19-5-2015 Challenge the future Delft University of Technology Stochastic FEM for analyzing static and dynamic pull-in of microsystems Stephan Hannot, Clemens.

Slides:

Advertisements

Similar presentations

Simulation in Materials Summary Friday, 12/6/2002.

Advertisements

1 Probabilistic Uncertainty Bounding in Output Error Models with Unmodelled Dynamics 2006 American Control Conference, June 2006, Minneapolis, Minnesota.

Course Introduction to virtual engineering Óbuda University John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Lecture.

Simulation - An Introduction Simulation:- The technique of imitating the behaviour of some situation or system (economic, military, mechanical, etc.) by.

Dialogue Policy Optimisation

PAPER BY : CHRISTOPHER R’E NILESH DALVI DAN SUCIU International Conference on Data Engineering (ICDE), 2007 PRESENTED BY : JITENDRA GUPTA.

DYNAMICS OF RANDOM BOOLEAN NETWORKS James F. Lynch Clarkson University.

Sensitivity Analysis In deterministic analysis, single fixed values (typically, mean values) of representative samples or strength parameters or slope.

Christopher Dougherty EC220 - Introduction to econometrics (review chapter) Slideshow: asymptotic properties of estimators: plims and consistency Original.

XI- ADVANTAGES SCHEDULING PROCESS

ASYMPTOTIC PROPERTIES OF ESTIMATORS: PLIMS AND CONSISTENCY

Chapter 17 Design Analysis using Inventor Stress Analysis Module

Sharif Rahman The University of Iowa Iowa City, IA January 2005 STOCHASTIC FRACTURE OF FUNCTIONALLY GRADED MATERIALS NSF Workshop on Probability.

Path Differentials for MC Rendering Frank Suykens Department of Computer Science K.U.Leuven, Belgium Dagstuhl 2001: Stochastic methods in Rendering.

Module F: Simulation. Introduction What: Simulation Where: To duplicate the features, appearance, and characteristics of a real system Why: To estimate.

Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Gary W. Chang Paulo F. Ribeiro Department.

Stochastic Differentiation Lecture 3 Leonidas Sakalauskas Institute of Mathematics and Informatics Vilnius, Lithuania EURO Working Group on Continuous.

Low Power Design for Wireless Sensor Networks Aki Happonen.

Discrete-Event Simulation: A First Course Steve Park and Larry Leemis College of William and Mary.

Job Release-Time Design in Stochastic Manufacturing Systems Using Perturbation Analysis By: Dongping Song Supervisors: Dr. C.Hicks & Dr. C.F.Earl Department.

1 Validation and Verification of Simulation Models.

Chapter 14 Simulation. Monte Carlo Process Statistical Analysis of Simulation Results Verification of the Simulation Model Computer Simulation with Excel.

Planning operation start times for the manufacture of capital products with uncertain processing times and resource constraints D.P. Song, Dr. C.Hicks.

Using ranking and DCE data to value health states on the QALY scale using conventional and Bayesian methods Theresa Cain.

Interval-based Inverse Problems with Uncertainties Francesco Fedele 1,2 and Rafi L. Muhanna 1 1 School of Civil and Environmental Engineering 2 School.

Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,

1 Assessment of Imprecise Reliability Using Efficient Probabilistic Reanalysis Farizal Efstratios Nikolaidis SAE 2007 World Congress.

Lecture 11 Implementation Issues – Part 2. Monte Carlo Simulation An alternative approach to valuing embedded options is simulation Underlying model “simulates”

Introduction to Monte Carlo Methods D.J.C. Mackay.

1 Hybrid methods for solving large-scale parameter estimation problems Carlos A. Quintero 1 Miguel Argáez 1 Hector Klie 2 Leticia Velázquez 1 Mary Wheeler.

Linear System Theory Instructor: Zhenhua Li Associate Professor Mobile ： School of Control Science and Engineering, Shandong.

Modeling & Simulation: An Introduction Some slides in this presentation have been copyrighted to Dr. Amr Elmougy.

1 Institute of Engineering Mechanics Leopold-Franzens University Innsbruck, Austria, EU H.J. Pradlwarter and G.I. Schuëller Confidence.

The Finite Element Method

Montecarlo Simulation LAB NOV ECON Montecarlo Simulations Monte Carlo simulation is a method of analysis based on artificially recreating.

IV&V Facility PI: Katerina Goseva – Popstojanova Students: Sunil Kamavaram & Olaolu Adekunle Lane Department of Computer Science and Electrical Engineering.

Probabilistic Mechanism Analysis. Outline Uncertainty in mechanisms Why consider uncertainty Basics of uncertainty Probabilistic mechanism analysis Examples.

A Multi-Scale Mechanics Method for Analysis of Random Concrete Microstructure David Corr Nathan Tregger Lori Graham-Brady Surendra Shah Collaborative Research:

Stochastic Linear Programming by Series of Monte-Carlo Estimators Leonidas SAKALAUSKAS Institute of Mathematics&Informatics Vilnius, Lithuania

Module 1: Statistical Issues in Micro simulation Paul Sousa.

Sampling W&W, Chapter 6. Rules for Expectation Examples Mean: E(X) =  xp(x) Variance: E(X-  ) 2 =  (x-  ) 2 p(x) Covariance: E(X-  x )(Y-  y ) =

Statistical Sampling-Based Parametric Analysis of Power Grids Dr. Peng Li Presented by Xueqian Zhao EE5970 Seminar.

Experimental Method and Data Process: “Monte Carlo Method” Presentation # 1 Nafisa Tasneem CHEP,KNU

Valuation of Asian Option Qi An Jingjing Guo. CONTENT Asian option Pricing Monte Carlo simulation Conclusion.

Reliability analysis of statically indeterminate steel frame (pilot study) David Pustka VŠB – Technical University of Ostrava Faculty of Civil Engineering.

Hybrid Simulation of Structural Collapse

An Efficient Sequential Design for Sensitivity Experiments Yubin Tian School of Science, Beijing Institute of Technology.

Dealing with Uncertainty in Statics 1. Outline Uncertainty in statics Why consider uncertainty Basics of uncertainty Uncertainty analysis in statics Examples.

Calculating Risk of Cost Using Monte Carlo Simulation with Fuzzy Parameters in Civil Engineering Michał Bętkowski Andrzej Pownuk Silesian University of.

PULL-IN IN OF A TILTED MIRROR Jan Erik Ramstad and Osvanny Ramos Problem: How to find pull-in Geometry shown in the figures Objective: Run simulations.

Monte-Carlo method for Two-Stage SLP Lecture 5 Leonidas Sakalauskas Institute of Mathematics and Informatics Vilnius, Lithuania EURO Working Group on Continuous.

Machine Design Under Uncertainty. Outline Uncertainty in mechanical components Why consider uncertainty Basics of uncertainty Uncertainty analysis for.

1 1 Slide Simulation Professor Ahmadi. 2 2 Slide Simulation Chapter Outline n Computer Simulation n Simulation Modeling n Random Variables and Pseudo-Random.

Separable Monte Carlo Separable Monte Carlo is a method for increasing the accuracy of Monte Carlo sampling when the limit state function is sum or difference.

Interval Finite Element Methods for Uncertainty Treatment in Structural Engineering Mechanics Rafi L. Muhanna Georgia Institute of Technology USA Second.

Why use landscape models?  Models allow us to generate and test hypotheses on systems Collect data, construct model based on assumptions, observe behavior.

Louisiana Department of Transportation and Development Forecasting Construction Cost Index Values Using Auto Regression Modeling Charles Nickel, P.E. Cost.

RELIABLE DYNAMIC ANALYSIS OF TRANSPORTATION SYSTEMS Mehdi Modares, Robert L. Mullen and Dario A. Gasparini Department of Civil Engineering Case Western.

System Analysis System – set of interdependent elements that interact in order to accomplish a one or more final outcomes. Constrained and affected by:

A stochastic scheduling algorithm for precedence constrained tasks on Grid Future Generation Computer Systems (2011) Xiaoyong Tang, Kenli Li, Guiping Liao,

Structural & Multidisciplinary Optimization Group Deciding How Conservative A Designer Should Be: Simulating Future Tests and Redesign Nathaniel Price.

6/11/2016Atomic Scale Simulation1 Definition of Simulation What is a simulation? –It has an internal state “S” In classical mechanics, the state = positions.

Introduction to emulators Tony O’Hagan University of Sheffield.

Finite element mesh and load definition

The Three Common Approaches for Calculating Value at Risk

CHAPTER 2 - EXPLICIT TRANSIENT DYNAMIC ANALYSYS

Finite Element Application

Professor S K Dubey,VSM Amity School of Business

Linear strain triangular Tieme Willems

Continuum Simulation Monday, 9/30/2002.

Presentation transcript:

Challenge the future Delft University of Technology Stochastic FEM for analyzing static and dynamic pull-in of microsystems Stephan Hannot, Clemens Verhoosel and Daniel Rixen

2 Stochastic FEM for analyzing pull-in Introduction Microsystems or Micro-Electro-Mechanical Systems. Typical dimensions 1~100 micrometers Microsystems

3 Stochastic FEM for analyzing pull-in Introduction At these small scales physical forces act different. For instances electrostatic forces can deform and move things. Electro-mechanical coupling

4 Stochastic FEM for analyzing pull-in Introduction Pull-in voltage

5 Stochastic FEM for analyzing pull-in Introduction Finite element model

6 Stochastic FEM for analyzing pull-in Contents Stochastic Finite Element Method Static pull-in FEM computation Sensitivities Stochastic analysis Dynamic pull-in FEM computation Sensitivities Stochastic analysis Conclusions

7 Stochastic FEM for analyzing pull-in Stochastic FEM A material property is not fixed, definitely at the microscale it can be an highly uncertain value. For instance in the 1D example Assume k is random, but normally distributed. What happens to the pull-in voltage? Problem definition

8 Stochastic FEM for analyzing pull-in Stochastic FEM Generate N different values of k and compute N pull-in voltages, subsequently determine the distribution of the pull-in voltages. Advantages Conceptually simple Very robust Disadvantage Computationally very expensive Crude Monte Carlo Simulation

9 Stochastic FEM for analyzing pull-in Compute the sensitivities of V with respect to k, and use these to approximate the distribution. Advantages Computationally very cheap Disadvantage Design sensitivities required Only information about mean and variance Stochastic FEM Perturbation Stochastic FEM

10 Stochastic FEM for analyzing pull-in Contents Stochastic Finite Element Method Static pull-in FEM computation Sensitivities Stochastic analysis Dynamic pull-in FEM computation Sensitivities Stochastic analysis Conclusions

11 Stochastic FEM for analyzing pull-in Static pull-in FEM model

12 Stochastic FEM for analyzing pull-in Static pull-in Pull-in resembles limit point buckling, therefore the classic limit point buckling sensitivity can be used: Sensitivities

13 Stochastic FEM for analyzing pull-in Static pull-in The perturbation FEM will be compared with crude Monte Carlo. It is assumed that the Young’s modulus of material is distributed normally with the following characteristics: Stochastic analysis

14 Stochastic FEM for analyzing pull-in Static pull-in In that case MC gives Stochastic analysis

15 Stochastic FEM for analyzing pull-in Static pull-in And perturbation FEM gives: Which is almost the same. Stochastic analysis

16 Stochastic FEM for analyzing pull-in Contents Stochastic Finite Element Method Static pull-in FEM computation Sensitivities Stochastic analysis Dynamic pull-in FEM computation Sensitivities Stochastic analysis Conclusions

17 Stochastic FEM for analyzing pull-in Dynamic pull-in FEM model Step load of 40 VoltStep load of 41 Volt

18 Stochastic FEM for analyzing pull-in Dynamic pull-in FEM model The transition is rather sharp

19 Stochastic FEM for analyzing pull-in Dynamic pull-in Sensitivities There is problem, mathematically it is difficult to define pull-in. However there is a work around.

20 Stochastic FEM for analyzing pull-in Dynamic pull-in Uncertainty analysis Monte CarloPerturbation approach

21 Stochastic FEM for analyzing pull-in Dynamic pull-in Reliability analysis Monte CarloPerturbation approach What is the chance that the dynamic pull-in is below a critical value of V=37 Compute critical E c, V(E c )=37 What is the chance that E<E c

22 Stochastic FEM for analyzing pull-in Contents Stochastic Finite Element Method Static pull-in FEM computation Sensitivities Stochastic analysis Dynamic pull-in FEM computation Sensitivities Stochastic analysis Conclusions

23 Stochastic FEM for analyzing pull-in Conclusions Analytical sensitivities of Static and dynamic pull-in were derived. These sensitivities are sufficient for performing a Stochastic analysis. A more robust definition of dynamic pull-in would be nice for a more robust sensitivity computation.

24 Stochastic FEM for analyzing pull-in Thank you for your attention