By S.G.K. Ananthasuresh
The box of "microelectromechanical systems," or "MEMS," has progressively advanced from a "discipline" populated by means of a small workforce of researchers to an "enabling expertise" aiding various items in such varied components as mechanical and inertial sensors, optical projection screens, telecommunications apparatus, and biology and medication. serious to the good fortune of those items is the facility to layout them, and this continuously contains designated modeling of proposed designs. during the last two decades, such modeling has turn into more and more subtle, with complete suites of MEMS-oriented computer-aided-design instruments now to be had around the world. yet there's one other both vital part to the layout procedure In my very own e-book, Microsystem understanding what to construct within the first position. layout, I selected to stress the modeling point of layout. the duty of realizing what to construct used to be outlined by way of a obscure step known as "creative thinking." I used sensible product examples to demonstrate the various refined features of winning designs, yet I made no try to systematize the new release ofdesign proposals or optimized designs. That systemization is termed "synthesis," that's the subjectofthis book.
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Additional resources for Optimal Synthesis Methods for MEMS
One way to combine the two inequalities in Eq. (10) is as shown below. (11) where n (> 1) is a known positive parameter chosen a priori. Equation (11) implies that the local stress measure has to be less than or equal to its allowable limit if the material is present at the site (Xi >E ). , for Xi =E which by itself makes the constraint active, the von Mises measure need not be restricted below its upper bound. Since E is very small, Eq. (11) may be modified as 27 2. Synthesis for mechanical behavior (12) The stress constraints in Eq.
II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. I. , Roark's Formulas for Stress and Strain, 7th edition, McGraw-Hill, New York. -H. and A. P. Pisano, "Optimum Structural Design of Micromechanical Crab-Leg Flexures with Microfabrication Constraints," Proc. ASME, DSC-v. 19, Microstructures, Sensors and Actuators, pp. 31-50, ASME Winter Annual Meeting, Nov. 1990. -C. , Judy, M. , and Howe, R. T. "Electrostatic Comb Drive of Lateral Polysilicon Resonators," Sensors and Actuators A, 21 (1990) 32831.
For this problem, it proceeds as follows. Differentiation of the objective function gives at 1 aA SE dX j A aSE SE dX j - = - - - -out+ -out-2 - - aX j (3) By differentiation ofEq. (1), we get (4) By making use of the fact F and F d (the load vectors corresponding to the input and unit dummy force respectively) in the equilibrium equations F = KU and F d = KV are both independent of the design variables, Eq. (4) can be simplified to the following form. (5) Differentiation and rearrangement of F d = KV results in 20 Chapter 2 (6) By combining (5) and (6), we get aLl Ou1 = _v T ax.