직사각형 MEMS 판 구조의 리츠 해석 (I);수식화 및 수치해법

Ritz Analysis of Rectangular MEMS Structures (I);Formulation and Its Implementation

  • 발행 : 2000.02.01


We apply the Rayleigh Ritz method to analyze multi-layered plates with residual stresses. The method is very simple, straight forward, and easily programmable, but it should be applied to structure s only in simple shapes. We derive coupled variational equations based on the principle of virtual displacement, and investigate what kind of basis functions is desirable for the analysis of rectangular plates with various boundary conditions. We demonstrate the effectiveness and usefulness of the method through several examples. The analysis results obtained with the method are in good agreement with those available in literature. A multi-layered MEMS plate example shows that the coupling effect should not be ignored and that residual stresses do influence the stiffness of the structure very much.


극미세기계구조;리츠 방법;다층판;변형의 연성;잔류 응력


  1. Ried, R. P., Kim, E. S., Hong, D. M. and Muller, R. S., 1993, 'Piezoelectric Microphone with On-Chip CMOS Circuits,' IEEE/ASME J. of Microelectromechanical Systems, Vol. 2, 111-120
  2. Ritz, W., 1909, 'Ueber eine Methode zur Loesung Gewisser VariationSprebleme der Mathematischen Physik,' J. Reine Angew. Math., Vol. 135, 1-61
  3. Timoshenko, S. and Woinowsky, Krieger S., 1959, Theory of Plates and Shells. 2nd Ed. Mc Graw Hill, New York
  4. Chang, C. C. and Conway, H. D.,1952, 'The Marcus Method Applied to Solution of Uniformly Loaded and Clamped Rectangular Plate Subjected to Forces in Its Plane,' J. of Appl. Mech., Vol. 19, 179-194
  5. Reddy, J. N., 1997, Mechanics of Laminated Composite Plates, Theory and Analysis, CRC Press, New York
  6. Ambartsumyan, S. A. and Kunin, I., 1991, Theory of Anisotropic Plates, Strength, Stability, and Vibrations. 2nd Ed. Hemisphere Pub. New York