Strong capillary forces are developed in the fabrication process of surface micromachined structures during the wet etch of sacrificial layers. The magnitude of these forces is in some cases sufficient to deform and pin these structures to the substrate resulting in device failure. The deflection, mechanical stability, and adhesion of thin micromechanical structure under capillary forces are examined. These phenomena are divided into two separate stages of mechanical collapse and adhesion to the underlying substrate. The basic theory of collapse is described. Approximate conditions are computed to prevent contact to the substrate. >

Mechanical stability and adhesion of microstructures under capillary forces. I. Basic theory

For pt.I see ibid., vol.2, p. 33 (1993). Strong capillary forces are developed in the fabrication process of surface micromachined structures during the wet etch of sacrificial layers. The magnitude of these forces is in some cases sufficient to deform and pin these structures to the substrate resulting in device failure. The deflection, mechanical stability, and adhesion of thin micromechanical structure under capillary forces are examined. Microstructure adhesion is considered and experimental data for polycrystalline silicon microstructures are presented. >

Mechanical stability and adhesion of microstructures under capillary forces. II. Experiments

The behavior of thin, rectangular, orthotropic elastic plates, with immovable edges and undergoing large deflections, is investigated by the numerical technique of differential quadrature. Approximate results are obtained, using the Newton-Raphson method and, alternatively, a finite-difference-based method to solve the nonlinear systems of equations. Bending stresses, membrane stresses, and deflections are calculated for plates with fully clamped and simply supported flexural edge conditions under uniform pressure loading. Results are compared with existing analytical, numerical, and experimental ones. The present method gives good accuracy and is computationally efficient.

Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature

Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method—I: The fundamental mode of isotropic plates

Finite element displacement method for large amplitude free flexural vibrations of beams and plates

As a result of the assumption that the strain energy due to the second invariant of the middle surface strains can be neglected when deriving the differential equations for a flat plate with large deflections, simplified equations are derived that can be solved readily. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses, and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.

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Howard M. Berger

Papers

A new approach to the analysis of large deflections of plates