This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend...This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.展开更多
基金supported by a grant from the National Science and Technology Council of the Republic of China(Grant Number:MOST 112-2221-E-006-048-MY2).
文摘This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.
