| Summary: | 博士 === 國立成功大學 === 土木工程學系 === 106 === A three-dimensional (3D) asymptotic theory is reformulated for the structural analysis of simply-supported, isotropic and orthotropic single-layered nanoplates and graphene sheets (GSs). Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these. The interactions between the nanoplates (or GSs) and their surrounding medium are modelled as a two-parameter Pasternak foundation. The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional (2D) nonlocal plate problems, the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory (CPT), although with different nonhomogeneous terms. Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions, we can obtain the Navier solutions of the leading-order problem, and the higher-order modifications can then be determined in a hierarchic and consistent manner. Therefore, some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory. The nonlocal elasticity solutions of the natural frequency parameters of nanoplates and GSs with and without being embedded in the elastic medium and their corresponding through-thickness distributions of modal field variables are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory. The nonlocal elasticity solutions of the critical load parameters of simply-supported, biaxially-loaded single-layered nanoplates and graphene sheets with and without being embedded in the elastic medium are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory.
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