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A Monolithic, FEM-Based Approach for the Coupled Squeeze Film Problem of an Oscillating Elastic Micro-Plate Using 3D 27-node Elements

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Journal of Applied Mathematics and Physics 2013年第6期1卷 20-25页

作者： Anish Roychowdhury Arup Nandy C. S. Jog Rudra Pratap 1Department of Mechanical Engineering Indian Institute of Science Bangalore India 2Center for Nano Science and Engineering Indian Institute of Science Bangalore India Department of Mechanical Engineering Indian Institute of Science Bangalore India

In this study we describe an FEM-based methodology to solve the coupled fluid-structure problem due to squeeze film effects present in vibratory MEMS devices, such as resonators, gyroscopes, and acoustic transducers. The aforementioned devices often consist of a plate-like structure that vibrates normal to a fixed substrate, and is generally not perfectly vacuum packed. This results in a thin film of air being sandwiched between the moving plate and the fixed substrate, which behaves like a squeeze film offering both stiffness and damping. Typically, such structures are actuated electro-statically, necessitating the thin air gap for improving the efficiency of actuation and the sensitivity of detection. To accurately model these devices the squeeze film effect must be incorporated. Extensive literature is present on mod- eling squeeze film effects for rigid motion for both perforated as well as non-perforated plates. Studies which model the plate elasticity often use approximate mode shapes as input to the 2D Reynolds Equation. Recent works which try to solve the coupled fluid elasticity problem, report iterative FEM-based solution strategies for the 2D Reynolds Equation coupled with the 3D elasticity Equation. In this work we present a FEM-based single step solution for the coupled problem at hand, using only one type of element (27 node 3D brick). The structure is modeled with 27 node brick elements of which the lowest layer of nodes is also treated as the fluid domain (2D) and the integrals over fluid domain are evaluated for these nodes only. We also apply an electrostatic loading to our model by considering an equivalent electro-static pressure load on the top surface of the structure. Thus we solve the coupled 2D-fluid-3D-structure problem in a single step, using only one element type. The FEM results show good agreement with both existing analytical solutions and published experimental data.

关键词： Squeeze Film Damping Coupled Problem 27-node Brick Micro-Plate

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Are “Higher-Order” and “Layer-wise Zig-Zag” Plate & Shell Theories Necessary for Functionally Graded Materials and Structures?

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Computer Modeling in Engineering & Sciences 2016年第7期112卷 1-32页

作者： Yaping Zhang Qifeng Fan Leiting Dong Satya NAtluri Taizhou Polytechnic College China School of Aeronautic Science and Engineering Beihang UniversityChina Department of Mechanical Engineering Texas Tech UniversityUSA

Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also widely popularized in the literature of the past two decades.However,such higher-order theories involve(1)postulating very complex assumptions for plate/shell kinematics in the thickness direction,(2)defining generalized variables of displacements,strains,and stresses,and(3)developing very complex governing equilibrium,compatibility,and constitutive equations in terms of newly-defined generalized kinematic and generalized kinetic variables.Their industrial applications are thus hindered by their inherent complexity,and the fact that it is difficult for end-users(front-line structural engineers)to completely understand all the newly-defined generalized DOFs for FEM in the higher-order and layer-wise theories.In an entirely different way,very simple 20-node and 27-node 3-D continuum solid-shell elements are developed in this paper,based on the simple theory of 3D solid mechanics,for static and dynamic analyses of functionally-graded plates and shells.A simple Over-Integration(a 4-point Gauss integration in the thickness direction)is used to evaluate the stiffness matrices of each element,while only a single element is used in the thickness direction without increasing the number of degrees of freedom.A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity in Cartesian as well as cylindrical polar coordinates.Comprehensive numerical results are presented for static and dynamic analyses of FG plates and shells,which agree well,either with the existing solutions in the published literature,or with the computationally very expensive solutions obtained by using simple 3D isoparametric elements(with standard Gauss Quadrature)available in NASTRAN(wherein many 3D elements are used in the thickness direction to capture the varying material

关键词： functionally graded plates and shells 20-node hexahedral element 27-node over-integration higher order theory layer-wise

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