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Size-dependent axisymmetric buckling and free vibration of FGP-microplate using well-posed nonlocal integral polar models

Chang Li and Hai Qing

Vol. 19 (2024), No. 3, 323–341
Abstract

Softening and toughening size-dependent axisymmetric elastic buckling and free vibration of functionally graded porous (FGP) Kirchhoff microplates with two different porous distribution patterns are investigated through strain-driven (𝜀D) and stress-driven (σD) two-phase local/nonlocal integral polar models (TPNIPM), respectively. The Hamilton’s principle is used to derive the differential governing equation and boundary conditions. A few nominal variables are introduced to simplify the differential governing equation and boundary conditions, and equivalent differential constitutive relations and constitutive constraints are expressed in united nominal forms. The general differential quadrature method is applied to discretize differential governing equation and constitutive relations as well as boundary conditions and constitutive constraints. L’Hospital’s rule is applied to deal with the boundary conditions and constitutive constraints at center for circular microplate. A general eigenvalue problem is obtained in matrix form, from which one can determine buckling loads and vibration frequency for different boundary conditions. The effects of nonlocal parameters, FGP distribution patterns, geometrical dimensions and buckling/vibration order on the buckling load and vibration frequency are investigated numerically for different boundary conditions, and consistent size-effects are obtained for 𝜀D- and σD-TPNIPMs TPNIPMs, respectively.

Keywords
elastic buckling, free vibration, size-effect, circular microplate, nonlocal integral polar model, general differential quadrature method
Milestones
Received: 28 February 2023
Revised: 9 September 2023
Accepted: 22 September 2023
Published: 27 March 2024
Authors
Chang Li
State Key Laboratory of Mechanics and Control of Mechanical Structures
Nanjing University of Aeronautics and Astronautics
Nanjing
China
Department of Mechanical Engineering
University of Alberta, Edmonton
Alberta
Canada
Hai Qing
State Key Laboratory of Mechanics and Control of Mechanical Structures
Nanjing University of Aeronautics and Astronautics
Nanjing
China