A short course on
Stiff Structures, Compliant Mechanisms, and MEMS
in August/September of 2003
at the Department of Mechanical Engineering, Indian Institute of
Science, Bangalore, India
Instructor: (Suresh) G. K.
Associate Professor of Mechanical Engineering and Applied Mechanics
University of Pennsylvania, Philadelphia, PA 19104-6315, USA.
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.
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
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,
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
If you wish to try out PennSyn software, please download the following
files and run pennsyn.m in Matlab.
- "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
- When you create an input file, say filename.yin, you need to
change line 9 in pennsyn.m to this filename.
- 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.
- 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.
- 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
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.