Page 280 - The Mechatronics Handbook

research sites frequently taking on new identities and partners and also expanding the range of services
they offer.

A. Widely Available Tools for General Numeric and Symbolic Computation
These tools are relatively easy to learn to use. Most engineering students will have mastered at least one
before obtaining a bachelor’s degree. They can be used to model a device “from scratch” and to perform
simple simulations. For more complex simulations, they are probably not appropriate for two reasons.
First, neither is optimized to execute long computations efficiently. Second, developing the routines
necessary to carry out a complex nodal or finite element analysis will in itself be a time-consuming task
and will in most cases only replicate functionality already available in other tools listed here.
• Mathematica [42]. In [36] Mathematica simulation results for a cantilever beam-capacitor system
are compared with results from several other tools.
• Matlab (integrated with Maple) [43]. In [44], for example, Matlab simulations are shown to give
good approximations for a variety of parameters for microfluidic system components.

B. Tools Originally Developed for Specific Energy Domains
Low-cost easy to use versions of some of these tools (e.g., SPICE, ANSYS) are also readily available.
Phenomena from other energy domains can be modeled using domain translation.
• SPICE (analog circuits) [13]. SPICE is the de facto standard for analog circuit simulators. It is
also used to support simulation of transistors and other components for digital systems. SPICE
implements numerical methods for nodal analysis. Several authors have used SPICE to simulate
MEMS behavior in other energy domains. In [35], for example, the equation for the motion of a
damped spring, which is being used to calculate pull-in voltage, is translated into the electrical
domain and reasonable simulation accuracy is obtained. In [45] steady-state thermal behavior for
flow-rate sensors is simulated by dividing the device to be modeled into three-dimensional “bricks,”
modeling each brick as a set of thermal resistors, and translating the resulting conduction and
convection equations into electrical equivalents.
• APLAC [22]. This object-oriented analog and mixed-signal simulator incorporates routines, which
allow statistical modeling of process variation.
• VHDL-AMS [14,26,27]. The VHDL-AMS language, designed to support digital, analog, and mixed-
signal simulation, will in fact support simulation of general algebraic and ordinary differential
equations. Thus mixed-energy domain simulations can be carried out. VHDL-AMS, which is
typically built on a SPICE kernel, uses the technique of nodal analysis. Some VHDL-AMS MEMS
models have been developed (see, e.g., [46,47]). Additional information about VHDL-AMS is
available at [48].
• ANSYS [49]. Student versions of the basic ANSYS software are widely available. ANSYS is now
partnering with MemsPro (see below). ANSYS models both mechanical and fluidic phenomena
using FEA techniques. A survey of the ANSYS MEMS initiative can be found at [50].
• CFD software [51]. This package, which also uses FEA, was developed to model fluid flow and
temperature phenomena.

C. Tools Developed Specifically for MEMS
The tools in this category use various simplifying techniques to provide reasonably accurate MEMS
simulations without all the computational overhead of FEA.

• SUGAR [40,52]. This free package is built on a Matlab core. It uses nodal analysis and modified
nodal analysis to model electrical and mechanical elements. Mechanical elements must be built
from a fixed set of components including beams and gaps.

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