Time and place
Wednesday & Friday, 3:30-5:00 PM, ME lecture hall, main building on the follwing dates

• August 20, 22
• August 27, 29
• September 3, 5

Outline of the course

Almost all Micro-Electro-Mechanical Systems (MEMS) devices rely on compliant structures/mechanisms. The studies on compliant mechanisms (CMs) lie at the interface of principles and procedures of structures and rigid-body mechanisms. The series of lectures will bring out the similarities and differences in structures, mechanisms, and CMs by focusing on analysis and optimal design techniques of CMs and MEMS devices. Analysis of electrostatically actuated MEMS, and synthesis of electro-thermally actuated MEMS will be highlighted. The underlying principles of calculus of variations, constrained minimization, and design parameterization and solution methods of topology optimization will be discussed.

The course consists of six lectures. The duration of each lecture is 90 minutes--with a short break.

Schedule, topics, and PowerPoint (PPT) files

• Lecture 1, August 20, 2003, Wednesday
  1a. The Role of Structures and Mechanisms in MEMS. Download PPT file (~7.04 MB).
  A general introduction to highlight the structural aspects of MEMS.
  1b. Analysis Download PPT file (~3.7 MB).
  Although geometrically nonlinear analysis of structures and compliant mechanisms (CMs) can be done using finite element analysis, it is not the only (and always the best) option. Alternate methods are discussed.

• Lecture 2, August 22, 2003, Friday
  2a. Mathematical preliminaries for optimal design Download PPT file (~0.17 MB).
  Essential basics of calculus of variations and constrained minimization.
  2b. Optimal design of regular structures for stiffness and flexibility Download PPT file (~0.51 MB).
  Principal features of optimal design of stiff structures, and their implication in the design of CMs are highlighted using analytical solutions of simple structural forms.

• Lecture 3, August 27, 2003, Wednesday
  3. Design as an inverse problem and its pitfalls Download PPT file (~1.1 MB).
  Design can be viewed as the inverse of the analysis problem but attention should be paid to the way the design problem is formulated. This is illustrated with a structural design problem for desired mode shapes.
  Summary of the compliant mechanism formulation is presented to help further lectures.

• Lecture 4, August 29, 2004, Friday
  4a. Design parameterization in structural optimization Download PPT file (~2.6 MB).
  Various ways of defining the design variables for shape and topology optimization are presented.
  4b. Highlights of some solution methods Download PPT file. (~0.29 MB)
  Important aspects of some common optimization algorithms used in topology optimization are presented.
  4f. Follow-up on some more results Download PPT file (~1.1 MB)
  How does the topology change when volume is reduced while other specifications remain the same?
  How does the topology change when the desired direction of the output is changed while other specifications remain the same?

• Lecture 5, September 3, 2003, Wednesday (rescheduled for Septemer 5, 2003)
  5. Analysis and Design of Electro-thermally Actuated MEMS Download PPT file. (~5.1 MB)
  Three sets of partial differential equations need to be solved to simulate this class of MEMS devices. Its implications on the design methods are presented.

• Lecture 6, September 5, 2003, Friday (rescheduled for Sep. 10, 2003)
  6. Analysis of Electrostatically Actuated Micro Devices Download PPT file. (~1.9 MB)
  The analysis of electrostatic micro devices involves solution of nonlinearly coupled field equations from electrostatics and elastomechanics. Some details of this are presented.

PennSyn software for stiff structures and compliant mechanims

If you wish to try out PennSyn software, please download the following files and run pennsyn.m in Matlab.
pennsyn.m
pennsynF.exe
iiscS.yin
iiscCM.yin

Notes

1. "iiscS.yin" and "iiscCM.m" are sample input files, repsectively, for stiff structure and compliant mechanism design problems. Based on these and instructions within the file, you can modify them to your specifications.
2. When you create an input file, say filename.yin, you need to change line 9 in pennsyn.m to this filename.
3. pennsyn.m uses filename.yin on line 9, runs pennsynF.exe, and shows the specifications and result in two figure windows. You simply need to type "pennsyn.m" in the Matlab command window.
4. If there are errors in the input file (filename.yin), unfortunately, no clear errors are reported. You just need to go through the input file to make sure that it is correct.
5. The deformation profile of the structure/mechanism is shown with a scale factor. The variable "scale" may need to be changed depending on your specifications. Please note that this program uses small deformations. So, the deformations shown by a large scale factors are unrealistic and serve only a visual demonstration of small deformation behavior.

Lecture given to the MEMS class
The following is the lecture given to the MEMS class on Sep. 18th, 2003, on thermal micro actuators (~5.5 MB). It is a variant of lecture 5 above.