|
|||||
 |
|
|
|
|
|
|
|
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 (D) and stress-driven (D) 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 D- and D-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 |
|
| © 2024 MSP (Mathematical Sciences Publishers). |
