| Affiliation: | 1. Department of Building and Real Estate, The Hong Kong Polytechnic University, Hong Kong, PR China
School of Mechanics and Engineering, Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu, PR China;2. Department of Building and Real Estate, The Hong Kong Polytechnic University, Hong Kong, PR China;3. Faculty of Engineering, China University of Geosciences, Wuhan, China;4. School of Mechanics and Engineering, Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu, PR China;5. Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu, PR China |
| Abstract: | In this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C1-type four-node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro-plates. This element is free of shape functions and shear locking. The C1-continuity requirements of deflection and rotation functions are accomplished by a fourth-order differential quadrature (DQ)-based geometric mapping scheme, which facilitates the conversion of the displacement parameters at Gauss-Lobatto quadrature (GLQ) points into those at element nodes. The appropriate application of DQ rule to non-rectangular domains is proceeded by the natural-to-Cartesian geometric mapping technique. Using GLQ and DQ rules, we discretize the total potential energy functional of a generic micro-plate element into a function of nodal displacement parameters. Then, we adopt the principle of minimum potential energy to determine element stiffness matrix, mass matrix, and load vector. The efficacy of the present element is validated through several examples associated with the static bending and free vibration problems of rectangular, annular sectorial, and elliptical micro-plates. Finally, the developed element is applied to study the behavior of freely vibrating moderately thick micro-plates with irregular shapes. It is shown that our element has better convergence and adaptability than that of Bogner-Fox-Schmit (BFS) one, and strain gradient effects can cause a significant increase in vibration frequencies and a certain change in vibration mode shapes. |
