validation experiments of vibration and shock tests. Applying the validated models, a case study was conducted investigating the response of the elec-tronic module to a typical free drop test scenario, in which one corner of the module's printed circuit board hits the rigid ground after falling from a height of 1 meter. In particular, the effect of the bound-ary conditions was assessed, which determine the specifics of loading and response. As practical consequence, the use of a drop plate of polished steel with a hardened surface is recommended for achieving most reproducible drop test results. In general, the paper demonstrates an FEM simulation procedure that provides trustworthy and detailed results on the free drop test.

Keywords

Drop test, BGA, electronic modules


1. Introduction With the advent of mobile electronic products (e.g. cell phones, palmtops), the dynamic mechanical reliability has become of major concern to microelectronics industry. Currently, three techniques are in use for characterizing the mechanical strength of electronic modules: vibration test applying sinusoidal loads, mechanical shock, in which the sample is attached to a shock table when sliding down towards the drop plate, and free drop tests, in which the sample is widely unconstraint. The free drop test is the most realistic one. It also creates the highest loads. Thus, it would be the most interesting test. How-ever, the free drop test also is the most expensive one, because it is not easy to repeat the experiment in a deterministic way. The exact position of the module during the drop is rather random and very of-ten hard to repeat. Hence, large sample sizes are needed to compensate for the big scatter of the test results. In addition, it is hard to measure any response parameter during the drop without changing the tests conditions and it is almost impossible to record the full history of stress and strain distribution throughout the test. This paper provides a method of validating numerical models of an electronic module by experimental results of vibration and mechanical shock. Afterwards, the model is used in the analysis of a free drop test, for which the direct correlation with experiment is not so easy to achieve. In particular, parame-ters of contact and friction definition are studied by their effect on the drop test results leading to rec-ommendations for improving the reproducibility of the drop test conditions.

2. FEM model The commercial FEA codes Ansys and LS-Dyna have been used to simulate mechanical tests of the electronic modules. The printed circuit board (PCB) of the memory module under consideration has a dimension of 133.35 x 50 x1.27 mm3. The total mass of the studied structure is 39 gram. It carries 38 electronic components mounted to either side of the PCB by means of solder joints. The presence of passive components such as tiny resistors and capacitors has been neglected in the numerical model because they are too small to be significant. The model has been composed of 40,400 nodes and 26,500 elements. Eight node bricks with a re-duced integration and hourglass mode stabilization were used. Additionally, a few degenerated bricks (6 node wedges) were needed. In case of LS-Dyna, the structure is split into three parts defined: PCB, solder layer and electronic components. The fig. 1 depicts the model of the studied structure. In the modal analysis, the structure was constrained in all directions along the side of the work holder and at the point of the screws (fig. 1). These boundary conditions represent the clamping of the mod-ule to the vibration shaker during experiment. It replicates the mounting conditions within the com-puters. The solder joints are the critical features of the electronic module. In the mechanical tests, they fail due to fatigue and mechanical overstress. Hence, the focus is set on these solder joints when model-ing of the mechanical test. On the other hand, the simulation runtime must be kept in reasonable bounds. Modeling each solder joint individually would exceed these bounds. The optimum has been reached by modeling the solder ball array as an effective layer with the stiffness and the mass density been decreased appropriately. All materials were modeled as linear elastic. In the transient analyses,

work holder

PCB

DRAM

screw

screw

REG

Components mounted to both sides of the PCB

Point A

Fig. 1 Numerical model details: The constraints are applied in the simulations of vibration and me-

chanical shock tests only. Point “A” indicates the result evaluation point used in for tests.


kinematic plasticity has been added to the solder model according to the Cowper-Symonds approach as shown in equ. 1. Table 1 lists the material laws applied to the individual simulations.

ε+⋅σ=σ

P1

0y C1

& (1)

Where: σy – Yield stress σ0 – Initial stress (static yield stress) ε& – Strain rate C, P – coefficients for Cowper-Symonds model In the cases of the mechanical shock and drop tests, 10% plastic strain has been used as threshold for the element failure.

3. Experiment validation The accuracy of the numerical model has been evaluated by comparing simulation and experimental results of vibration and mechanical shock tests starting with calibration by the vibration test. The main goal of this stage was to calibrate material properties of the PCB by an optimization scheme. First, the natural frequencies were checked. In the case of numerical simulations, the modal analysis considered the frequencies between 0 Hz and 4000 Hz in order to surely catch all modes possible in the quasi-static frequency sweep between 20 Hz and 2000 Hz performed in the experiment. Fig. 2 depicts the natural frequencies found by simulation and experiment after tuning the elastic constants of the PCB model. A good ±10% agreement between the results can be seen throughout the fre-

1 2 3 4 5 6 7 8

270450

800

1200

1561 16111787

280

447

738

1065

1299

1569

1679

20550

500

1000

1500

2000

2500

Nat

ural

Fre

quen

cy [H

z]

Mode #

Simulation Experiment

Fig. 2 Natural frequencies in the vibration test found by experiment and modal simulation analysis

Table 1. Material models

Constitutive law # Part Modal & harmonic analyses – ANSYS

Vibration, shock & free drop tests Transient analysis – LS-DYNA

Mechanical shock and free drop test

1 PCB Linear anisotropic Linear anisotropic

2 Component Linear isotropic Linear isotropic

3 Solder Linear isotropic Plastic kinematic (Cowper-Symonds)


quency range. Mode #8 was not found in the experiment because it occurs above the maximum fre-quency included in the test. Having the results of modal analysis at hand, harmonic simulations were conducted for all natural fre-quencies in order to obtain the steady state responses of the structure to the sinusoidal load. This means, the quantitative results of the displacement, the velocity and the acceleration was obtained for any point of the structure as well as the magnitudes of stress and strain. A comparison between the experimental and the simulation displacement results is given as figure 3.

0.0

0.5

1.0

1.5

2.0

0 500 1000 1500 2000Frequency [Hz]

u z0 [

mm

]

0.0

0.5

1.0

1.5

2.0

0 500 1000 1500 2000Frequency [Hz]

u z0 [

mm

]

a) Experiment b) Simulation

Fig. 3 Displacement amplitude vs. frequency at point A (see fig. 1) in the vibration test

The displacement results of harmonic analysis consist of amplitude u0 and phase angle ϕ. In order to get the results of stress and strain, the transformation of the results from the frequency domain to the time domain is needed as seen in equation 2. In general, it allows obtaining the full set of stress and strain distributions at any point in time for each of the natural frequencies found. However, this com-plete set of information is actually not needed as the highest stress can safely be assumed to occur at the natural frequency causing the maximum displacement amplitude u0. In this study, this clearly is mode #1 (figs. 2 & 3), where the calculated peak displacement at the evaluation point A of the PCB was umax= 1.77 mm at a frequency of 280 Hz while the experimental values were 1.80 mm and 270 Hz. This very close match between displacement results assured the stress and strain results that can be obtained from simulation only to be accurate as well.

Figure 4 shows the distribution of the von Mises strain within the PCB. It can be seen that the highest magnitudes exist close to the con-tact finger area, where the module is clamped by the work holder during the test. In the experiment, exactly this region was identified as the most critical one. Only here, cracks occurred in the coo-per trace on the PCB. The second highest strain magnitudes were found next to both of the notches with the screws (see fig. 1). This result perfectly coincides with the experiment as was since the com-ponents next to these screws ac-tually were the only ones that ever failed in the vibration tests. In order to check the transient response of the structure, a me-chanical shock simulation has

( ) ( )ϕ+⋅Ω⋅= tutu 0 sin (2) Where: u, u0 – displacement, displacement amplitude Ω – angular frequency t – time ϕ – phase angle

FailedDRAM

FailedDRAM

damaged tracesdamaged traces

Fig. 4 Von Mises strain distribution on the PCB – harmonic analysis – comparison with experiment

1.80 mm @ 270 Hz 1.77 mm @ 280 Hz


been conducted by means of LS-Dyna. Similar to the vibration test, the load was applied along the work holder and along the notches (fig. 1). Again, all these nodes were constrained in X and Y direc-tions. However, the load was different to of the vibration case. This time, a single half-sinusoidal shock pulse in Z direction was applied. According to JEDEC condition B [4], the peak acceleration was 1500 G and the duration was 0.5 ms. As result, the computed distribution of the first principal strain is shown in fig. 5. The highest magnitudes are seen at the notches and close to the contact finger area. Correspondingly, the location of the critical components failing first has been identified. Again, this simulation outcome was checked by the experiments. The result was a perfect match. No component other than those marked in fig. 5 have ever failed in experimental shock tests. In summary, the two types of mechanical tests, vibration and mechanical shock, have provided the means of calibrating and validating the material part of the FEM model. Ultimately, a perfect agree-ment of the computed stress and strain distributions as well as location of the most critical compo-nents to the experimental observations could be achieved and double–checked. Therefore, these FEM models can now be used in simulations of other mechanical tests as well – such as the free drop test.

4. Free drop test simulation The big advantage of the FEM simulation is its capability to obtain acceleration, displacement, and strain results at any location of the structure. In experiments, this is not possible. In particular, quanti-tative measurement is not feasible at many places of the electronic module. The rough topology caused by all the components attached to the PCB does not leave room enough for mounting accel-eration sensors or strain gages, respectively. In addition, cables needed for these measurements may substantially change the free drop conditions for the module. Contactless experimental techniques applying high-speed cameras [7], laser vibrometer scaners [8], or other dedicated equipment all suffer from limitations in spatial and time resolution as well as with respect of the area of coverage. In addi-tion, those techniques are tedious and expensive. Thus, FEM simulations based on models, which are calibrated and validated by vibration and shock experiments comprehensively, appear to offer a very good alternative. They allow assessments on all the modal and transient effect occurring during the free drop of the electronic components and modules without influencing them.The results to be achieved for the free drop are assumed to be as trustworthy as in the cases of vibration and shock. As long as the global responses of the modules stay linear, the differences between the three mechanical tests are determined by the specifics of the loading conditions only. These conditions can be captured by the FEM models very well. In the case of the free drop, they are characterized by the absence of all the constraints to be considered for vibration and shock. Instead, a contact needs to be modeled. Re-moving all the constraints cannot introduce an error. The exact conditions at the touch down point, however, may well be delicate. Therefore, the subsequent study focuses on the effect of changing the contact and the friction definitions at this touch down point. The effect of different materials and sur-face states of the drop plate is investigated this way. Qualitatively, the outcome of this simulation study

Failed DRAMFailed DRAM

Fig. 5 First principal strain distribution on the PCB – mechanical shock


can still be checked against experimental results. Even with quantitative results not being available, the load model of highest validity can clearly be found this way. Modeling free drop tests, both kinds of FEM codes, implicit and explicit, are usually ap-plied. Implicit codes (ANSYS) are preferred for performing the modal analysis, i.e., for estimating the natural frequencies of the electronic module under the free droop con-ditions, which are quite different to them found for vibration and shock because of the removal of all the constraints. An explicit code (LS-Dyna) is preferred for computing the transient response of the module. Here, the explicit codes are generally more time effective than the implicit counterparts. In addition, they usually provide more options

for defining nonlinearities. In the case of this study, two kinds of nonlinearities were considered, the contact at the touch down point and rate dependency of the solder material. Being a load condition specific to the free drop and a local effect, respectively, both of the nonlinearities do not disturb the over-all linear behavior of the global response. Hence, the geometric and the material parts of the FEM models calibrated by vibration and validated by shock test are applicable to the free drop test as well. In the particular free drop test simulated, the electronic module falls down from 1 m height on to a drop plate. After each drop, the functionality and integrity of the module is tested. The number of drops to failure strongly depends on position and angle of the module when hitting the drop plate as well as on the surface specifics of this plate. Up to now, there is no JEDEC or other standard defining the free drop test conditions. Therefore, a typical scenario has freely been chosen for this study. In the drop test studied, the module hits the drop plate tilted by 45° with respect to all three axes of this plate. This means, the impact occurs at one corner of the module as shown in the fig. 6. The drop plate is modeled as a rigid body. The properties of it are also shown in fig. 6. The velocity of the structure has been calculated based on equation 3. Modeling friction and contact conditions was the subject of this study. Equation 4 describes the friction force as minimum of kinetic and viscous friction. The friction coefficient is calculated based on equa-

hg2v = (3) Where: v – velocity g – acceleration of gravity h – height

⋅⋅µ

=CONT

NC AVC

FF min (4)

Where: FC – friction force at the contact site µ – frictional coefficient FN – normal force VC – coefficient for viscous friction ACONT – area of contact

( ) ( )( )relvDCFDFSFD −⋅−+=µ exp (5) Where: FS – static friction coefficient FD – dynamic friction coefficient DC – exponential decay coefficient vrel – relative velocity of contact surfaces

Steel Plate 100 x 100 mm²

Gravity GGravity G

1.0 m

vv00

Drop plate –polished steel:ρ = 7.85 g/cm³E = 2.1e5 MPaν = 0.3 σy = 500 MPa

orientation of the module: z=45°, x=45°, y=45°

Steel Plate 100 x 100 mm²

Gravity GGravity G

1.0 m1.0 m

vv00

Drop plate –polished steel:ρ = 7.85 g/cm³E = 2.1e5 MPaν = 0.3 σy = 500 MPa

orientation of the module: z=45°, x=45°, y=45°

Fig. 6 Scheme of the free drop test


tion 5 accounting for static and dynamic contributions and for the relative velocity (vrel) of the two sur-faces that come into contact. The coefficient of viscous friction is described by means of equation 6 depending on the yield stress of the contacted material. That means, changes of the drop plate mate-rial also changes the result of the simulation result as it is experienced in experimental. In total, five different models were studied. Table 2 lists the corresponding sets of contact and friction parameters. SHLTHK indicates whether or not shell thickness is considered in the simulation. SLSFAC sets the scale factor for a sliding interfaces. The other parameters presented in the table were discussed earlier.

Table 2. Definition of contact and friction parameters of studied model

SHLTHK SLSFAC VDC FS FD DC VC1 YES 0.1 0.00 0.00 0.00 Frictionless sliding after contact - soft contact2 NO 0.1 0.05 0.78 0.42 0.001 289 No sliding after contact - soft contact3 NO 1.0 0.05 0.78 0.42 0.001 289 No sliding after contact - stiff contact4 NO 1.0 0.05 0.20 0.11 0.001 289 Coulomb friction after contact5 NO 1.0 0.05 0.00 0.00 Frictionless sliding after contact - stiff contact

CommentStudied case

NOT REQUIRED

NOT REQUIRED

Definition of contact Definition of friction

5. Results evaluation Again, a modal analysis has been performed before the transient simulation. The result shows the first six modes being equal zero. They just correspond to the rigid body motion of this unconstrained sys-tem (mode 1…3 – translation, 4…6 – rotation). The subsequent modes #7… #14 cover the frequency range up to 2000 Hz. The natural frequencies are listed in table 3. Figure 7 depicts the first three non-trivial modes of the electronic module under free drop conditions. After the transient analysis, these results will be used as benchmark to determine the most critical mode.

Table 3. Natural frequencies of a unconstrained structure

Mode f_7 f_8 f_9 f_10 f_11 f_12 f_13 f_14

Frequency [Hz] 181 381 503 881 954 1319 1377 1564

a) 7th mode b) 8th mode c) 9th mode

Fig. 7 Modal analysis results: The electronic module during the free drop

Within the transient analysis, studying the first 10 ms after the impact was found to be sufficient for quantifying the effect of the contact and friction parameters as well as for finding the stress-strain dis-tributions within the PCB and all other parts of the structure. Based on them, the plastic strain energy that is accumulated in the solder layers was computed for all the five simulation cases. Applying the criterion of 10% plastic strain, the components were identified, which are expected to fail first in each

3

VC Yσ= (6)

Where: σY – yield stress of drop plate material


of the particular drop test scenarios. Figure 8 shows these results for the simulation case 1, in which a frictionless sliding is assumed to occur after the impact. Figure 8a plots the plastic strain energy ac-cumulated in the solder layers in the first 10 ms after the module hits the drop plate. Circles highlight the individual events of failing solder joints. Figure 8b shows the components predicted to have failed after the 10 ms. The other simulation cases investigated the effect of surface roughness and reaction force. Altering, the stiffness and the hardness of the drop plate surface, the number of drops to failure changes dra-matically. Most reproducible conditions can be achieved when the surface is smooth and hard. Con-sequently, a polished and hardened steel plate with a yield stress of 500 MPa or more is recom-mended to use as drop plate. Besides maximum reproducibility, this hard plate also provides for the most abrupt impact inducing the highest stresses in the solder joint layers, i.e., it represents the worst case of the drop test scenario under investigation. Similar to vibration and shock test, the main response of the module to the free drop impact is a vibra-tion mode deformation of the PCB. However, the strain amplitudes caused by these post impact vibra-tions are twice as high as in the case of mechanical shock test and more than four times that of the vibration test (table 4). Nevertheless, even the peaks of the global response do not exceed the linear range. In real drop tests, the module elastically bounces back from the drop plate with the PCB show-ing no irreversible deformation. Hence, the material and geometric parts of the FEM model calibrated and validated before may also be applied in the case of these free drop tests. Figure 9 plots the first principal strain of the top and bottom side of the PCB at the point A (fig. 1) in the simulation case 4. Based on that graph, a post impact frequency of 178 Hz is determined. This is quite similar to the 7th mode of natural frequency found by means of modal analysis for unconstrained model (table 3). Obviously, the shape of PCB deformation expected after the impact is most similar to this of mode 7 (fig. 7). Higher modi (e.g. mode 8 and 9) may contribute to the actual shape by overlay-ing but with an amplitude much smaller than that of the mode 7. Obviously, low frequency vibration of the PCB has been excited by the impact. This way, the large displacement amplitude found in the simulation of the free drop impact (table 4) is explained. Figure 10 finally plots the strain energy accumulated in the solder layers throughout the drop test for all simulation cases listed in table 2. It can be seen that the lowest strain energy accumulation was found in case 2, in which the deepest penetration into the drop plate of all cases studied was com-

solder element fails

Stra

inEn

ergy

Sol

der[

mJ]

0

20

40

60

80

0 2 4 6 8 10Time [ms]


Stra

inEn

ergy

Sol

der[

mJ]

0

20

40

60

80

0 2 4 6 8 10Time [ms]

Stra

inEn

ergy

Sol

der[

mJ]

0

20

40

60

80

0 2 4 6 8 10Time [ms]

Failed DRAM

0.0075

0.0

a) Accumulated strain energy in the solder b) Failed components after 10 ms (Plastic strain in the solder >10%)

Fig. 8 Transient results of the free drop test (simulation case 1 – Table 2)

Table 4. Comparison of simulated strain peaks in PCB for three simulated test: vibration, mechanical shock and free drop test

Vibration (20G) 0.9 % Mechanical shock (1500G) 2.0 % Free drop test 4.0 %


puted. This seems to be too optimistic. Increased penetration means re-duced acceleration. Most likely, this overestimates the lifetime of the solder joints under the free drop conditions. Case 3 is similar to case 2. After penetrating the drop plate, the module is also rebound straightly without any rolling and without any sliding along the surface. However, higher strain energy is accumulated in the solder layer and a smaller pene-

tration depth is seen in case 3 because of the higher penalty scale factor (SLSFAC) chosen. Still, the depth is quite larger than that typically observed in the scratches on the surfaces of the real drop plates. In addition, the static and dynamic friction coefficients chosen in both cases (2 and 3) might not have been most valid for this PCB-to-steel contact since they were assumed based on published data for steel-to-steel contacts [2]. Cases 1 and 5 assume situations of frictionless sliding. This way, no horizontal force exists, which could constrain the module after hitting the drop plate. Therefore, the module does not penetrate the surface of the drop plate but slides along it largely, rebounds and starts to roll as consequence of the momentum cased by only one corner hitting the drop plate. Looking at the strain energy (fig. 10), these cases appear as most critical. Right after the impact, many elements are deleted because the 10% strain threshold is exceeded. This causes sharp local peaks in the graph at 1 ms, 3 ms, 5 ms, and 7 ms as highlighted by the circles (fig. 10). Since the cases showing perfect rebounding without any sliding seem to be as unrealistic as those showing a frictionless sliding, yet another set of coefficients was applied in case 4: FS = 0.2 and FD = 0.1. Taking this set of intermediate parameters, a very shallow penetration was computed. Its depth was much smaller than in the cases 2 and 3 but large enough to just leave a whiff of a scratch on the drop plate's surface as it is typically observed in real test. In addition, this set of parameters caused some sliding along the drop plate but not as exaggerated as in cases 1 and 5. Even the path the module took after the rebound looked very similar to what is seen in real tests. Finally, the defor-mation shape of the module PCB after the rebound clearly appeared dominated by mode 7 (fig. 7) yet somewhat influenced by mode 8 and just touched by mode 9. Thus, it looked very reasonable as well. In this case 4, the strain energy accumulated in the solder layers reached an intermediate level (fig. 10). Element failures immediately after the drop impact were not found. This corresponds to the

Peaks(1) (2) (3)5.6 ms

Top side

Bottom side

Max

. Prin

cipa

lStr

ain

[E-3

]

0

0.5

1.0

1.5

2.0

0 2 4 6 8 10Time [ms]

Peaks(1) (2) (3)5.6 ms

Top side

Bottom side

Max

. Prin

cipa

lStr

ain

[E-3

]

0

0.5

1.0

1.5

2.0

0 2 4 6 8 10Time [ms]

Fig. 9 First principal strain – drop test, simulation case #4 (table 2)

Case 5

Case 2

Case 4

Case 3

Case 1


Stra

inEn

ergy

Sol

der[

mJ]

0

20

40

60

80

0 2 4 6 8 10Time [ms]

Fig. 10 Accumulated strain energy in the solder: Results of all five simulation cases as listed in table 2


fact that real modules usually do not fail after the first drop. Still, it is not known whether case 4 also quantitatively is perfectly realistic. However, it shows at least no contradiction to any detail of practical experience but a very close match to them instead, while nei-ther frictionless sliding nor straight rebounds is seen in real 45°/45°/45° free drop tests. Therefore, contact and friction conditions chosen according to the simulation case 4 seems to provide for realistic assessments of free drop test details by trustworthy simulations indeed.

6. Conclusions FEM analyses have been run to study the mechanical behavior of a typical electronic module under free drop test conditions. The validation of the FEM models has been achieved and shown by means the modal and load analyses of vibration and mechanical shock tests. Afterwards, the free drop test could be simulated based on these validated models. Doing so, the effect of contact and friction pa-rameters on the results of the free 45°/45°/45° drop test was investigated and compared to the obser-vations made in practical tests. It was found that the global post impact response of the module changed quite significantly depending on the magnitudes of these parameters. The modules slight freely and rebound unnaturally when static and dynamic friction is neglected. On the other hand, the modules rebound straightly and may penetrate the drop plate of hardened steel deeply when the fric-tion coefficients are too large. This even is completely unrealistic. In addition to the deformation shapes, the plastic strain energy accumulated in solder layer varied by almost 400% between these extreme cases. Based on the limiting cases mentioned so far, the optimum set of contact and friction coefficients was finally found by taking FS = 0.2 and FD = 0.1, which leads to simulation results that matches all details of practical experiences gained in practical free drop tests.

7. References [1] A. Mueller, J. Reichelt, S. Rzepka, Assessment of Lead-free Modules Under Forced Mechanical

Vibrations by Linear Dynamic Finite Element Methods: Results Evaluation and Calibration by Ex-periments, Proceedings of 1st Electronics and System Integration Technology Conference ESTC 2006, pp. 1393-1400

[2] E. A. Avallone, T. Baumeister, A. Sadegh, Marks' Standard Handbook for Mechanical Engineers, McGraw-Hill Professional, 10th Edition, 1996

[3] JESD22-B103-B, Vibration, Variable Frequency, JEDEC Solid State Technology Association, Ar-lington, 2002

[4] JESD22-B104-C, Mechanical Shock, JEDEC Solid State Technology Association, Arlington, 2002 [5] ANSYS Inc., Help manual, Ansys Release 10.0, 2005 [6] Livermore Software Technology Corporation, LS-Dyna Keyword Manual 970, April 2003 [7] P. Lall, Computation Methods and High Speed Imaging Methodologies for Transient-Shock Reli-

ability of Electronic, Proceedings of 8th International Conference on Thermal, Mechanical and Mul-tiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2007, pp.147-59

[8] M. Ebert, F. Neumann, R. Gerbach, J. Bagdahn, Measurement of Dynamic Properties of MEMS and Possibilities of Parameter Identification by Simulation, Proceedings of 8th International Confer-ence on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2007, pp.166-71

2007 ansys conf gromala mue

Documents