A Hermite reproducing kernel (HRK) Galerkin meshfree formulation is presented for free vibration analysis of thin plates. In the HRK approximation the plate deflection is approximated by the deflection as well as slope nodal variables. The nth order reproducing conditions are imposed simultaneously on both the deflectional and rotational degrees of freedom. The resulting meshfree shape function turns out to have a much smaller necessary support size than its standard reproducing kernel counterpart. Obviously this reduction of minimum support size will accelerate the computation of meshfree shape function. To meet the bending exactness in the static sense and to remain the spatial stability the domain integration for stiffness as well as mass matrix is consistently carried out by using the sub-domain stabilized conforming integration (SSCI). Subsequently the proposed formulation is applied to study the free vibration of various benchmark thin plate problems. Numerical results uniformly reveal that the present method produces favorable solutions compared to those given by the high order Gauss integration (GI)-based Galerkin meshfree formulation. Moreover the effect of sub-domain refinement for the domain integration is also investigated.
A dispersion analysis is carried out to study the dynamic behavior of the Hermite reproducing kernel (HRK) Galerkin meshfree formulation for thin beam and plate problems. The HRK approximation utilizes both the nodal deflectional and rotational variables to construct the meshfree approximation of the deflection field within the reproducing kernel framework. The discrete Galerkin formulation is fulfilled with the method of sub-domain stabilized conforming integration. In the dispersion analysis following the HRK Galerkin meshfree semi-discretization, both the deflectional and rotational nodal variables are expressed by harmonic functions and then substituted into the semi-discretized equation to yield the characteristic equation. Subsequently the numerical frequency and phase speed can be obtained. The transient analysis with full-discretization is performed by using the central difference time integration scheme. The results of dispersion analysis of thin beams and plates show that compared to the conventional Gauss integration-based meshfree formulation, the proposed method has more favorable dispersion performance. Thereafter the superior performance of the present method is also further demonstrated by several transient analysis examples.Keywords Hermite reproducing kernel approximation · Meshfree method · Thin beam and plate · Sub-domain stabilized conforming integration · Dispersion analysis · Transient analysis
High abundance proteins (HAP) were often removed from crude serum sample when finding biomarkers of diagnosing cancers, however, it will surely filtrate many potential biomarkers bound to HAP. In order to enable the detection of these potential biomarkers, saving the HAP will be of great significance for finding more biomarkers. Here, a serum proteomics technology was developed for finding biomarkers of liver-cancer from crude human serum without depletion of HAP. The crude human serum (CHS) was dispersed in a lysis buffer that has capacities for improving the protein resolution, and then separated with two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) for proteomic analysis. The differentially expressed proteins from Crude male serum (CMS) compared to crude serum of male patient with liver cancer (LCMPCS) were found and identified by a combined off-line approach of 2D-PAGE and matrix-assisted laser desorption/ ionization-time of flight mass spectrometry (MALDI-TOF). Approximately 800 protein spots on a 2D-PAGE gel were detected by Melanie 4 software from samples both CMS and LCMPCS in the present of the lysis buffer. Significantly different expression of 24 proteins were detected in the LCMPCS compared to that in the CMS. Among these proteins, fifty were found up-regulated and eleven were found down-regulated. Most of these differently regulated proteins were identified by PMF and database search. These differential expression proteins were reported participating in some key pathway or biology process in cancer cells, indicating that they may present a biomarkers profile and may be helpful for liver-cancer diagnosis.
Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.
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