A nonlinear thick plate formulation based on the modified strain gradient theory
Mechanics of Advanced Materials and Structures, 2018, 25(10): 813-819.
A geometric nonlinear first-order shear deformation theory-based formulation is presented to analyze microplates. The formulations derived herein are based on a modified strain gradient theory and the von Karman nonlinear strains. The modified strain gradient theory includes five material length scale parameters capable to capture the size effects in small scales. The governing equations of motion and the most general form of boundary conditions of an arbitrary-shaped plate are derived using the principle of virtual displacements. The analysis is general and can be reduced to the modified couple stress plate model or the classical plate model.
Arbitrary shaped plate; first-order shear deformation theory; geometric nonlinearity; size effects; Hamilton's principle; modified strain gradient theory