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
Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along...Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.展开更多
The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and bounda...The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.展开更多
目的采用微孔板式微生物法对婴幼儿配方乳粉中泛酸含量进行测定。方法采用微孔板法将合适浓度的植物乳杆菌液接种至含有试样液与培养液的无菌微孔板中,培养一定时间后测定吸光度值,根据泛酸含量与吸光度值的标准曲线计算出试样中泛酸的...目的采用微孔板式微生物法对婴幼儿配方乳粉中泛酸含量进行测定。方法采用微孔板法将合适浓度的植物乳杆菌液接种至含有试样液与培养液的无菌微孔板中,培养一定时间后测定吸光度值,根据泛酸含量与吸光度值的标准曲线计算出试样中泛酸的含量。通过精密度实验、准确度实验、加标回收实验对此方法进行评价。结果微孔板式微生物法的标准曲线线性良好,相关系数r=0.9965,精密度实验的相对标准偏差(relative standard deviation,RSD)为1.90%~5.32%。实验结果表明质控样品的泛酸含量各平行检测值均在定量值范围内,且平均值为6.91 mg/100 g,测定值结果间RSD为1.08%,回收率为89.7%~108.2%。结论该方法操作简便、结果准确,能够降低工作量,提高工作效率,且方法精密度较高,对样品检测结果准确性较高,方法系统误差小,能够应用于实验室对婴幼儿配方乳粉中泛酸含量的测定。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.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Research Fund of State Key Laboratory of Mechanicsthe Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.
基金supported in part by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
文摘目的采用微孔板式微生物法对婴幼儿配方乳粉中泛酸含量进行测定。方法采用微孔板法将合适浓度的植物乳杆菌液接种至含有试样液与培养液的无菌微孔板中,培养一定时间后测定吸光度值,根据泛酸含量与吸光度值的标准曲线计算出试样中泛酸的含量。通过精密度实验、准确度实验、加标回收实验对此方法进行评价。结果微孔板式微生物法的标准曲线线性良好,相关系数r=0.9965,精密度实验的相对标准偏差(relative standard deviation,RSD)为1.90%~5.32%。实验结果表明质控样品的泛酸含量各平行检测值均在定量值范围内,且平均值为6.91 mg/100 g,测定值结果间RSD为1.08%,回收率为89.7%~108.2%。结论该方法操作简便、结果准确,能够降低工作量,提高工作效率,且方法精密度较高,对样品检测结果准确性较高,方法系统误差小,能够应用于实验室对婴幼儿配方乳粉中泛酸含量的测定。
